Subjects -> MATHEMATICS (Total: 1013 journals)
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APPLIED MATHEMATICS (92 journals)

Showing 1 - 82 of 82 Journals sorted alphabetically
Advances in Applied Mathematics     Full-text available via subscription   (Followers: 15)
Advances in Applied Mathematics and Mechanics     Full-text available via subscription   (Followers: 6)
Advances in Applied Mechanics     Full-text available via subscription   (Followers: 15)
AKCE International Journal of Graphs and Combinatorics     Open Access  
American Journal of Applied Mathematics and Statistics     Open Access   (Followers: 11)
American Journal of Applied Sciences     Open Access   (Followers: 22)
American Journal of Modeling and Optimization     Open Access   (Followers: 3)
Annals of Actuarial Science     Full-text available via subscription   (Followers: 2)
Applied Mathematical Modelling     Full-text available via subscription   (Followers: 22)
Applied Mathematics and Computation     Hybrid Journal   (Followers: 31)
Applied Mathematics and Mechanics     Hybrid Journal   (Followers: 4)
Applied Mathematics and Nonlinear Sciences     Open Access  
Applied Mathematics and Physics     Open Access   (Followers: 2)
Biometrical Letters     Open Access  
British Actuarial Journal     Full-text available via subscription   (Followers: 2)
Bulletin of Mathematical Sciences and Applications     Open Access  
Communication in Biomathematical Sciences     Open Access   (Followers: 2)
Communications in Applied and Industrial Mathematics     Open Access   (Followers: 1)
Communications on Applied Mathematics and Computation     Hybrid Journal   (Followers: 1)
Differential Geometry and its Applications     Full-text available via subscription   (Followers: 4)
Discrete and Continuous Models and Applied Computational Science     Open Access  
Discrete Applied Mathematics     Hybrid Journal   (Followers: 10)
Doğuş Üniversitesi Dergisi     Open Access  
e-Journal of Analysis and Applied Mathematics     Open Access  
Engineering Mathematics Letters     Open Access   (Followers: 1)
European Actuarial Journal     Hybrid Journal  
Foundations and Trends® in Optimization     Full-text available via subscription   (Followers: 3)
Frontiers in Applied Mathematics and Statistics     Open Access   (Followers: 1)
Fundamental Journal of Mathematics and Applications     Open Access  
International Journal of Advances in Applied Mathematics and Modeling     Open Access   (Followers: 1)
International Journal of Applied Mathematics and Statistics     Full-text available via subscription   (Followers: 3)
International Journal of Computer Mathematics : Computer Systems Theory     Hybrid Journal  
International Journal of Data Mining, Modelling and Management     Hybrid Journal   (Followers: 10)
International Journal of Engineering Mathematics     Open Access   (Followers: 7)
International Journal of Fuzzy Systems     Hybrid Journal  
International Journal of Swarm Intelligence     Hybrid Journal   (Followers: 2)
International Journal of Theoretical and Mathematical Physics     Open Access   (Followers: 13)
International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems     Hybrid Journal   (Followers: 3)
Journal of Advanced Mathematics and Applications     Full-text available via subscription   (Followers: 1)
Journal of Advances in Mathematics and Computer Science     Open Access  
Journal of Applied & Computational Mathematics     Open Access  
Journal of Applied Intelligent System     Open Access  
Journal of Applied Mathematics & Bioinformatics     Open Access   (Followers: 6)
Journal of Applied Mathematics and Physics     Open Access   (Followers: 9)
Journal of Computational Geometry     Open Access   (Followers: 3)
Journal of Innovative Applied Mathematics and Computational Sciences     Open Access   (Followers: 6)
Journal of Mathematical Sciences and Applications     Open Access   (Followers: 2)
Journal of Mathematics and Music: Mathematical and Computational Approaches to Music Theory, Analysis, Composition and Performance     Hybrid Journal   (Followers: 12)
Journal of Mathematics and Statistics Studies     Open Access  
Journal of Physical Mathematics     Open Access   (Followers: 2)
Journal of Symbolic Logic     Hybrid Journal   (Followers: 2)
Letters in Biomathematics     Open Access   (Followers: 1)
Mathematical and Computational Applications     Open Access   (Followers: 3)
Mathematical Models and Computer Simulations     Hybrid Journal   (Followers: 3)
Mathematics and Computers in Simulation     Hybrid Journal   (Followers: 3)
Modeling Earth Systems and Environment     Hybrid Journal   (Followers: 1)
Moscow University Computational Mathematics and Cybernetics     Hybrid Journal  
Multiscale Modeling and Simulation     Hybrid Journal   (Followers: 2)
Pacific Journal of Mathematics for Industry     Open Access  
Partial Differential Equations in Applied Mathematics     Open Access   (Followers: 1)
Ratio Mathematica     Open Access  
Results in Applied Mathematics     Open Access   (Followers: 1)
Scandinavian Actuarial Journal     Hybrid Journal   (Followers: 2)
SIAM Journal on Applied Dynamical Systems     Hybrid Journal   (Followers: 3)
SIAM Journal on Applied Mathematics     Hybrid Journal   (Followers: 11)
SIAM Journal on Computing     Hybrid Journal   (Followers: 11)
SIAM Journal on Control and Optimization     Hybrid Journal   (Followers: 18)
SIAM Journal on Discrete Mathematics     Hybrid Journal   (Followers: 8)
SIAM Journal on Financial Mathematics     Hybrid Journal   (Followers: 3)
SIAM Journal on Imaging Sciences     Hybrid Journal   (Followers: 7)
SIAM Journal on Mathematical Analysis     Hybrid Journal   (Followers: 4)
SIAM Journal on Matrix Analysis and Applications     Hybrid Journal   (Followers: 3)
SIAM Journal on Numerical Analysis     Hybrid Journal   (Followers: 7)
SIAM Journal on Optimization     Hybrid Journal   (Followers: 12)
SIAM Journal on Scientific Computing     Hybrid Journal   (Followers: 16)
SIAM Review     Hybrid Journal   (Followers: 9)
SIAM/ASA Journal on Uncertainty Quantification     Hybrid Journal   (Followers: 2)
Swarm Intelligence     Hybrid Journal   (Followers: 3)
Theory of Probability and its Applications     Hybrid Journal   (Followers: 2)
Uniform Distribution Theory     Open Access  
Universal Journal of Applied Mathematics     Open Access   (Followers: 2)
Universal Journal of Computational Mathematics     Open Access   (Followers: 3)
Similar Journals
Journal Cover
SIAM Journal on Control and Optimization
Journal Prestige (SJR): 1.399
Citation Impact (citeScore): 2
Number of Followers: 18  
 
  Hybrid Journal Hybrid journal (It can contain Open Access articles)
ISSN (Print) 0363-0129 - ISSN (Online) 1095-7138
Published by Society for Industrial and Applied Mathematics Homepage  [17 journals]
  • A Probabilistic Method for a Class of Non-Lipschitz BSDEs with Application
           to Fund Management

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      Authors: Jinhui Han, Sheung Chi Phillip Yam
      Pages: 1193 - 1222
      Abstract: SIAM Journal on Control and Optimization, Volume 60, Issue 3, Page 1193-1222, June 2022.
      The present work is devoted to a study of the solvability of a class of non-Lipschitz and noncanonical backward stochastic differential equations (BSDEs) that naturally arises from an intertemporal mutual fund management problem; to this end, we propose a method of combining the techniques of Malliavin calculus and a discussion on the Jacobian flow of the BSDE. Specifically, based on the intimate relationship between $Y_t$ and $Z_t$ of the BSDE via the Malliavin derivative of the former, namely, $D_tY_t=Z_t$, we construct an iterative Picard converging scheme for approximating the underlying solution pair by first obtaining $Z_t$ from the derived BSDE with respect to the Malliavin derivative and then recovering $Y_t$ from the underlying BSDE. A local unique existence result is first warranted over a short time horizon with carefully examined a priori estimates; indeed, each term in the iterative sequence is related to different Girsanov transforms for change of measure, and comparing them demands a delicate analysis. The use of Jacobian flow further enables us to properly control the lower and upper bounds for a certain product of the forward process and $Z_t$, which enables us to extend the solution globally by an inductive argument. Our proposed method is fundamentally different from other probabilistic methods that also involve estimating or bounding Malliavin traces such as [E. Pardoux and S. Peng, Some Backward SDEs with Non-Lipschitz Coefficients, Technical note, Université de Provence, Aix-en-Provence, France, 1996] and [M. C. Zedouri, Equations Différentielles Stochastiques Rétrogrades avec Générateurs Lipschitiziens Stochastiques, Master's Thesis, Université Mohammed Seddik Ben Yahia-Jijel, Jijel, Algeria, 2010]. We believe that our new approach proposed here can be potentially applied to resolve many other general non-Lipschitz forward-backward stochastic differential equations (FBSDEs) encountered in economics and finance, especially in the presence of generic utility functions.
      Citation: SIAM Journal on Control and Optimization
      PubDate: 2022-05-03T07:00:00Z
      DOI: 10.1137/21M140609X
      Issue No: Vol. 60, No. 3 (2022)
       
  • Moment Dynamics and Observer Design for a Class of Quasilinear Quantum
           Stochastic Systems

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      Authors: Igor G. Vladimirov, Ian R. Petersen
      Pages: 1223 - 1249
      Abstract: SIAM Journal on Control and Optimization, Volume 60, Issue 3, Page 1223-1249, June 2022.
      This paper is concerned with a class of open quantum systems whose dynamic variables have an algebraic structure, similar to that of the Pauli matrices pertaining to finite-level systems. The system interacts with external bosonic fields, and its Hamiltonian and coupling operators depend linearly on the system variables. This results in a Hudson--Parthasarathy quantum stochastic differential equation (QSDE) whose drift and dispersion terms are affine and linear functions of the system variables. The quasilinearity of the QSDE leads to tractable dynamics of mean values and higher-order multipoint moments of the system variables driven by vacuum input fields. This allows for the closed-form computation of the quasi-characteristic function of the invariant quantum state of the system and infinite-horizon asymptotic growth rates for a class of cost functionals. The tractability of the moment dynamics is also used for mean square optimal Luenberger observer design in a measurement-based filtering problem for a quasilinear quantum plant, which leads to a Kalman-like quantum filter.
      Citation: SIAM Journal on Control and Optimization
      PubDate: 2022-05-05T07:00:00Z
      DOI: 10.1137/20M1386529
      Issue No: Vol. 60, No. 3 (2022)
       
  • State-Dependent Temperature Control for Langevin Diffusions

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      Authors: Xuefeng Gao, Zuo Quan Xu, Xun Yu Zhou
      Pages: 1250 - 1268
      Abstract: SIAM Journal on Control and Optimization, Volume 60, Issue 3, Page 1250-1268, June 2022.
      We study the temperature control problem for Langevin diffusions in the context of nonconvex optimization. The classical optimal control of such a problem is of the bang-bang type, which is overly sensitive to errors. A remedy is to allow the diffusions to explore other temperature values and hence smooth out the bang-bang control. We accomplish this by a stochastic relaxed control formulation incorporating randomization of the temperature control and regularizing its entropy. We derive a state-dependent, truncated exponential distribution, which can be used to sample temperatures in a Langevin algorithm, in terms of the solution to an Hamilton--Jacobi--Bellman partial differential equation. We carry out a numerical experiment on a one-dimensional baseline example, in which the Hamilton--Jacobi--Bellman equation can be easily solved, to compare the performance of the algorithm with three other available algorithms in search of a global optimum.
      Citation: SIAM Journal on Control and Optimization
      PubDate: 2022-05-16T07:00:00Z
      DOI: 10.1137/21M1429424
      Issue No: Vol. 60, No. 3 (2022)
       
  • Optimal Dividend Strategies with Reinsurance under Contagious Systemic
           Risk

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      Authors: Ming Qiu, Zhuo Jin, Shuanming Li
      Pages: 1269 - 1293
      Abstract: SIAM Journal on Control and Optimization, Volume 60, Issue 3, Page 1269-1293, June 2022.
      This paper studies the multidimensional mixed singular-regular stochastic control problems subject to reduced-form default driven by contagious intensities. The dynamic process of surplus is given by a system of diffusion processes with two controls, and the intensity of the reduced-form model increases when defaults occur. We derive the recursive Hamilton--Jacobi--Bellman variational inequalities by the dynamic programming principle and present analytical and recursive solutions. We prove that the solutions are classical and recursively associated with each other by the default states. The verification theorem is presented.
      Citation: SIAM Journal on Control and Optimization
      PubDate: 2022-05-16T07:00:00Z
      DOI: 10.1137/21M1422318
      Issue No: Vol. 60, No. 3 (2022)
       
  • Proportional Local Assignability of the Dichotomy Spectrum of One-Sided
           Discrete Time-Varying Linear Systems

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      Authors: Pham The Anh, Artur Babiarz, Adam Czornik, Thai Son Doan
      Pages: 1294 - 1319
      Abstract: SIAM Journal on Control and Optimization, Volume 60, Issue 3, Page 1294-1319, June 2022.
      We consider a problem of assignability of the dichotomy spectrum for one-sided discrete time-varying linear systems. Our purpose is to prove that uniform complete controllability is a sufficient condition for proportional local assignability of the dichotomy spectrum.
      Citation: SIAM Journal on Control and Optimization
      PubDate: 2022-05-19T07:00:00Z
      DOI: 10.1137/21M1410932
      Issue No: Vol. 60, No. 3 (2022)
       
  • Finite-Time Stability of Polyhedral Sweeping Processes with Application to
           Elastoplastic Systems

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      Authors: Ivan Gudoshnikov, Oleg Makarenkov, Dmitrii Rachinskii
      Pages: 1320 - 1346
      Abstract: SIAM Journal on Control and Optimization, Volume 60, Issue 3, Page 1320-1346, June 2022.
      We use the ideas of Adly, Attouch, and Cabot [in Nonsmooth Mechanics and Analysis, Adv. Mech. Math. 12, Springer, New York, 2006, pp. 289--304] on finite-time stabilization of dry friction oscillators to establish a theorem on finite-time stabilization of differential inclusions with a moving polyhedral constraint (known as polyhedral sweeping processes) of the form $C+c(t)$. We then employ the ideas of Moreau [in New Variational Techniques in Mathematical Physics (Centro Internaz. Mat. Estivo (CIME), II Ciclo, Bressanone, 1973), Edizioni Cremonese, Rome, 1974, pp. 171--322] to apply our theorem to a system of elastoplastic springs with a displacement-controlled loading. We show that verifying the condition of the theorem ultimately leads to the following two problems: (i) identifying the active vertex “A” or the active face “A” of the polyhedron that the vector $c'(t)$ points at; (ii) computing the distance from $c'(t)$ to the normal cone to the polyhedron at “A.” We provide a computational guide for solving problems (i)--(ii) in the case of an arbitrary elastoplastic system and apply it to a particular example. Due to the simplicity of the particular example, we can solve (i)--(ii) by the methods of linear algebra and basic combinatorics.
      Citation: SIAM Journal on Control and Optimization
      PubDate: 2022-05-19T07:00:00Z
      DOI: 10.1137/20M1388796
      Issue No: Vol. 60, No. 3 (2022)
       
  • On the Lipschitz Regularity for Minima of Functionals Depending on $x$,
           $u$, and $\nabla{u}$ under the Bounded Slope Condition

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      Authors: F. Giannetti, G. Treu
      Pages: 1347 - 1364
      Abstract: SIAM Journal on Control and Optimization, Volume 60, Issue 3, Page 1347-1364, June 2022.
      We prove the existence of a global Lipschitz minimizer of functionals of the form $\mathcal I(u)=\int_\Omega f(\nabla u(x))+g(x,u(x))\,dx$, $u\in\phi+W^{1,1}_0(\Omega)$, assuming that $\phi$ satisfies the bounded slope condition (BSC). Our assumptions on the Lagrangian allow the function $f$ to be strongly degenerate.
      Citation: SIAM Journal on Control and Optimization
      PubDate: 2022-05-23T07:00:00Z
      DOI: 10.1137/21M1396617
      Issue No: Vol. 60, No. 3 (2022)
       
  • Lagrangian Discretization of Variational Mean Field Games

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      Authors: Clément Sarrazin
      Pages: 1365 - 1392
      Abstract: SIAM Journal on Control and Optimization, Volume 60, Issue 3, Page 1365-1392, June 2022.
      In this article, we introduce a method to approximate solutions of some variational mean field game problems with congestion by finite sets of player trajectories. These trajectories are obtained by solving a minimization problem similar to the initial variational problem. In this discretized problem, congestion is penalized by a Moreau envelope with 2-Wasserstein distance. Study of this envelope as well as efficient computation of its values and variations is done using semi-discrete optimal transport. We show convergence of the discrete sets of trajectories toward a solution of the mean field game, as well as conditions on the discretization in order to get this convergence.
      Citation: SIAM Journal on Control and Optimization
      PubDate: 2022-05-24T07:00:00Z
      DOI: 10.1137/20M1377291
      Issue No: Vol. 60, No. 3 (2022)
       
  • A Note on Riccati Matrix Difference Equations

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      Authors: Pierre Del Moral, Emma Horton
      Pages: 1393 - 1409
      Abstract: SIAM Journal on Control and Optimization, Volume 60, Issue 3, Page 1393-1409, June 2022.
      Discrete algebraic Riccati equations and their fixed points are well understood and arise in a variety of applications; however, the time-varying equations have not yet been fully explored in the literature. In this article we provide a self-contained study of discrete time Riccati matrix difference equations. In particular, we provide a novel Riccati semigroup duality formula and a new Floquet-type representation for these equations. Due to the aperiodicity of the underlying flow of the solution matrix, conventional Floquet theory does not apply in this setting and thus further analysis is required. We illustrate the impact of these formulae with an explicit description of the solution of time-varying Riccati difference equations and its fundamental-type solution in terms of the fixed point of the equation and an invertible linear matrix map as well as uniform upper and lower bounds on the Riccati maps. These are the first results of this type for time-varying Riccati matrix difference equations.
      Citation: SIAM Journal on Control and Optimization
      PubDate: 2022-05-24T07:00:00Z
      DOI: 10.1137/21M1437226
      Issue No: Vol. 60, No. 3 (2022)
       
  • An Approximation Scheme for Distributionally Robust PDE-Constrained
           Optimization

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      Authors: Johannes Milz, Michael Ulbrich
      Pages: 1410 - 1435
      Abstract: SIAM Journal on Control and Optimization, Volume 60, Issue 3, Page 1410-1435, June 2022.
      We develop a sampling-free approximation scheme for distributionally robust PDE-constrained optimization problems, which are min-max control problems. We define the ambiguity set through moment and entropic constraints. We use second-order Taylor's expansions of the reduced objective function w.r.t. uncertain parameters, allowing us to compute the expected value of the quadratic function explicitly. The objective function of the approximated min-max problem separates into a trust-region problem and a semidefinite program. We construct smoothing functions for the optimal value functions defined by these problems. We prove the existence of optimal solutions for the distributionally robust control problem, and the approximated and smoothed problems, and show that a worst-case distribution exists. For the numerical solution of the approximated problem, we develop a homotopy method that computes a sequence of stationary points of smoothed problems while decreasing smoothing parameters to zero. The adjoint approach is used to compute derivatives of the smoothing functions. Numerical results for two nonlinear optimization problems are presented.
      Citation: SIAM Journal on Control and Optimization
      PubDate: 2022-05-26T07:00:00Z
      DOI: 10.1137/20M134664X
      Issue No: Vol. 60, No. 3 (2022)
       
  • Unbounded Control, Infimum Gaps, and Higher Order Normality

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      Authors: Monica Motta, Michele Palladino, Franco Rampazzo
      Pages: 1436 - 1462
      Abstract: SIAM Journal on Control and Optimization, Volume 60, Issue 3, Page 1436-1462, June 2022.
      In optimal control theory one sometimes extends the minimization domain of a given problem, with the aim of achieving the existence of an optimal control. However, this issue is naturally confronted with the possibility of a gap between the original infimum value and the extended one. Avoiding this phenomenon is not a trivial issue, especially when the trajectories are subject to endpoint constraints. However, since the seminal works by Warga, some authors have recognized “normality” of an extended minimizer as a condition guaranteeing the absence of an infimum gap. Yet, normality is far from being necessary for this goal, a fact that makes the search for weaker assumptions a reasonable aim. In relation to a control-affine system with unbounded controls, in this paper we prove a sufficient no-gap condition based on a notion of higher order normality, which is less demanding than the standard normality and involves iterated Lie brackets of the vector fields defining the dynamics.
      Citation: SIAM Journal on Control and Optimization
      PubDate: 2022-05-26T07:00:00Z
      DOI: 10.1137/21M1431692
      Issue No: Vol. 60, No. 3 (2022)
       
  • Linear Filtering with Fractional Noises: Large Time and Small Noise
           Asymptotics

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      Authors: Danielle Afterman, Pavel Chigansky, Marina Kleptsyna, Dmytro Marushkevych
      Pages: 1463 - 1487
      Abstract: SIAM Journal on Control and Optimization, Volume 60, Issue 3, Page 1463-1487, June 2022.
      The classical state-space approach to optimal estimation of stochastic processes is efficient when the driving noises are generated by martingales. In particular, the weight function of the optimal linear filter, which solves a complicated operator equation in general, simplifies to the Riccati ordinary differential equation in the martingale case. This reduction lies in the foundations of the Kalman--Bucy approach to linear optimal filtering. In this paper we consider a basic Kalman--Bucy model with noises, generated by independent fractional Brownian motions, and develop a new method of asymptotic analysis of the integro-differential filtering equation arising in this case. We establish existence of the steady-state error limit and find its asymptotic scaling in the high signal-to-noise regime. Closed form expressions are derived in a number of important cases.
      Citation: SIAM Journal on Control and Optimization
      PubDate: 2022-05-26T07:00:00Z
      DOI: 10.1137/20M1360359
      Issue No: Vol. 60, No. 3 (2022)
       
  • Backward Stackelberg Differential Game with Constraints: A Mixed
           Terminal-Perturbation and Linear-Quadratic Approach

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      Authors: Xinwei Feng, Ying Hu, Jianhui Huang
      Pages: 1488 - 1518
      Abstract: SIAM Journal on Control and Optimization, Volume 60, Issue 3, Page 1488-1518, June 2022.
      We discuss an open-loop backward Stackelberg differential game involving a single leader and single follower. Unlike most Stackelberg game literature, the state to be controlled is characterized by a backward stochastic differential equation for which the terminal- instead of the initial-condition is specified a priori; the decisions of the leader consist of a static terminal-perturbation and a dynamic linear-quadratic control. In addition, the terminal control is subject to (convex-closed) pointwise and (affine) expectation constraints. Both constraints arise from real applications such as mathematical finance. For the information pattern, the leader announces both terminal and open-loop dynamic decisions at the initial time while taking into account the best response of the follower. Then, two interrelated optimization problems are sequentially solved by the follower (a backward linear-quadratic problem) and the leader (a mixed terminal-perturbation and backward-forward LQ problem). Our open-loop Stackelberg equilibrium is represented by some coupled backward-forward stochastic differential equations (BFSDEs) with mixed initial-terminal conditions. Our BFSDEs also involve a nonlinear projection operator (due to pointwise constraint) combining with a Karush--Kuhn--Tucker system (due to expectation constraint) via Lagrange multiplier. The global solvability of such BFSDEs is also discussed in some nontrivial cases. Our results are applied to one financial example.
      Citation: SIAM Journal on Control and Optimization
      PubDate: 2022-05-31T07:00:00Z
      DOI: 10.1137/20M1340769
      Issue No: Vol. 60, No. 3 (2022)
       
  • Distributed Order Estimation of ARX Model under Cooperative Excitation
           Condition

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      Authors: Die Gan, Zhixin Liu
      Pages: 1519 - 1545
      Abstract: SIAM Journal on Control and Optimization, Volume 60, Issue 3, Page 1519-1545, June 2022.
      In this paper, we consider the distributed estimation problem of a linear stochastic system described by an autoregressive model with exogenous inputs when both the system orders and parameters are unknown. We design distributed algorithms to estimate the unknown orders and parameters by combining the proposed local information criterion with the distributed least squares method. The simultaneous estimation for both the system orders and parameters brings challenges for the theoretical analysis. Some analysis techniques, such as double array martingale limit theory, stochastic Lyapunov functions, and martingale convergence theorems are employed. For the case where the upper bounds of the true orders are available, we introduce a cooperative excitation condition, under which the strong consistency of the estimation for the orders and parameters is established. Moreover, for the case where the upper bounds of true orders are unknown, a similar distributed algorithm is proposed to estimate both the orders and parameters, and the corresponding convergence analysis for the proposed algorithm is provided. We remark that our results are obtained without relying on the independency or stationarity assumptions of regression vectors, and the cooperative excitation conditions can show that all sensors can cooperate to fulfill the estimation task even though any individual sensor cannot.
      Citation: SIAM Journal on Control and Optimization
      PubDate: 2022-05-31T07:00:00Z
      DOI: 10.1137/21M1421362
      Issue No: Vol. 60, No. 3 (2022)
       
  • Steklov Eigenvalues of Nearly Spherical Domains

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      Authors: Robert Viator, Braxton Osting
      Pages: 1546 - 1562
      Abstract: SIAM Journal on Control and Optimization, Volume 60, Issue 3, Page 1546-1562, June 2022.
      We consider Steklov eigenvalues of three-dimensional, nearly spherical domains. In previous work, we have shown that the Steklov eigenvalues are analytic functions of the domain perturbation parameter. Here, we compute the first-order term of the asymptotic expansion, which can explicitly be written in terms of the Wigner 3-$j$ symbols. We analyze the asymptotic expansion and prove the isoperimetric result that, if $\ell$ is a square integer, the volume-normalized $\ell$th Steklov eigenvalue is stationary for a ball.
      Citation: SIAM Journal on Control and Optimization
      PubDate: 2022-05-31T07:00:00Z
      DOI: 10.1137/21M1411925
      Issue No: Vol. 60, No. 3 (2022)
       
  • Null Controllability for Fourth Order Stochastic Parabolic Equations

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      Authors: Qi Lü, Yu Wang
      Pages: 1563 - 1590
      Abstract: SIAM Journal on Control and Optimization, Volume 60, Issue 3, Page 1563-1590, June 2022.
      We establish the null controllability for fourth order stochastic parabolic equations. Utilizing the duality argument, the null controllability is reduced to the observability for fourth order backward stochastic parabolic equations, and the desired observability estimate is obtained by a new global Carleman estimate. Our Carleman estimate is based on a new fundamental identity for a fourth order stochastic parabolic operator.
      Citation: SIAM Journal on Control and Optimization
      PubDate: 2022-05-31T07:00:00Z
      DOI: 10.1137/22M1472620
      Issue No: Vol. 60, No. 3 (2022)
       
  • On Identification of Boolean Control Networks

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      Authors: Biao Wang, Jun-e Feng, Daizhan Cheng
      Pages: 1591 - 1612
      Abstract: SIAM Journal on Control and Optimization, Volume 60, Issue 3, Page 1591-1612, June 2022.
      A new analytical framework consisting of two phenomena, a single sample and multiple samples, is proposed to formulate the identification problem of Boolean control networks (BCNs) systematically and comprehensively. Under this framework, the existing works on identification can be categorized as special cases of these two phenomena. Several effective criteria for determining the identifiability and the corresponding identification algorithms are proposed. Two novel and important results are derived for the multiple-samples case: (1) A Boolean network is identifiable if and only if it is observable. (2) A BCN is identifiable if it is O1-observable, where O1-observability is the most general form of the existing observability terms. In addition, remarks present some challenging future research and contain a preliminary attempt about how to identify unobservable systems.
      Citation: SIAM Journal on Control and Optimization
      PubDate: 2022-05-31T07:00:00Z
      DOI: 10.1137/20M1373773
      Issue No: Vol. 60, No. 3 (2022)
       
  • Reference Tracking and Observer Design for Space Fractional Partial
           Differential Equation Modeling Gas Pressures in Fractured Media

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      Authors: Lilia Ghaffour, Taous-Meriem Laleg-Kirati
      Pages: 1613 - 1641
      Abstract: SIAM Journal on Control and Optimization, Volume 60, Issue 3, Page 1613-1641, June 2022.
      This paper considers a class of space fractional partial differential equations (FPDEs) that describe gas pressures in fractured media. First, the well-posedness, uniqueness, and stability of the considered FPDEs are investigated. Then, the reference tracking problem is studied to track the pressure gradient at a downstream location of a channel. This requires manipulation of gas pressure at the downstream location and the use of pressure measurements at an upstream location. To achieve this, the backstepping approach is adapted to the space FPDEs. The key challenge in this adaptation is the nonapplicability of the Lyapunov theory, which is typically used to prove the stability of the target system as the obtained target system is fractional in space. In addition, a backstepping adaptive observer is designed to jointly estimate both the system's state and the disturbance. The stability of the closed loop (reference tracking controller/observer) is also investigated. Finally, numerical simulations are given to evaluate the efficiency of the proposed method.
      Citation: SIAM Journal on Control and Optimization
      PubDate: 2022-06-01T07:00:00Z
      DOI: 10.1137/21M1424810
      Issue No: Vol. 60, No. 3 (2022)
       
  • Existence and Uniqueness for Non-Markovian Triangular Quadratic BSDEs

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      Authors: Joe Jackson, Gordan Žitković
      Pages: 1642 - 1666
      Abstract: SIAM Journal on Control and Optimization, Volume 60, Issue 3, Page 1642-1666, June 2022.
      We prove the existence and uniqueness of solutions to a class of quadratic backward SDE (BSDE) systems which we call triangular quadratic. Our results generalize several existing results about diagonally quadratic BSDEs in the non-Markovian setting. As part of our analysis, we obtain new results about linear BSDEs with unbounded coefficients, which may be of independent interest. Through a nonuniqueness example, we answer a “crucial open question” raised by Harter and Richou by showing that the stochastic exponential of an $n \times n$ matrix-valued bounded mean oscillation martingale need not satisfy a reverse Hölder inequality.
      Citation: SIAM Journal on Control and Optimization
      PubDate: 2022-06-02T07:00:00Z
      DOI: 10.1137/21M1435689
      Issue No: Vol. 60, No. 3 (2022)
       
  • A Game Theory Approach for the Groundwater Pollution Control

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      Authors: Emmanuelle Augeraud-Véron, Catherine Choquet, Éloïse Comte, Moussa M. Diédhiou
      Pages: 1667 - 1689
      Abstract: SIAM Journal on Control and Optimization, Volume 60, Issue 3, Page 1667-1689, June 2022.
      A differential game modeling the noncooperative outcome of pollution in groundwater is studied. Spatio-temporal objectives are constrained by a convection-diffusion-reaction equation ruling the spread of the pollution in the aquifer, and the velocity of the flow solves an elliptic partial differential equation. The existence of a Nash equilibrium is proved using a fixed point strategy. A uniqueness result for the Nash equilibrium is also proved under some additional assumptions. Some numerical illustrations are provided.
      Citation: SIAM Journal on Control and Optimization
      PubDate: 2022-06-07T07:00:00Z
      DOI: 10.1137/19M1278223
      Issue No: Vol. 60, No. 3 (2022)
       
  • Path-Dependent Hamilton--Jacobi Equations with Super-Quadratic Growth in
           the Gradient and the Vanishing Viscosity Method

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      Authors: Erhan Bayraktar, Christian Keller
      Pages: 1690 - 1711
      Abstract: SIAM Journal on Control and Optimization, Volume 60, Issue 3, Page 1690-1711, June 2022.
      The nonexponential Schilder-type theorem in Backhoff-Veraguas, Lacker, and Tangpi [Ann.\Appl. Probab., 30 (2020), pp. 1321--1367] is expressed as a convergence result for path-dependent partial differential equations with appropriate notions of generalized solutions. This entails a non-Markovian counterpart to the vanishing viscosity method. We show uniqueness of maximal subsolutions for path-dependent viscous Hamilton--Jacobi equations related to convex super-quadratic backward stochastic differential equations. We establish well-posedness for the Hamilton--Jacobi--Bellman equation associated to a Bolza problem of the calculus of variations with path-dependent terminal cost. In particular, uniqueness among lower semicontinuous solutions holds, and state constraints are admitted.
      Citation: SIAM Journal on Control and Optimization
      PubDate: 2022-06-13T07:00:00Z
      DOI: 10.1137/21M1395557
      Issue No: Vol. 60, No. 3 (2022)
       
  • Continuous-Time Convergence Rates in Potential and Monotone Games

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      Authors: Bolin Gao, Lacra Pavel
      Pages: 1712 - 1731
      Abstract: SIAM Journal on Control and Optimization, Volume 60, Issue 3, Page 1712-1731, June 2022.
      In this paper, we provide exponential rates of convergence to the interior Nash equilibrium for continuous-time dual-space game dynamics such as mirror descent (MD) and actor-critic (AC). We perform our analysis in $N$-player continuous concave games that satisfy certain monotonicity assumptions while possibly also admitting potential functions. In the first part of this paper, we provide a novel relative characterization of monotone games and show that MD and its discounted version converge with $\mathcal{O}(e^{-\beta t})$ in relatively strongly and relatively hypomonotone games, respectively. In the second part of this paper, we specialize our results to games that admit a relatively strongly concave potential and show that AC converges with $\mathcal{O}(e^{-\beta t})$. These rates extend their known convergence conditions. Simulations are performed which empirically back up our results.
      Citation: SIAM Journal on Control and Optimization
      PubDate: 2022-06-14T07:00:00Z
      DOI: 10.1137/20M1381873
      Issue No: Vol. 60, No. 3 (2022)
       
  • Optimal Control Problems Governed by Fractional Differential Equations
           with Control Constraints

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      Authors: B. T. Kien, V. E. Fedorov, T. D. Phuong
      Pages: 1732 - 1762
      Abstract: SIAM Journal on Control and Optimization, Volume 60, Issue 3, Page 1732-1762, June 2022.
      A class of optimal control problems governed by fractional differential equations with control constraints and free right end point is considered. We first prove a result on the existence of optimal solutions for the case where the state equation may be nonlinear in control variable. Then we establish first- and second-order optimality conditions for locally optimal solutions to the general problem. When $\frac{1}2
      Citation: SIAM Journal on Control and Optimization
      PubDate: 2022-06-14T07:00:00Z
      DOI: 10.1137/21M1430728
      Issue No: Vol. 60, No. 3 (2022)
       
  • Error Estimates for a Pointwise Tracking Optimal Control Problem of a
           Semilinear Elliptic Equation

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      Authors: Alejandro Allendes, Francisco Fuica, Enrique Otárola
      Pages: 1763 - 1790
      Abstract: SIAM Journal on Control and Optimization, Volume 60, Issue 3, Page 1763-1790, June 2022.
      We consider a pointwise tracking optimal control problem for a semilinear elliptic partial differential equation. We derive the existence of optimal solutions and analyze first and, necessary and sufficient, second order optimality conditions. We devise two strategies of discretization to approximate a solution of the optimal control problem: a semidiscrete scheme where the control variable is not discretized---the so-called variational discretization approach---and a fully discrete scheme where the control variable is discretized with piecewise constant functions. For both solution techniques, we analyze convergence properties of discretizations and derive error estimates.
      Citation: SIAM Journal on Control and Optimization
      PubDate: 2022-06-14T07:00:00Z
      DOI: 10.1137/20M1364151
      Issue No: Vol. 60, No. 3 (2022)
       
  • A Global Stochastic Maximum Principle for Forward-Backward Stochastic
           Control Systems with Quadratic Generators

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      Authors: Mingshang Hu, Shaolin Ji, Rundong Xu
      Pages: 1791 - 1818
      Abstract: SIAM Journal on Control and Optimization, Volume 60, Issue 3, Page 1791-1818, June 2022.
      We study a stochastic optimal control problem for forward-backward control systems with quadratic generators. In order to establish the first- and second-order variational and adjoint equations, we obtain a new estimate for one-dimensional linear backward stochastic differential equations (BSDEs) with unbounded stochastic Lipschitz coefficients involving bounded mean oscillation martingales and prove the solvability for a class of multidimensional BSDEs with this type. Finally, a new global stochastic maximum principle is deduced.
      Citation: SIAM Journal on Control and Optimization
      PubDate: 2022-06-14T07:00:00Z
      DOI: 10.1137/20M137238X
      Issue No: Vol. 60, No. 3 (2022)
       
  • Subdifferentiation of Nonconvex Sparsity-Promoting Functionals on Lebesgue
           Spaces

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      Authors: Patrick Mehlitz, Gerd Wachsmuth
      Pages: 1819 - 1839
      Abstract: SIAM Journal on Control and Optimization, Volume 60, Issue 3, Page 1819-1839, June 2022.
      Sparsity-promoting terms are incorporated into the objective functions of optimal control problems in order to ensure that optimal controls vanish on large parts of the underlying domain. Typical candidates for those terms are integral functions on Lebesgue spaces based on the $\ell_p$-metric for $p\in[0,1)$, which are nonconvex as well as non-Lipschitz and, thus, variationally challenging. In this paper, we derive exact formulas for the Fréchet, limiting, and singular subdifferential of these functionals. These generalized derivatives can be used for the derivation of necessary optimality conditions for optimal control problems comprising such sparsity-promoting terms.
      Citation: SIAM Journal on Control and Optimization
      PubDate: 2022-06-21T07:00:00Z
      DOI: 10.1137/21M1435173
      Issue No: Vol. 60, No. 3 (2022)
       
  • Staticization and Iterated Staticization

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      Authors: William M. McEneaney, Ruobing Zhao
      Pages: 1840 - 1862
      Abstract: SIAM Journal on Control and Optimization, Volume 60, Issue 3, Page 1840-1862, June 2022.
      Conservative dynamical systems propagate as stationary points of the action functional. Using this representation, it has previously been demonstrated that one may obtain fundamental solutions for two-point boundary value problems for some classes of conservative systems via a solution of an associated dynamic program. It is also known that the gravitational and Coulomb potentials may be represented as stationary points of cubicly parameterized quadratic functionals. Hence, stationary points of the action functional may be represented via iterated “staticization” of polynomial functionals, where the staticization operator (introduced and discussed in [J. Differential Equations, 264 (2018), pp. 525--549] and [Automatica J. IFAC, 81 (2017), pp. 56--67]) maps a function to the function value(s) at its stationary (i.e., critical) points. This leads to representations through operations on sets of solutions of differential Riccati equations. A key step in this process is the reordering of staticization operations. Conditions under which this reordering is allowed are obtained, and it is shown that the conditions are satisfied for an astrodynamics problem.
      Citation: SIAM Journal on Control and Optimization
      PubDate: 2022-06-21T07:00:00Z
      DOI: 10.1137/19M1251278
      Issue No: Vol. 60, No. 3 (2022)
       
  • Controlling Swarms toward Flocks and Mills

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      Authors: José A. Carrillo, Dante Kalise, Francesco Rossi, Emmanuel Trélat
      Pages: 1863 - 1891
      Abstract: SIAM Journal on Control and Optimization, Volume 60, Issue 3, Page 1863-1891, June 2022.
      Self-organization and control around flocks and mills is studied for second-order swarming systems involving self-propulsion and potential terms. It is shown that through the action of constrained control, it is possible to control any initial configuration to a flock or a mill. The proof builds on an appropriate combination of several arguments: the LaSalle invariance principle and Lyapunov-like decreasing functionals, control linearization techniques, and quasi-static deformations. A stability analysis of the second-order system guides the design of feedback laws for the stabilization to flock and mills, which are also assessed computationally.
      Citation: SIAM Journal on Control and Optimization
      PubDate: 2022-06-21T07:00:00Z
      DOI: 10.1137/21M1404314
      Issue No: Vol. 60, No. 3 (2022)
       
  • Gradual-Impulsive Control for Continuous-Time Markov Decision Processes
           with Total Undiscounted Costs and Constraints: Linear Programming Approach
           via a Reduction Method

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      Authors: Alexey Piunovskiy, Yi Zhang
      Pages: 1892 - 1917
      Abstract: SIAM Journal on Control and Optimization, Volume 60, Issue 3, Page 1892-1917, June 2022.
      We consider the constrained optimal control problem for a continuous-time Markov decision process (CTMDP) with gradual-impulsive control. The performance criteria are the expected total undiscounted costs (from the running cost and the impulsive cost). We justify fully a reduction method, and close an open issue in the previous literature. The reduction method induces an equivalent but simpler standard CTMDP model with gradual control only, based on which, we establish effectively, under rather natural conditions, a linear programming approach for solving the concerned constrained optimal control problem.
      Citation: SIAM Journal on Control and Optimization
      PubDate: 2022-06-27T07:00:00Z
      DOI: 10.1137/21M1444060
      Issue No: Vol. 60, No. 3 (2022)
       
  • Special Section on Mathematical Modeling, Analysis, and Control of
           Epidemics

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      Authors: Carolyn Beck, Francesco Bullo, Giacomo Como, Kimon Drakopoulos, Dang H. Nguyen, Cameron Nowzari, Victor M. Preciado, Shreyas Sundaram
      Abstract: SIAM Journal on Control and Optimization, Volume 60, Issue 2, Page Si-Sii, April 2022.
      This special section of the SIAM Journal on Control and Optimization (SICON) addresses the fundamental challenges inherent in the mathematical modeling, analysis, and control of epidemics. The ongoing COVID-19 pandemic has brought into the spotlight the critical importance of understanding complex epidemic processes. Yet the modeling, analysis, estimation, and control of these processes presents several formidable challenges. Epidemics inherently exhibit nonlinear dynamics as they spread through populations, requiring analytical techniques that can accurately capture both the transient and the steady-state aspects of the disease. Furthermore, careful attention must be paid to the resolution at which to model the epidemics, ranging from coarse mass-action models to metapopulation and individual-level models. Each of these approaches provides different insights and challenges for analysis and control. Models that operate at finer resolutions will also come with an increase in complexity, necessitating tractable abstractions ranging from mean-field models to deterministic and stochastic ODEs and PDEs. In the context of estimation of epidemics, the key challenge is to determine the important parameters of the epidemic (often in real time) based on data gathered from the affected population, in conjunction with dynamical models of the spreading process. Finally, formulating techniques to optimally control and address an ongoing epidemic (through either a centralized intervention, decentralized incentive mechanisms, or resource allocation policies) remains a critical challenge. The special section gathers contributions from the intersection of the fields of systems and control theory and the mathematical study of epidemic spread processes. A total of 16 papers represents a wide range of topics in modeling, identification, dynamic analysis, control, and optimization. Regarding modeling problems, the section covers contributions on Polya contagion networks, networked bivirus epidemic models, and age-differentiated compartmental models. For dynamic analysis, the section highlights contributions on explicit solutions and control design for simplified models, convergence and equilibria analysis, as well as the role of delays and saturations in closed loop settings. For identification and estimation problems, contributions are offered on the identifiability of model parameters and on parameter estimation using limited measurements. Most of the contributed articles focus on control design, optimization, and game theoretic problems. Centralized and distributed strategies are proposed. Actuation mechanisms include edge deletion, test allocation, optimal incentives, optimal switching between lockdown and opening the economy, screening, and curing policies. We believe this special section presents an excellent cross section of current research and hope that it will be of great interest to the broad readership of SICON. We offer our deepest thanks to all authors who submitted their work and to all reviewers who contributed their time and energy to the peer-review process. We would also like to thank the proficient and timely editorial support provided by Brian Fauth and the insightful and gracious advice that we received from the SICON Editor-in-Chief George Yin. Carolyn Beck University of Illinois at Urbana-Champaign Francesco Bullo University of California, Santa Barbara Giacomo Como Politecnico di Torino Kimon Drakopoulos University of Southern California Dang H. Nguyen University of Alabama Cameron Nowzari George Mason University Victor M. Preciado University of Pennsylvania Shreyas Sundaram Purdue University, Guest editors
      Citation: SIAM Journal on Control and Optimization
      PubDate: 2022-04-28T07:00:00Z
      DOI: 10.1137/22N975470
      Issue No: Vol. 60, No. 2 (2022)
       
  • A Unification of Weighted and Unweighted Particle Filters

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      Authors: Ehsan Abedi, Simone Carlo Surace, Jean-Pascal Pfister
      Pages: 597 - 619
      Abstract: SIAM Journal on Control and Optimization, Volume 60, Issue 2, Page 597-619, April 2022.
      Particle filters (PFs), which are successful methods for approximating the solution of the filtering problem, can be divided into two types: weighted and unweighted PFs. It is well known that weighted PFs suffer from the weight degeneracy and curse of dimensionality. To sidestep these issues, unweighted PFs have been gaining attention, though they have their own challenges. The existing literature on these types of PFs is based on distinct approaches. In order to establish a connection, we put forward a framework that unifies weighted and unweighted PFs in the continuous-time filtering problem. We show that the stochastic dynamics of a particle system described by a pair process, representing particles and their importance weights, should satisfy two necessary conditions in order for its distribution to match the solution of the Kushner--Stratonovich equation. In particular, we demonstrate that the bootstrap particle filter (BPF), which relies on importance sampling, and the feedback particle filter (FPF), which is an unweighted PF based on optimal control, arise as special cases from a broad class and that there is a smooth transition between the two. The freedom in designing the PF dynamics opens up potential ways to address the existing issues in the aforementioned algorithms, namely weight degeneracy in the BPF and gain estimation in the FPF.
      Citation: SIAM Journal on Control and Optimization
      PubDate: 2022-03-01T08:00:00Z
      DOI: 10.1137/20M1382404
      Issue No: Vol. 60, No. 2 (2022)
       
  • A Stochastic Model of Economic Growth in Time-Space

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      Authors: Fausto Gozzi, Marta Leocata
      Pages: 620 - 651
      Abstract: SIAM Journal on Control and Optimization, Volume 60, Issue 2, Page 620-651, April 2022.
      We deal with an infinite horizon, infinite dimensional stochastic optimal control problem arising in the study of economic growth in time-space. Such a problem has been the object of various papers in deterministic cases when the possible presence of stochastic disturbances is ignored (see, e.g., [P. Brito, The Dynamics of Growth and Distribution in a Spatially Heterogeneous World, working paper 2004/14, ISEG-Lisbon School of Economics and Management, University of Lisbon, 2004], [R. Boucekkine, C. Camacho, and G. Fabbri, J. Econom. Theory, 148 (2013), pp. 2719--2736], [G. Fabbri, J. Econom. Theory, 162 (2016), pp. 114--136], and [R. Boucekkine, G. Fabbri, S. Federico, and F. Gozzi, J. Econom. Geography, 19 (2019), pp. 1287--1318]). Here we propose and solve a stochastic generalization of such models where the stochastic term, in line with the standard stochastic economic growth models (see, e.g., the books [A. G. Malliaris and W. A. Brock, Stochastic Methods in Economics and Finance, Advanced Textbooks in Economics 17, North Holland, 1982, Chapter 3] and [H. Morimoto, Stochastic Control and Mathematical Modeling: Applications in Economics, Cambridge Books, 2010, Chapter 9]), is a multiplicative one, driven by a cylindrical Wiener process. The problem is studied using the dynamic programming approach. We find an explicit solution of the associated HJB equation, use a verification type result to prove that such a solution is the value function, and find the optimal feedback strategies. Finally, we use this result to study the asymptotic behavior of the optimal trajectories.
      Citation: SIAM Journal on Control and Optimization
      PubDate: 2022-03-01T08:00:00Z
      DOI: 10.1137/21M1414206
      Issue No: Vol. 60, No. 2 (2022)
       
  • Constructive Exact Control of Semilinear 1D Wave Equations by a
           Least-Squares Approach

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      Authors: Arnaud Münch, Emmanuel Trélat
      Pages: 652 - 673
      Abstract: SIAM Journal on Control and Optimization, Volume 60, Issue 2, Page 652-673, April 2022.
      It has been proved by Zuazua in the nineties that the internally controlled semilinear 1D wave equation $\partial_{tt}y-\partial_{xx}y + g(y)=f 1_{\omega}$, with Dirichlet boundary conditions, is exactly controllable in $H^1_0(0,1)\cap L^2(0,1)$ with controls $f\in L^2((0,1)\times(0,T))$, for any $T>0$ and any nonempty open subset $\omega$ of (0,1), assuming that $g\in \mathcal{C}^1(\mathbb{R})$ does not grow faster than $\beta\vert x\vert \ln^{2}\vert x\vert$ at infinity for some $\beta>0$ small enough. The proof, based on the Leray--Schauder fixed point theorem, is, however, not constructive. In this article, we design a constructive proof and algorithm for the exact controllability of semilinear 1D wave equations. Assuming that $g^\prime$ does not grow faster than $\beta \ln^{2}\vert x\vert$ at infinity for some $\beta>0$ small enough and that $g^\prime$ is uniformly Hölder continuous on $\mathbb{R}$ with exponent $s\in[0,1]$, we design a least-squares algorithm yielding an explicit sequence converging to a controlled solution for the semilinear equation, at least with order $1+s$ after a finite number of iterations.
      Citation: SIAM Journal on Control and Optimization
      PubDate: 2022-03-07T08:00:00Z
      DOI: 10.1137/20M1380661
      Issue No: Vol. 60, No. 2 (2022)
       
  • A Constructive Approach to Existence of Equilibria in Time-Inconsistent
           Stochastic Control Problems

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      Authors: Jiang Yu Nguwi, Nicolas Privault
      Pages: 674 - 698
      Abstract: SIAM Journal on Control and Optimization, Volume 60, Issue 2, Page 674-698, April 2022.
      We extend the construction of equilibria for linear-quadratic and mean-variance portfolio problems available in the literature to a large class of mean-field time-inconsistent stochastic control problems in continuous time. Our approach relies on a time discretization of the control problem via $n$-person games, which are characterized via the maximum principle using backward stochastic differential equations. The existence of equilibria is proved by applying weak convergence arguments to the solutions of $n$-person games. A numerical implementation is provided by approximating $n$-person games using finite Markov chains.
      Citation: SIAM Journal on Control and Optimization
      PubDate: 2022-03-09T08:00:00Z
      DOI: 10.1137/20M1370446
      Issue No: Vol. 60, No. 2 (2022)
       
  • On the Continuous Finite-Time Stabilization of the Double Integrator

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      Authors: Arturo Zavala-Río, Tonametl Sanchez, Griselda I. Zamora-Gómez
      Pages: 699 - 719
      Abstract: SIAM Journal on Control and Optimization, Volume 60, Issue 2, Page 699-719, April 2022.
      Continuous finite-time stabilization is often treated under the analytical framework of homogeneity and has been frequently illustrated in the context of the feedback control of the double integrator. For such a simple system, the simplest considered continuous finite-time controller is composed of gained (proportional) exponentially weighted position and velocity error correction terms, with the exponential weights generally less than unity and constrained to satisfy a particular relation among them under homogeneity. What happens for less-than-unity exponential weights that do not satisfy such a homogeneity-based relation' Does the finite-time stabilization hold' Through a Lyapunov function--based study, we analyze and give more concrete answers to such questions than those partially provided by previous studies on the topic. We do find a more exhaustive spectrum of the exponential weights that give rise to finite-time stability of the trivial solution. Other types of stability properties are further found to take place for less-than-or-equal-to-unity exponential weights. Moreover, through complementary analysis, local or ultimate behavior of the system solutions is further characterized. The analytical findings are further illustrated through computer simulations.
      Citation: SIAM Journal on Control and Optimization
      PubDate: 2022-03-09T08:00:00Z
      DOI: 10.1137/20M136459X
      Issue No: Vol. 60, No. 2 (2022)
       
  • Euclidean Distance Bounds for Linear Matrix Inequalities Analytic Centers
           Using a Novel Bound on the Lambert Function

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      Authors: Biel Roig-Solvas, Mario Sznaier
      Pages: 720 - 731
      Abstract: SIAM Journal on Control and Optimization, Volume 60, Issue 2, Page 720-731, April 2022.
      Linear matrix inequalities (LMIs) are ubiquitous in modern control theory, as well as in a variety of other fields in science and engineering. Their analytic centers, i.e. the maximum determinant elements of the feasible set spanned by these LMIs, are the solution of many well-known problems in statistics, communications, geometry, and control and can be approximated to arbitrary precision by semidefinite programs (SDPs). The quality of these approximations is measured with respect to the difference in log-determinant of both the exact and the approximate solutions to these SDPs, a quantity that follows directly from the duality theory of semidefinite programming. However, in many applications the relevant parameters are functions of the entries of the LMI argument $X$. In these cases it is of interest to develop metrics that quantify the quality of approximate solutions based on the error of these parameters, something that the log-determinant error fails to capture due to the nonlinear interaction of all the matrix entries. In this work we develop upper bounds on the Frobenius norm error between suboptimal solutions $X_f$ and the exact optimizer $X_*$ of maximum determinant problems, a metric that provides a direct translation to the entrywise error of $X$ and thus to the relevant parameters of the application. We show that these bounds can be expressed through the use of the Lambert function $W(x)$, i.e., the solution of the equation $W(x) e^{W(x)}= x$, and derive novel bounds for one of its branches to generate efficient closed-form bounds on the Euclidean distance to the LMI analytic center. Finally, we test the quality of these bounds numerically in the context of interior point methods termination criteria.
      Citation: SIAM Journal on Control and Optimization
      PubDate: 2022-03-15T07:00:00Z
      DOI: 10.1137/20M1349928
      Issue No: Vol. 60, No. 2 (2022)
       
  • Continuous Rendezvous Algorithm for Memoryless Agents with Limited
           Visibility in the Euclidean Space

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      Authors: Doheon Kim
      Pages: 732 - 757
      Abstract: SIAM Journal on Control and Optimization, Volume 60, Issue 2, Page 732-757, April 2022.
      A continuous-in-time rendezvous algorithm for memoryless agents with limited visibility on the Euclidean plane was proposed in [N. Gordon, I. A. Wagner, and A. M. Bruckstein in Ant Colony Optimization and Swarm Intelligence, Springer, Berlin, 2004, pp. 142--153] and was formulated as a system of differential equations in [L. I. Bellaiche and A. Bruckstein, Swarm Intell., 11 (2017), pp. 271--293]. We generalize this algorithm by letting the agents move in the Euclidean space of arbitrary dimension. And we provide a rigorous existence theory for this algorithm, which was not done before this work, even for the original algorithm for agents on a plane. Finally, for dimension not greater than three, we show that rendezvous is achieved in finite time, which is robust with respect to the number of the agents.
      Citation: SIAM Journal on Control and Optimization
      PubDate: 2022-03-17T07:00:00Z
      DOI: 10.1137/20M1387584
      Issue No: Vol. 60, No. 2 (2022)
       
  • A Class of Stochastic Games and Moving Free Boundary Problems

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      Authors: Xin Guo, Wenpin Tang, Renyuan Xu
      Pages: 758 - 785
      Abstract: SIAM Journal on Control and Optimization, Volume 60, Issue 2, Page 758-785, April 2022.
      In this paper we propose and analyze a class of $N$-player stochastic games that include finite fuel stochastic games as a special case. We first derive sufficient conditions for the Nash equilibrium (NE) in the form of a verification theorem. The associated quasi-variational-inequalities include an essential game component regarding the interactions among players, which may be interpreted as the analytical representation of the conditional optimality for NEs. The derivation of NEs involves solving first a multidimensional free boundary problem and then a Skorokhod problem. Finally, we present an intriguing connection between these NE strategies and controlled rank-dependent stochastic differential equations.
      Citation: SIAM Journal on Control and Optimization
      PubDate: 2022-03-17T07:00:00Z
      DOI: 10.1137/20M1322558
      Issue No: Vol. 60, No. 2 (2022)
       
  • Feedforward Neural Networks and Compositional Functions with Applications
           to Dynamical Systems

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      Authors: Wei Kang, Qi Gong
      Pages: 786 - 813
      Abstract: SIAM Journal on Control and Optimization, Volume 60, Issue 2, Page 786-813, April 2022.
      In this paper we develop an algebraic framework for analyzing neural network approximation of compositional functions, a rich class of functions that are frequently encountered in applications. The framework is developed in a way so that it supports the error analysis for not only functions as input-output relations, but also numerical algorithms. This capability is critical because it enables the analysis of neural network approximation errors for problems for which analytic solutions are not available, such as differential equations and optimal control. A set of key compositional features as well as its relationship with the complexity of neural network approximations are identified. We prove that in the approximation of functions, differential equations and optimal control, the complexity of neural networks is bounded by a polynomial function of the key features and error tolerance. The results shed light on the reason why using neural network approximations helps to avoid the curse of dimensionality.
      Citation: SIAM Journal on Control and Optimization
      PubDate: 2022-03-17T07:00:00Z
      DOI: 10.1137/21M1391596
      Issue No: Vol. 60, No. 2 (2022)
       
  • Moment-Driven Predictive Control of Mean-Field Collective Dynamics

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      Authors: Giacomo Albi, Michael Herty, Dante Kalise, Chiara Segala
      Pages: 814 - 841
      Abstract: SIAM Journal on Control and Optimization, Volume 60, Issue 2, Page 814-841, April 2022.
      The synthesis of control laws for interacting agent-based dynamics and their mean-field limit is studied. A linearization-based approach is used for the computation of suboptimal feedback laws obtained from the solution of differential matrix Riccati equations. Quantification of dynamic performance of such control laws leads to theoretical estimates on suitable linearization points of the nonlinear dynamics. Subsequently, the feedback laws are embedded into a nonlinear model predictive control framework where the control is updated adaptively in time according to dynamic information on moments of linear mean-field dynamics. The performance and robustness of the proposed methodology is assessed through different numerical experiments in collective dynamics.
      Citation: SIAM Journal on Control and Optimization
      PubDate: 2022-03-24T07:00:00Z
      DOI: 10.1137/21M1391559
      Issue No: Vol. 60, No. 2 (2022)
       
  • Robustness to Incorrect Priors and Controlled Filter Stability in
           Partially Observed Stochastic Control

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      Authors: Curtis McDonald, Serdar Yüksel
      Pages: 842 - 870
      Abstract: SIAM Journal on Control and Optimization, Volume 60, Issue 2, Page 842-870, April 2022.
      We study controlled filter stability and its effects on the robustness properties of optimal control policies designed for systems with incorrect priors applied to a true system. Filter stability refers to the correction of an incorrectly initialized filter for a partially observed stochastic dynamical system (controlled or control-free) with increasing measurements. This problem has been studied extensively in the control-free context, and except for the standard machinery for linear Gaussian systems involving the Kalman filter, few studies exist for the controlled setup. One of the main differences between control-free and controlled partially observed Markov chains is that the filter is always Markovian under the former, whereas under a controlled model the filter process may not be Markovian since the control policy may depend on past measurements in an arbitrary (measurable) fashion. This complicates the dependency structure and therefore results from the control-free literature do not directly apply to the controlled setup. In this paper, we study the filter stability problem for controlled stochastic dynamical systems and provide sufficient conditions for when a falsely initialized filter merges with the correctly initialized filter over time. These stability results are applied to robust stochastic control problems: under filter stability, we bound the difference in the expected cost incurred for implementing an incorrectly designed control policy compared to an optimal policy. A conclusion is that filter stability leads to stronger robustness results to incorrect priors (compared with results in [A. D. Kara and S. Yüksel, SIAM J. Control Optim., 57 (2019), pp. 1929--1964] without controlled filter stability). Furthermore, if the optimum cost is the same for each prior, the cost of mismatch between the true prior and the assumed prior is zero.
      Citation: SIAM Journal on Control and Optimization
      PubDate: 2022-04-04T07:00:00Z
      DOI: 10.1137/21M1417442
      Issue No: Vol. 60, No. 2 (2022)
       
  • On a Fractional Diffusion Equation with Moving Control

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      Authors: Sorin Micu, Constantin Niţă
      Pages: 871 - 889
      Abstract: SIAM Journal on Control and Optimization, Volume 60, Issue 2, Page 871-889, April 2022.
      This article considers a one-dimensional fractional parabolic equation, which may serve as a mathematical model for anomalous diffusion phenomena. It is known that, if the support of the control is fixed, this equation is not even spectrally controllable. We show that, when the control support is shifted in time with constant velocity $c$, the system is null-controllable in a sufficiently large time depending on $c$.
      Citation: SIAM Journal on Control and Optimization
      PubDate: 2022-04-04T07:00:00Z
      DOI: 10.1137/20M1385056
      Issue No: Vol. 60, No. 2 (2022)
       
  • Geometrical Characterization of Sensor Placement for Cone-Invariant and
           Multi-Agent Systems against Undetectable Zero-Dynamics Attacks

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      Authors: Jianqi Chen, Jieqiang Wei, Wei Chen, Henrik Sandberg, Karl Henrik Johansson, Jie Chen
      Pages: 890 - 916
      Abstract: SIAM Journal on Control and Optimization, Volume 60, Issue 2, Page 890-916, April 2022.
      Undetectable attacks are an important class of malicious attacks threatening the security of cyber-physical systems, which can modify a system's state but leave the system output measurements unaffected and hence cannot be detected from the output. This paper studies undetectable attacks on cone-invariant systems and multi-agent systems. We first provide a general characterization of zero-dynamics attacks, which characterizes fully undetectable attacks targeting the nonminimum phase zeros of a system. This geometrical characterization makes it possible to develop a defense strategy seeking to place a minimal number of sensors to detect and counter the zero-dynamics attacks on the system's actuators. The detect and defense scheme amounts to computing a set containing potentially vulnerable actuator locations and nodes and a defense union for feasible placement of sensors based on the geometrical properties of the cones under consideration.
      Citation: SIAM Journal on Control and Optimization
      PubDate: 2022-04-07T07:00:00Z
      DOI: 10.1137/21M1403618
      Issue No: Vol. 60, No. 2 (2022)
       
  • Localized Stability Certificates for Spatially Distributed Systems over
           Sparse Proximity Graphs

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      Authors: Nader Motee, Qiyu Sun
      Pages: 917 - 944
      Abstract: SIAM Journal on Control and Optimization, Volume 60, Issue 2, Page 917-944, April 2022.
      In this paper, we focus on localized conditions to verify exponential stability of spatially distributed linear systems whose interconnection structures are defined using a geodesic on proximity coupling graphs. We reformulate the exponential stability condition in the form of a feasibility condition that is amenable to localized implementations. Using finite truncation techniques, we obtain decentralized necessary and sufficient stability certificates. In order to guarantee global stability, it suffices to certify localized conditions over a graph covering, where the computational complexity of the verification of the proposed localized certificate is independent of network size. Several robustness conditions against local matrix perturbations are obtained that are useful for tuning network parameters in a decentralized manner while ensuring global exponential stability.
      Citation: SIAM Journal on Control and Optimization
      PubDate: 2022-04-11T07:00:00Z
      DOI: 10.1137/19M1298834
      Issue No: Vol. 60, No. 2 (2022)
       
  • Stationary Markov Nash Equilibria for Nonzero-Sum Constrained ARAT Markov
           Games

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      Authors: François Dufour, Tomás Prieto-Rumeau
      Pages: 945 - 967
      Abstract: SIAM Journal on Control and Optimization, Volume 60, Issue 2, Page 945-967, April 2022.
      We consider a nonzero-sum Markov game on an abstract measurable state space with compact metric action spaces. The goal of each player is to maximize his respective discounted payoff function under the condition that some constraints on a discounted payoff are satisfied. We are interested in the existence of a Nash or noncooperative equilibrium. Under suitable conditions, which include absolute continuity of the transitions with respect to some reference probability measure, additivity of the payoffs and the transition probabilities (ARAT condition), and continuity in action of the payoff functions and the density function of the transitions of the system, we establish the existence of a constrained stationary Markov Nash equilibrium, that is, the existence of stationary Markov strategies for each of the players yielding an optimal profile within the class of all history-dependent profiles.
      Citation: SIAM Journal on Control and Optimization
      PubDate: 2022-04-11T07:00:00Z
      DOI: 10.1137/21M144565X
      Issue No: Vol. 60, No. 2 (2022)
       
  • On the Time-Inconsistent Deterministic Linear-Quadratic Control

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      Authors: Hongyan Cai, Danhong Chen, Yunfei Peng, Wei Wei
      Pages: 968 - 991
      Abstract: SIAM Journal on Control and Optimization, Volume 60, Issue 2, Page 968-991, April 2022.
      A fundamental theory of deterministic linear-quadratic (LQ) control is the equivalent relationship between control problems, two-point boundary value problems, and Riccati equations. In this paper, we extend the equivalence to a general time-inconsistent deterministic LQ problem, where the inconsistency arises from nonexponential discount functions. By studying the solvability of the Riccati equation, we show the existence and uniqueness of the linear equilibrium for the time-inconsistent LQ problem.
      Citation: SIAM Journal on Control and Optimization
      PubDate: 2022-04-18T07:00:00Z
      DOI: 10.1137/21M1419611
      Issue No: Vol. 60, No. 2 (2022)
       
  • Event-Triggered Distributed Estimation with Decaying Communication Rate

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      Authors: Xingkang He, Yu Xing, Junfeng Wu, Karl H. Johansson
      Pages: 992 - 1017
      Abstract: SIAM Journal on Control and Optimization, Volume 60, Issue 2, Page 992-1017, April 2022.
      We study distributed estimation of a high-dimensional static parameter vector through a group of sensors whose communication network is modeled by a fixed directed graph. Different from existing time-triggered communication schemes, an event-triggered asynchronous scheme is investigated in order to reduce communication while preserving estimation convergence. A distributed estimation algorithm with a single step size is first proposed based on an event-triggered communication scheme with a time-dependent decaying threshold. With the event-triggered scheme, each sensor sends its estimate to neighbor sensors only when the difference between the current estimate and the last sent-out estimate is larger than the triggering threshold. Different sensors can have different step sizes and triggering thresholds, enabling the parameter estimation process to be conducted in a fully distributed way. We prove that the proposed algorithm has mean-square and almost-sure convergence, respectively, under an integrated condition of sensor network topology and sensor measurement matrices. The condition is satisfied if the topology is a balanced digraph containing a spanning tree and the system is collectively observable. The collective observability is the possibly mildest condition, since it is a spatially and temporally collective condition of all sensors and allows sensor measurement matrices to be time-varying, stochastic, and nonstationary. Moreover, we provide estimates for the convergence rates, which are related to the step size as well as the triggering threshold. Furthermore, as an essential metric of sensor communication intensity in the event-triggered distributed algorithms, the communication rate is proved to decay to zero with a certain speed almost surely as time goes to infinity. In addition, we show that it is feasible to tune the threshold and the step size such that requirements of algorithm convergence and communication rate decay are satisfied simultaneously. We also show that given the step size, adjusting the decay speed of the triggering threshold can lead to a tradeoff between the convergence rate of the estimation error and the decay speed of the communication rate. Specifically, increasing the decay speed of the threshold would make the communication rate decay faster but reduce the convergence rate of the estimation error. Numerical simulations are provided to illustrate the developed results.
      Citation: SIAM Journal on Control and Optimization
      PubDate: 2022-04-19T07:00:00Z
      DOI: 10.1137/21M1405083
      Issue No: Vol. 60, No. 2 (2022)
       
  • Necessary Second-Order Conditions for a Local Infimum in an Optimal
           Control

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      Authors: E. R. Avakov, G. G. Magaril-Il'yaev
      Pages: 1018 - 1038
      Abstract: SIAM Journal on Control and Optimization, Volume 60, Issue 2, Page 1018-1038, April 2022.
      Necessary second-order conditions for a local infimum in an optimal control problem are proved (the concept of a local infimum generalizes that of an optimal trajectory). The results obtained strengthen the Pontryagin maximum principle and the known necessary second-order optimality conditions.
      Citation: SIAM Journal on Control and Optimization
      PubDate: 2022-04-21T07:00:00Z
      DOI: 10.1137/21M1389973
      Issue No: Vol. 60, No. 2 (2022)
       
  • Optimal Ergodic Harvesting under Ambiguity

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      Authors: Asaf Cohen, Alexandru Hening, Chuhao Sun
      Pages: 1039 - 1063
      Abstract: SIAM Journal on Control and Optimization, Volume 60, Issue 2, Page 1039-1063, April 2022.
      We consider an ergodic harvesting problem with model ambiguity that arises from biology. To account for the ambiguity, the problem is constructed as a stochastic game with two players: the decision maker (DM) chooses the “best” harvesting policy, and an adverse player chooses the “worst” probability measure. The main result is establishing an optimal strategy (also referred to as a control) of the DM and showing that it is a threshold policy. The optimal threshold and the optimal payoff are obtained by solving a free-boundary problem emerging from the Hamilton--Jacobi--Bellman (HJB) equation. As part of the proof, we fix a gap that appeared in the HJB analysis of [Alvarez and Hening, Stochastic Process. Appl., 2019, in press], a paper that analyzed the risk-neutral version of the ergodic harvesting problem. Finally, we study the dependence of the optimal threshold and the optimal payoff on the ambiguity parameter and show that if the ambiguity goes to 0, the problem converges to the risk-neutral problem.
      Citation: SIAM Journal on Control and Optimization
      PubDate: 2022-04-21T07:00:00Z
      DOI: 10.1137/21M1413262
      Issue No: Vol. 60, No. 2 (2022)
       
  • An Enhanced Strategy for Adaptive Output-Feedback Control of Uncertain
           Nonlinear Systems

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      Authors: Yuan Wang, Yungang Liu
      Pages: 1064 - 1091
      Abstract: SIAM Journal on Control and Optimization, Volume 60, Issue 2, Page 1064-1091, April 2022.
      We are concerned with global practical tracking for uncertain nonlinear systems with intrinsic dependence on unmeasured states. Typically, we aim to remove the polynomial restrictions on system growth rates in relevant works, admitting the rates to be of arbitrary function-of-output type. Note that such highly nonlinear rates could alter so drastically in magnitude that no polynomial can upper bound them on any unbounded region, and would undermine the design rationale and the analysis route that are followed in polynomial rate scenarios. This entails refining/integrating state-of-the-art techniques and developing new ones, from design to analysis. Concretely, to circumvent the need for knowledge on polynomials, dual dynamic high gains are devised ingeniously which particularly incorporate certain highly nonlinear components to counteract the arbitrary function-of-output rates and other inherent nonlinearities and uncertainties. But unfavorable impacts of the components would also arise putting the effectiveness of the high gains at risk, which necessitates noticeable changes in the choice of vital variables/functions. In addition, to provide tractable observer error dynamics for control design and analysis, a nonlinear high-gain observer is pursued, which is filter based and of reduced order, following the design methodologies in relevant works. In terms of performance analysis, practical tracking suffers extra time variants and additive uncertainties which together with the highly nonlinear rates would carry over to stability analysis inevitably and in turn ruin the existing analysis routes. Hence, a new analysis route is paved to verify the anticipated performance. Notably, by unfolding an important implication, the performance verification boils down largely to the boundedness of the high gains. This makes plain and intelligible the verification, although sophisticated integration of multiple composite Lyapunov functions is still required. An exception, i.e., asymptotic stabilization, is presented to demonstrate its close connection with practical tracking.
      Citation: SIAM Journal on Control and Optimization
      PubDate: 2022-04-25T07:00:00Z
      DOI: 10.1137/20M1389182
      Issue No: Vol. 60, No. 2 (2022)
       
  • The Structure of Optimal Protocols for a Mathematical Model of
           Chemotherapy with Antiangiogenic Effects

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      Authors: Urszula Ledzewicz, Heinz Schättler
      Pages: 1092 - 1116
      Abstract: SIAM Journal on Control and Optimization, Volume 60, Issue 2, Page 1092-1116, April 2022.
      We analyze a mathematical model for cancer chemotherapy which includes antiangiogenic effects of the cytotoxic agent. Assuming that the total amount of agents to be given has been determined a priori based on a medical assessment of its side effects, we consider the problem how to best administer this amount. The model assumes a homogenous tumor and if the aim is to minimize the tumor volume, then optimal controls administer the total dose in a single maximum dose session. As, however, angiogenic effects of the agent are taken into account, this no longer is optimal. Lower dose strategies determined by an optimal singular arc with significantly reduced dose rates give a better response over time. In this paper, for the medically realistic domain of the mathematical model, the concatenation structure of optimal controlled trajectories as segments of bang and singular arcs is determined. This leads to simple numerical minimization procedures for the computation of globally optimal controls.
      Citation: SIAM Journal on Control and Optimization
      PubDate: 2022-04-25T07:00:00Z
      DOI: 10.1137/21M1395326
      Issue No: Vol. 60, No. 2 (2022)
       
  • Global Stabilization of Compressible Flow between Two Moving Pistons

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      Authors: Iasson Karafyllis, Miroslav Krstic
      Pages: 1117 - 1142
      Abstract: SIAM Journal on Control and Optimization, Volume 60, Issue 2, Page 1117-1142, April 2022.
      This paper studies the global feedback stabilization problem of a system with two pistons and the area between them containing a viscous compressible fluid (gas) modeled by the Navier--Stokes equations. The control input is the force applied on the left piston (boundary input) and the overall system consists of two nonlinear partial differential equations and four nonlinear ordinary differential equations. Global feedback stabilizers are designed for the overall system by means of the control Lyapunov functional methodology. The closed-loop system exhibits global asymptotic stability with an exponential convergence rate. The proposed stabilizing boundary feedback laws do not require measurement of the density and velocity profiles inside the area between the pistons and simply require measurements of the gas density and velocity at the position of the actuated piston.
      Citation: SIAM Journal on Control and Optimization
      PubDate: 2022-04-27T07:00:00Z
      DOI: 10.1137/21M1413869
      Issue No: Vol. 60, No. 2 (2022)
       
  • On Singularities of Minimum Time Control-Affine Systems

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      Authors: Jean-Baptiste Caillau, Jacques Féjoz, Michaël Orieux, Robert Roussarie
      Pages: 1143 - 1162
      Abstract: SIAM Journal on Control and Optimization, Volume 60, Issue 2, Page 1143-1162, April 2022.
      Affine control problems arise naturally from controlled mechanical systems. Building on previous results [Agrachev and Biolo, J. Dyn. Control Syst., 23 (2017), pp. 577--595; Caillau and Daoud, SIAM J. Control Optim., 50 (2012), pp. 3178--3202], we prove that, in the case of time minimization with control on the disk, the extremal flow given by Pontrjagin's maximum principle is smooth along the strata of a well-chosen stratification. We also study this flow in terms of regular-singular transition and prove that the singularity along time-minimizing extremals crossing these strata is at most logarithmic. We then apply these results to mechanical systems, paying special attention to the case of the controlled three-body problem.
      Citation: SIAM Journal on Control and Optimization
      PubDate: 2022-04-27T07:00:00Z
      DOI: 10.1137/20M1366861
      Issue No: Vol. 60, No. 2 (2022)
       
  • A Nash-Type Fictitious Game Framework to Time-Inconsistent Stochastic
           Control Problems

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      Authors: Yuan-Hua Ni, Binbin Si, Xinzhen Zhang
      Pages: 1163 - 1189
      Abstract: SIAM Journal on Control and Optimization, Volume 60, Issue 2, Page 1163-1189, April 2022.
      In this paper, a Nash-type fictitious game framework is introduced for handling time-inconsistent linear-quadratic (LQ) optimal control problems. The Nash-type game in this framework is called fictitious as it is between the decision maker (called real player) and an auxiliary control variable (called fictitious player) with the real player and fictitious player looking for time-consistent policy and precommitted optimal policy, respectively. Namely, the fictitious game framework is actually an auxiliary-variable-based mechanism where the fictitious player is our particular design. Noting that the real player's cost functional is revised in accordance with that of the fictitious player, the equilibrium policy of the real player is called an open-loop self-coordination control of the original LQ problem. As a generalization, a time-inconsistent nonzero-sum stochastic linear-quadratic dynamic game is investigated, where one player looks for a precommitted optimal policy and the other player searches for a time-consistent policy. Necessary and sufficient conditions are presented to ensure the existence of open-loop equilibrium of the nonzero-sum game, which resort to a set of Riccati-like equations and linear equations. By applying the developed theory of nonzero-sum game, open-loop self-coordination control of the LQ optimal control is fully characterized, and multiperiod mean-variance portfolio selection is also investigated.
      Citation: SIAM Journal on Control and Optimization
      PubDate: 2022-04-27T07:00:00Z
      DOI: 10.1137/19M1281885
      Issue No: Vol. 60, No. 2 (2022)
       
  • ERRATUM: LP Formulations of Discrete Time Long-Run Average Optimal Control
           Problems: The Nonergodic Case

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      Authors: Vivek S. Borkar, Vladimir Gaitsgory, Ilya Shvartsman
      Pages: 1190 - 1192
      Abstract: SIAM Journal on Control and Optimization, Volume 60, Issue 2, Page 1190-1192, April 2022.
      One of the proofs in our paper [SIAM J. Control Optim., 57 (2019), pp. 1783--1817] contains an error. This erratum addresses the issue.
      Citation: SIAM Journal on Control and Optimization
      PubDate: 2022-04-28T07:00:00Z
      DOI: 10.1137/21M1466359
      Issue No: Vol. 60, No. 2 (2022)
       
  • Revisiting SIR in the Age of COVID-19: Explicit Solutions and Control
           Problems

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      Authors: Vivek S. Borkar, D. Manjunath
      Abstract: SIAM Journal on Control and Optimization, Ahead of Print.
      The nonpopulation conserving SIR (SIR-NC) model to describe the spread of infections in a community is studied. Unlike the standard SIR model, this does not assume population conservation. Although similar in form to the standard SIR, SIR-NC admits a closed form solution while allowing us to model mortality and also provides a different, and arguably a more realistic, interpretation of model parameters. Numerical comparisons of this SIR-NC model with the standard, population conserving, SIR model are provided. Extensions to include imported infections, interacting communities, and models that include births and deaths are presented and analyzed. Several numerical examples are also presented to illustrate these models. A discrete time control problem for the SIR-NC epidemic model is presented in which the cost function depends on variables that correspond to the levels of lockdown, the level of testing and quarantine, and the number of infections. We include a switching cost for moving between lockdown levels. Numerical experiments are presented.
      Citation: SIAM Journal on Control and Optimization
      PubDate: 2022-04-11T07:00:00Z
      DOI: 10.1137/20M1372913
       
  • Optimal Incentives to Mitigate Epidemics: A Stackelberg Mean Field Game
           Approach

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      Authors: Alexander Aurell, René Carmona, Gökçe Dayanikli, Mathieu Laurière
      Abstract: SIAM Journal on Control and Optimization, Ahead of Print.
      Motivated by the models of epidemic control in large populations, we consider a Stackelberg mean field game model between a principal and a mean field of agents whose states evolve in a finite state space. The agents play a noncooperative game in which they control their rates of transition between states to minimize an individual cost. The principal influences the nature of the resulting Nash equilibrium through incentives to optimize its own objective. We analyze this game using a probabilistic approach. We then propose an application to an epidemic model of SIR type in which the agents control the intensities of their interactions, and the principal is a regulator acting with nonpharmaceutical interventions. To compute the solutions, we propose an innovative numerical approach based on Monte Carlo simulations and machine learning tools for stochastic optimization. We conclude with numerical experiments illustrating the impact of the agents' and the regulator's optimal decisions in two specific models: a basic SIR model with semiexplicit solutions and a more complex model with a larger state space.
      Citation: SIAM Journal on Control and Optimization
      PubDate: 2022-04-07T07:00:00Z
      DOI: 10.1137/20M1377862
       
  • Convergence and Equilibria Analysis of a Networked Bivirus Epidemic Model

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      Authors: Mengbin Ye, Brian D. O. Anderson, Ji Liu
      Abstract: SIAM Journal on Control and Optimization, Ahead of Print.
      This paper studies a networked bivirus model, in which two competing viruses spread across a network of interconnected populations; each node represents a population with a large number of individuals. The viruses may spread through possibly different network structures, and an individual cannot be simultaneously infected with both viruses. Focusing on convergence and equilibria analysis, a number of new results are provided. First, we show that for networks with generic system parameters, there exist a finite number of equilibria. Exploiting monotone systems theory, we further prove that for bivirus networks with generic system parameters, convergence to an equilibrium occurs for all initial conditions, except possibly for a set of measure zero. Given the network structure of one virus, a method is presented to construct an infinite family of network structures for the other virus that results in an infinite number of equilibria in which both viruses coexist. Necessary and sufficient conditions are derived for the local stability/instability of boundary equilibria, in which one virus is present and the other is extinct. A sufficient condition for a boundary equilibrium to be almost globally stable is presented. Then, we show how to use monotone systems theory to generate conclusions on the ordering of stable and unstable equilibria, and in some instances identify the number of equilibria via rapid simulation testing. Last, we provide an analytical method for computing equilibria in networks with only two nodes, and show that it is possible for a bivirus network to have an unstable coexistence equilibrium and two locally stable boundary equilibria.
      Citation: SIAM Journal on Control and Optimization
      PubDate: 2022-04-07T07:00:00Z
      DOI: 10.1137/20M1369014
       
  • A Finite Memory Interacting Pólya Contagion Network and Its
           Approximating Dynamical Systems

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      Authors: Somya Singh, Fady Alajaji, Bahman Gharesifard
      Abstract: SIAM Journal on Control and Optimization, Ahead of Print.
      We introduce a new model for contagion spread using a network of interacting finite memory two-color Pólya urns, which we refer to as the finite memory interacting Pólya contagion network. The urns interact in the sense that the probability of drawing a red ball (which represents an infection state) for a given urn, not only depends on the ratio of red balls in that urn but also on the ratio of red balls in the other urns in the network, hence accounting for the effect of spatial contagion. The resulting networkwide contagion process is a discrete-time finite-memory ($M$th order) Markov process, whose transition probability matrix is determined. The stochastic properties of the network contagion Markov process are analytically examined, and for homogeneous system parameters, we characterize the limiting state of infection in each urn. For the nonhomogeneous case, given the complexity of the stochastic process, and in the same spirit as the well-studied SIS models, we use a mean-field type approximation to obtain a discrete-time dynamical system for the finite memory interacting Pólya contagion network. Interestingly, for $M=1$, we obtain a linear dynamical system which exactly represents the corresponding Markov process. For $M>1$, we use mean-field approximation to obtain a nonlinear dynamical system. Furthermore, noting that the latter dynamical system admits a linear variant (realized by retaining its leading linear terms), we study the asymptotic behavior of the linear systems for both memory modes and characterize their equilibrium. Finally, we present simulation studies to assess the quality of the approximation purveyed by the linear and nonlinear dynamical systems.
      Citation: SIAM Journal on Control and Optimization
      PubDate: 2022-04-07T07:00:00Z
      DOI: 10.1137/20M1370525
       
  • Adaptive Test Allocation for Outbreak Detection and Tracking in Social
           Contact Networks

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      Authors: Pau Batlle, Joan Bruna, Carlos Fernandez-Granda, Victor M. Preciado
      Abstract: SIAM Journal on Control and Optimization, Ahead of Print.
      We present a general framework for adaptive allocation of viral tests in social contact networks and arbitrary epidemic models. We pose and solve several complementary problems. First, we consider the design of a social sensing system whose objective is the early detection of a novel epidemic outbreak. In particular, we propose an algorithm to select a subset of individuals to be tested in order to detect the onset of an epidemic outbreak as fast as possible. We pose this problem as a hitting time probability maximization problem and use submodularity optimization and Monte Carlo techniques to obtain solutions with explicit quality guarantees. Second, once an epidemic outbreak has been detected, we consider the problem of using the data from the sensing system to obtain estimates of the initial patient and the current status of the epidemic. Finally, we consider the problem of adaptively distributing viral tests over time in order to maximize the information gained about the current state of the epidemic. We formalize this problem in terms of mutual information and propose an adaptive allocation strategy with quality guarantees. For these problems, we derive analytical solutions for any stochastic compartmental epidemic model with Markovian dynamics, as well as efficient Monte Carlo--based algorithms for non-Markovian dynamics or large networks. We illustrate the performance of the proposed framework in numerical experiments involving a model of COVID-19 applied to a real human contact network.
      Citation: SIAM Journal on Control and Optimization
      PubDate: 2022-04-04T07:00:00Z
      DOI: 10.1137/20M1377874
       
  • Edge Deletion Algorithms for Minimizing Spread in SIR Epidemic Models

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      Authors: Yuhao Yi, Liren Shan, Philip E. Paré, Karl Henrik Johansson
      Abstract: SIAM Journal on Control and Optimization, Ahead of Print.
      This paper studies algorithmic strategies to effectively reduce the number of infections in susceptible-infected-recovered (SIR) epidemic models. We consider a Markov chain SIR model and its two instantiations in the deterministic SIR (D-SIR) model and the independent cascade SIR (IC-SIR) model. We investigate the problem of minimizing the number of infections by restricting contacts under realistic constraints. Under moderate assumptions on the reproduction number, we prove that the infection numbers are bounded by supermodular functions in the D-SIR model and the IC-SIR model for large classes of random networks. We propose efficient algorithms with approximation guarantees to minimize infections. The theoretical results are illustrated by numerical simulations.
      Citation: SIAM Journal on Control and Optimization
      PubDate: 2022-03-31T07:00:00Z
      DOI: 10.1137/20M1377011
       
  • A Distributed Optimal Control Model Applied to COVID-19 Pandemic

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      Authors: Raimund M. Kovacevic, Nikolaos I. Stilianakis, Vladimir M. Veliov
      Abstract: SIAM Journal on Control and Optimization, Ahead of Print.
      In this paper, a distributed optimal control epidemiological model is presented. The model describes the dynamics of an epidemic with social distancing as a control policy. The model belongs to the class of continuous-time models, usually involving ordinary/partial differential equations, but has a novel feature. The core model---a single integral equation---does not explicitly use transition rates between compartments. Instead, it is based on statistical information on the disease status of infected individuals, depending on the time since infection. The approach is especially relevant for the coronavirus disease 2019 (COVID-19) in which infected individuals are infectious before onset of symptoms during a relatively long incubation period. Based on the analysis of the proposed optimal control problem, including necessary optimality conditions, this paper outlines some efficient numerical approaches. Numerical solutions show some interesting features of the optimal policy for social distancing, depending on the weights attributed to the number of isolated individuals with symptoms and to economic losses due to the enforcement of the control policy. The general nature of the model allows for inclusion of additional epidemic features with minor adaptations in the basic equations. Therefore, the modeling approach may contribute to the analysis of combined intervention strategies and to the guidance of public health decisions.
      Citation: SIAM Journal on Control and Optimization
      PubDate: 2022-03-24T07:00:00Z
      DOI: 10.1137/20M1373840
       
  • Respect the Unstable: Delays and Saturation in Contact Tracing for Disease
           Control

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      Authors: Richard Pates, Andres Ferragut, Elijah Pivo, Pengcheng You, Fernando Paganini, Enrique Mallada
      Abstract: SIAM Journal on Control and Optimization, Ahead of Print.
      Motivated by the novel coronavirus disease (COVID-19) pandemic, this paper aims to apply Gunter Stein's cautionary message of respecting the unstable to the problem of controlling the spread of an infectious disease. With this goal, we study the effect that delays and capacity constraints have in the test, trace, and isolate (TeTrIs) process, and how they impact its ability to prevent exponential disease spread. Our analysis highlights the critical importance of speed and scale in the TeTrIs process. Precisely, ensuring that the delay in the TeTrIs process is much smaller than the doubling time of the disease spread is necessary for achieving acceptable performance. Similarly, limited TeTrIs capacity introduces a threshold on the size of an outbreak beyond which the disease spreads almost like the uncontrolled case. Along the way, we provide numerical illustrations to highlight these points.
      Citation: SIAM Journal on Control and Optimization
      PubDate: 2022-03-09T08:00:00Z
      DOI: 10.1137/20M1377825
       
  • Initialization and Curing Policies for Pólya Contagion Networks

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      Authors: Greg Harrington, Fady Alajaji, Bahman Gharesifard
      Abstract: SIAM Journal on Control and Optimization, Ahead of Print.
      We investigate optimization policies for resource distribution in network epidemics using a model that derives from the classical Pólya process. This model, called the Pólya network contagion process, is based on a modified urn sampling scheme that accounts for both temporal and spatial contagion between neighboring nodes in a network. We study two infection mitigation problems---one which takes place upon initialization and one which occurs continually as the Pólya network process develops. We frame these problems as resource allocation problems with fixed budgets and analyze a suite of potential policies. Due to the complexity of these problems, we introduce effective proxy measures for the average infection rate in each case. We also prove that the two-sided infection-curing game on the so-called expected network exposure admits a Nash equilibrium. In both the curing and initialization scenarios, we introduce heuristic policies that primarily function on the basis of limiting the number of targeted nodes within a particular network setup. Simulations are run for mid-to-large--scale networks to compare performance of our heuristics to provably convergent gradient descent algorithms run on the simplified proxy measures.
      Citation: SIAM Journal on Control and Optimization
      PubDate: 2022-01-24T08:00:00Z
      DOI: 10.1137/20M1358803
       
  • How Much Testing and Social Distancing is Required to Control
           COVID-19' Some Insight Based on an Age-Differentiated Compartmental
           Model

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      Authors: Sara Grundel, Stefan Heyder, Thomas Hotz, Tobias K. S. Ritschel, Philipp Sauerteig, Karl Worthmann
      Abstract: SIAM Journal on Control and Optimization, Ahead of Print.
      In this paper, we provide insights on how much testing and social distancing is required to control COVID-19. To this end, we develop a compartmental model that accounts for key aspects of the disease: incubation time, age-dependent symptom severity, and testing and hospitalization delays; the model's parameters are chosen based on medical evidence, and, for concreteness, adapted to the German situation. Then, optimal mass-testing and age-dependent social distancing policies are determined by solving optimal control problems both in open loop and within a model predictive control framework. We aim to minimize testing and/or social distancing until herd immunity sets in under a constraint on the number of available intensive care units. We find that an early and short lockdown is inevitable but can be slowly relaxed over the following months.
      Citation: SIAM Journal on Control and Optimization
      PubDate: 2022-01-13T08:00:00Z
      DOI: 10.1137/20M1377783
       
  • The Role of Asymptomatic Infections in the COVID-19 Epidemic via Complex
           Networks and Stability Analysis

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      Authors: Leonardo Stella, Alejandro Pinel Martínez, Dario Bauso, Patrizio Colaneri
      Abstract: SIAM Journal on Control and Optimization, Ahead of Print.
      Italy was the first country to be affected by the COVID-19 epidemic in Europe. In the past months, predictive mathematical models have been used to understand the proportion of this epidemic and identify effective policies to control it, but few have considered the impact of asymptomatic or paucisymptomatic infections in a structured setting. A critical problem that hinders the accuracy of these models is indeed given by the presence of a large number of asymptomatic individuals in the population. This number is estimated to be large, sometimes between 3 and 10 times the diagnosed patients. We focus on this aspect through the formulation of a model that captures two types of interactions---one with asymptomatic individuals and another with symptomatic infected. We also extend the original model to capture the interactions in the population via complex networks, and, in particular, the Watts--Strogatz model, which is the most suitable for social networks. The contributions of this paper include (i) the formulation of an epidemic model, which we call SAIR, that discriminates between asymptomatic and symptomatic infected through different measures of interactions and the corresponding stability analysis of the system in feedback form through the calculation of the $\mathcal R_0$ as $H_\infty$ gain; (ii) the analysis of the corresponding structured model involving the Watts and Strogatz interaction topology, to study the case of heterogeneous connectivity in the population; (iii) a case study on the Italian case, where we take into account the Istat seroprevalence study in the homogeneous case first, and then we analyze the impact of summer tourism and of the start of school in September in the heterogeneous case.
      Citation: SIAM Journal on Control and Optimization
      PubDate: 2022-01-11T08:00:00Z
      DOI: 10.1137/20M1373335
       
 
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