Subjects -> MATHEMATICS (Total: 1013 journals)
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MATHEMATICS (714 journals)            First | 1 2 3 4     

Showing 601 - 538 of 538 Journals sorted alphabetically
Results in Control and Optimization     Open Access  
Results in Mathematics     Hybrid Journal  
Results in Nonlinear Analysis     Open Access  
Review of Symbolic Logic     Full-text available via subscription   (Followers: 2)
Reviews in Mathematical Physics     Hybrid Journal   (Followers: 1)
Revista Baiana de Educação Matemática     Open Access  
Revista Bases de la Ciencia     Open Access  
Revista BoEM - Boletim online de Educação Matemática     Open Access  
Revista Colombiana de Matemáticas     Open Access   (Followers: 1)
Revista de Ciencias     Open Access  
Revista de Educación Matemática     Open Access  
Revista de la Escuela de Perfeccionamiento en Investigación Operativa     Open Access  
Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales. Serie A. Matematicas     Partially Free  
Revista de Matemática : Teoría y Aplicaciones     Open Access   (Followers: 1)
Revista Digital: Matemática, Educación e Internet     Open Access  
Revista Electrónica de Conocimientos, Saberes y Prácticas     Open Access  
Revista Integración : Temas de Matemáticas     Open Access  
Revista Internacional de Sistemas     Open Access  
Revista Latinoamericana de Etnomatemática     Open Access  
Revista Latinoamericana de Investigación en Matemática Educativa     Open Access  
Revista Matemática Complutense     Hybrid Journal  
Revista REAMEC : Rede Amazônica de Educação em Ciências e Matemática     Open Access  
Revista SIGMA     Open Access  
Ricerche di Matematica     Hybrid Journal  
RMS : Research in Mathematics & Statistics     Open Access  
Royal Society Open Science     Open Access   (Followers: 7)
Russian Journal of Mathematical Physics     Full-text available via subscription  
Russian Mathematics     Hybrid Journal  
Sahand Communications in Mathematical Analysis     Open Access  
Sampling Theory, Signal Processing, and Data Analysis     Hybrid Journal  
São Paulo Journal of Mathematical Sciences     Hybrid Journal  
Science China Mathematics     Hybrid Journal   (Followers: 1)
Science Progress     Full-text available via subscription   (Followers: 1)
Sciences & Technologie A : sciences exactes     Open Access  
Selecta Mathematica     Hybrid Journal   (Followers: 1)
SeMA Journal     Hybrid Journal  
Semigroup Forum     Hybrid Journal   (Followers: 1)
Set-Valued and Variational Analysis     Hybrid Journal  
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 Mathematics of Data Science     Hybrid Journal   (Followers: 1)
SIAM Journal on Matrix Analysis and Applications     Hybrid Journal   (Followers: 3)
SIAM Journal on Optimization     Hybrid Journal   (Followers: 12)
Siberian Advances in Mathematics     Hybrid Journal  
Siberian Mathematical Journal     Hybrid Journal  
Sigmae     Open Access  
SILICON     Hybrid Journal  
SN Partial Differential Equations and Applications     Hybrid Journal  
Soft Computing     Hybrid Journal   (Followers: 7)
Statistics and Computing     Hybrid Journal   (Followers: 14)
Stochastic Analysis and Applications     Hybrid Journal   (Followers: 3)
Stochastic Partial Differential Equations : Analysis and Computations     Hybrid Journal   (Followers: 2)
Stochastic Processes and their Applications     Hybrid Journal   (Followers: 6)
Stochastics and Dynamics     Hybrid Journal   (Followers: 2)
Studia Scientiarum Mathematicarum Hungarica     Full-text available via subscription   (Followers: 1)
Studia Universitatis Babeș-Bolyai Informatica     Open Access  
Studies In Applied Mathematics     Hybrid Journal   (Followers: 1)
Studies in Mathematical Sciences     Open Access   (Followers: 1)
Superficies y vacio     Open Access  
Suska Journal of Mathematics Education     Open Access   (Followers: 1)
Swiss Journal of Geosciences     Hybrid Journal   (Followers: 1)
Synthesis Lectures on Algorithms and Software in Engineering     Full-text available via subscription   (Followers: 2)
Synthesis Lectures on Mathematics and Statistics     Full-text available via subscription   (Followers: 1)
Tamkang Journal of Mathematics     Open Access  
Tatra Mountains Mathematical Publications     Open Access  
Teaching Mathematics     Full-text available via subscription   (Followers: 10)
Teaching Mathematics and its Applications: An International Journal of the IMA     Hybrid Journal   (Followers: 4)
Teaching Statistics     Hybrid Journal   (Followers: 8)
Technometrics     Full-text available via subscription   (Followers: 8)
The Journal of Supercomputing     Hybrid Journal   (Followers: 1)
The Mathematica journal     Open Access  
The Mathematical Gazette     Full-text available via subscription   (Followers: 1)
The Mathematical Intelligencer     Hybrid Journal  
The Ramanujan Journal     Hybrid Journal  
The VLDB Journal     Hybrid Journal   (Followers: 2)
Theoretical and Mathematical Physics     Hybrid Journal   (Followers: 7)
Theory and Applications of Graphs     Open Access  
Topological Methods in Nonlinear Analysis     Full-text available via subscription  
Transactions of the London Mathematical Society     Open Access   (Followers: 1)
Transformation Groups     Hybrid Journal  
Turkish Journal of Mathematics     Open Access  
Ukrainian Mathematical Journal     Hybrid Journal  
Uniciencia     Open Access  
Uniform Distribution Theory     Open Access  
Unisda Journal of Mathematics and Computer Science     Open Access  
Unnes Journal of Mathematics     Open Access   (Followers: 1)
Unnes Journal of Mathematics Education     Open Access   (Followers: 2)
Unnes Journal of Mathematics Education Research     Open Access   (Followers: 1)
Ural Mathematical Journal     Open Access  
Vestnik Samarskogo Gosudarstvennogo Tekhnicheskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki     Open Access  
Vestnik St. Petersburg University: Mathematics     Hybrid Journal  
VFAST Transactions on Mathematics     Open Access   (Followers: 1)
Vietnam Journal of Mathematics     Hybrid Journal  
Vinculum     Full-text available via subscription  
Visnyk of V. N. Karazin Kharkiv National University. Ser. Mathematics, Applied Mathematics and Mechanics     Open Access   (Followers: 2)
Water SA     Open Access   (Followers: 1)
Water Waves     Hybrid Journal  
Zamm-Zeitschrift Fuer Angewandte Mathematik Und Mechanik     Hybrid Journal   (Followers: 1)
ZDM     Hybrid Journal   (Followers: 2)
Zeitschrift für angewandte Mathematik und Physik     Hybrid Journal   (Followers: 2)
Zeitschrift fur Energiewirtschaft     Hybrid Journal  
Zetetike     Open Access  

  First | 1 2 3 4     

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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]
  • Local Minimum Principle for an Optimal Control Problem with a Nonregular
           Mixed Constraint

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      Authors: Andrei Dmitruk, Nikolai Osmolovskii
      Pages: 1919 - 1941
      Abstract: SIAM Journal on Control and Optimization, Volume 60, Issue 4, Page 1919-1941, August 2022.
      We consider the simplest optimal control problem with one nonregular mixed constraint $G(x,u)\le0,$ i.e., such a constraint that the gradient $G_u(x, u)$ can vanish on the surface $G = 0.$ Using the Dubovitskii--Milyutin theorem on the approximate separation of convex cones, we prove a first order necessary condition for a weak minimum in the form of the so-called local minimum principle, which is formulated in terms of functions of bounded variation, integrable functions, and Lebesgue--Stieltjes measures and does not use functionals from $(L^\infty)^*$. Two illustrative examples are provided. The work is based on the book by Milyutin [Maximum Principle in the General Problem of Optimal Control, Fizmatlit, Moscow, 2001 (in Russian)].
      Citation: SIAM Journal on Control and Optimization
      PubDate: 2022-07-05T07:00:00Z
      DOI: 10.1137/21M1411469
      Issue No: Vol. 60, No. 4 (2022)
       
  • Multipopulation Minimal-Time Mean Field Games

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      Authors: Saeed Sadeghi Arjmand, Guilherme Mazanti
      Pages: 1942 - 1969
      Abstract: SIAM Journal on Control and Optimization, Volume 60, Issue 4, Page 1942-1969, August 2022.
      In this paper, we consider a mean field game model inspired by crowd motion in which several interacting populations evolving in $\mathbbm R^d$ aim at reaching given target sets in minimal time. The movement of each agent is described by a control system depending in their position, the distribution of other agents in the same population, and the distribution of agents on other populations. Thus, interactions between agents occur through their dynamics. In this paper we consider the existence of Lagrangian equilibria to this mean field game, their asymptotic behavior, and their characterization as solutions of a mean field game system, under few regularity assumptions on agents' dynamics. In particular, the mean field game system is established without relying on semiconcavity properties of the value function.
      Citation: SIAM Journal on Control and Optimization
      PubDate: 2022-07-05T07:00:00Z
      DOI: 10.1137/21M1407306
      Issue No: Vol. 60, No. 4 (2022)
       
  • Running Primal-Dual Gradient Method for Time-Varying Nonconvex Problems

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      Authors: Yujie Tang, Emiliano Dall'Anese, Andrey Bernstein, Steven Low
      Pages: 1970 - 1990
      Abstract: SIAM Journal on Control and Optimization, Volume 60, Issue 4, Page 1970-1990, August 2022.
      This paper focuses on a time-varying constrained nonconvex optimization problem, and considers the synthesis and analysis of online regularized primal-dual gradient methods to track a Karush--Kuhn--Tucker (KKT) trajectory. The proposed regularized primal-dual gradient method is implemented in a running fashion, in the sense that the underlying optimization problem changes during the execution of the algorithms. In order to study its performance, we first derive its continuous-time limit as a system of differential inclusions. We then study sufficient conditions for tracking a KKT trajectory, and also derive asymptotic bounds for the tracking error (as a function of the time-variability of a KKT trajectory). Further, we provide a set of sufficient conditions for the KKT trajectories not to bifurcate or merge, and also investigate the optimal choice of the parameters of the algorithm. Illustrative numerical results for a time-varying nonconvex problem are provided.
      Citation: SIAM Journal on Control and Optimization
      PubDate: 2022-07-07T07:00:00Z
      DOI: 10.1137/20M1371063
      Issue No: Vol. 60, No. 4 (2022)
       
  • A Q-Learning Algorithm for Discrete-Time Linear-Quadratic Control with
           Random Parameters of Unknown Distribution: Convergence and Stabilization

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      Authors: Kai Du, Qingxin Meng, Fu Zhang
      Pages: 1991 - 2015
      Abstract: SIAM Journal on Control and Optimization, Volume 60, Issue 4, Page 1991-2015, August 2022.
      This paper studies an infinite horizon optimal control problem for discrete-time linear systems and quadratic criteria, both with random parameters which are independent and identically distributed with respect to time. A classical approach is to solve an algebraic Riccati equation that involves mathematical expectations and requires certain statistical information of the parameters. In this paper, we propose an iterative algorithm in the spirit of Q-learning for the situation where only one random sample of parameters emerges at each time step. The first theorem proves the equivalence of three properties: the convergence of the learning sequence, the well-posedness of the control problem, and the solvability of the algebraic Riccati equation. The second theorem shows that the adaptive feedback control in terms of the learning sequence stabilizes the system as long as the control problem is well-posed. Numerical examples are presented to illustrate our results.
      Citation: SIAM Journal on Control and Optimization
      PubDate: 2022-07-07T07:00:00Z
      DOI: 10.1137/20M1379605
      Issue No: Vol. 60, No. 4 (2022)
       
  • The Most Likely Evolution of Diffusing and Vanishing Particles:
           Schrödinger Bridges with Unbalanced Marginals

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      Authors: Yongxin Chen, Tryphon T. Georgiou, Michele Pavon
      Pages: 2016 - 2039
      Abstract: SIAM Journal on Control and Optimization, Volume 60, Issue 4, Page 2016-2039, August 2022.
      Stochastic flows of an advective-diffusive nature are ubiquitous in biology and the physical sciences. Of particular interest is the problem of reconciling observed marginal distributions with a given prior posed by Schrödinger in 1932 and known as the Schrödinger Bridge Problem (SBP). It turns out that Schrödinger's problem can be viewed as both a modeling problem and a control problem. Due to their fundamental significance, the SBP and its deterministic (zero-noise limit) counterpart of Optimal Mass Transport (OMT) have recently received interest within a broad spectrum of disciplines, including physics, stochastic control, computer science, probability theory, and geometry. Yet, while the mathematics and applications of the SBP/OMT have been developing at a considerable pace, accounting for marginals of unequal mass has received scant attention; the problem of interpolating between “unbalanced” marginals has been approached by introducing source/sink terms into the transport equations, in an ad hoc manner, chiefly driven by applications in image registration. Nevertheless, losses are inherent in many physical processes, and thereby models that account for lossy transport may also need to be reconciled with observed marginals following Schrödinger's dictum; that is, it is necessary to adjust the probability of trajectories of particles, including those that do not make it to the terminal observation point, so that the updated law represents the most likely way that particles may have been transported, or have vanished, at some intermediate point. Thus, the purpose of this work is to develop such a natural generalization of the SBP for stochastic evolution with losses, whereupon particles are “killed” (jump into a coffin/extinction state) according to a probabilistic law, and thereby mass is gradually lost along their stochastically driven flow. Through a suitable embedding we turn the problem into an SBP for stochastic processes that combine diffusive and jump characteristics. Then, following a large-deviations formalism in the style of Schrödinger, given a prior law that allows for losses, we ask for the most probable evolution of particles along with the most likely killing rate as the particles transition between the specified marginals. Our approach differs sharply from previous work involving a Feynman--Kac multiplicative reweighing of the reference measure: The latter, as we argue, is far from Schrödinger's quest. An iterative scheme, generalizing the celebrated Fortet-IPF-Sinkhorn algorithm, permits us to compute the new drift and the new killing rate of the path-space solution measure. We finally formulate and solve a related fluid-dynamic control problem for the flow of one-time marginals where both the drift and the new killing rate play the role of control variables.
      Citation: SIAM Journal on Control and Optimization
      PubDate: 2022-07-11T07:00:00Z
      DOI: 10.1137/21M1447672
      Issue No: Vol. 60, No. 4 (2022)
       
  • Characterizations of Complete Stabilizability

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      Authors: Hanbing Liu, Gengsheng Wang, Yashan Xu, Huaiqiang Yu
      Pages: 2040 - 2069
      Abstract: SIAM Journal on Control and Optimization, Volume 60, Issue 4, Page 2040-2069, August 2022.
      We present several characterizations, via some weak observability inequalities, on the complete stabilizability for a control system $[A,B]$, i.e., $y'(t)=Ay(t)+Bu(t)$, $t\geq 0$, where $A$ generates a $C_0$-semigroup on a Hilbert space $X$ and $B$ is a linear and bounded operator from another Hilbert space $U$ to $X$. We then extend the aforementioned characterizations in two directions: first, the control operator $B$ is unbounded; second, the control system is time periodic. We also give some sufficient conditions, from the perspective of the spectral projections, to ensure the weak observability inequalities. As applications, we provide several examples, which are not null controllable, but can be verified, via the weak observability inequalities, to be completely stabilizable.
      Citation: SIAM Journal on Control and Optimization
      PubDate: 2022-07-11T07:00:00Z
      DOI: 10.1137/20M1386761
      Issue No: Vol. 60, No. 4 (2022)
       
  • Infinite Horizon Optimal Control Problems for a Class of Semilinear
           Parabolic Equations

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      Authors: Eduardo Casas, Karl Kunisch
      Pages: 2070 - 2094
      Abstract: SIAM Journal on Control and Optimization, Volume 60, Issue 4, Page 2070-2094, August 2022.
      Infinite horizon open loop optimal control problems for semilinear parabolic equations are investigated. The controls are subject to a cost functional which promotes sparsity in time. The focus is put on deriving first order optimality conditions. This is achieved without relying on a well-defined control-to-state mapping in a neighborhood of minimizers. The technique of proof is based on the approximation of the original problem by a family of finite horizon problems. The optimality conditions allow deduction of sparsity properties of the optimal controls in time.
      Citation: SIAM Journal on Control and Optimization
      PubDate: 2022-07-13T07:00:00Z
      DOI: 10.1137/21M1464816
      Issue No: Vol. 60, No. 4 (2022)
       
  • Fictitious Play in Zero-Sum Stochastic Games

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      Authors: Muhammed O. Sayin, Francesca Parise, Asuman Ozdaglar
      Pages: 2095 - 2114
      Abstract: SIAM Journal on Control and Optimization, Volume 60, Issue 4, Page 2095-2114, August 2022.
      We present a novel variant of fictitious play dynamics combining classical fictitious play with $Q$-learning for stochastic games and analyze its convergence properties in two-player zero-sum stochastic games. Our dynamics involves players forming beliefs on the opponent strategy and their own continuation payoff ($Q$-function), and playing a greedy best response by using the estimated continuation payoffs. Players update their beliefs from observations of opponent actions. A key property of the learning dynamics is that update of the beliefs on $Q$-functions occurs at a slower timescale than update of the beliefs on strategies. We show that in both the model-based and model-free cases (without knowledge of player payoff functions and state transition probabilities), the beliefs on strategies converge to a stationary mixed Nash equilibrium of the zero-sum stochastic game.
      Citation: SIAM Journal on Control and Optimization
      PubDate: 2022-07-13T07:00:00Z
      DOI: 10.1137/21M1426675
      Issue No: Vol. 60, No. 4 (2022)
       
  • On an Approximation of Average Cost per Unit Time Impulse Control of
           Markov Processes

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      Authors: Lukasz Stettner
      Pages: 2115 - 2131
      Abstract: SIAM Journal on Control and Optimization, Volume 60, Issue 4, Page 2115-2131, August 2022.
      In this paper we consider impulse control of continuous time Markov processes with average cost per unit time functional. This problem is approximated using impulse control problems stopped at the first exit time from an increasing sequence of open sets. We find a solution to the Bellman equation corresponding to the original problem and show that stopped impulse control problems approximate optimal value of the cost functional.
      Citation: SIAM Journal on Control and Optimization
      PubDate: 2022-07-13T07:00:00Z
      DOI: 10.1137/21M1434143
      Issue No: Vol. 60, No. 4 (2022)
       
  • Optimal Control of Port-Hamiltonian Descriptor Systems with Minimal Energy
           Supply

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      Authors: Timm Faulwasser, Bernhard Maschke, Friedrich Philipp, Manuel Schaller, Karl Worthmann
      Pages: 2132 - 2158
      Abstract: SIAM Journal on Control and Optimization, Volume 60, Issue 4, Page 2132-2158, August 2022.
      We consider the singular optimal control problem of minimizing the energy supply of linear dissipative port-Hamiltonian descriptor systems. We study the reachability properties of the system and prove that optimal states exhibit a turnpike behavior with respect to the conservative subspace. Further, we derive a input-state turnpike toward a subspace for optimal control of port-Hamiltonian ordinary differential equations with a feed-through term and a turnpike property for the corresponding adjoint states toward zero. In an appendix we characterize the class of dissipative Hamiltonian matrices and pencils.
      Citation: SIAM Journal on Control and Optimization
      PubDate: 2022-07-26T07:00:00Z
      DOI: 10.1137/21M1427723
      Issue No: Vol. 60, No. 4 (2022)
       
  • Analysis of the Implicit Euler Time-Discretization of Semiexplicit
           Differential-Algebraic Linear Complementarity Systems

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      Authors: Bernard Brogliato
      Pages: 2159 - 2183
      Abstract: SIAM Journal on Control and Optimization, Volume 60, Issue 4, Page 2159-2183, August 2022.
      This article is largely concerned with the time-discretization of differential-algebraic equations (DAEs) with complementarity constraints, which we name differential-algebraic linear complementarity systems (DALCSs). Specifically, the Euler implicit discretization of DALCSs is analyzed: the one-step nonsmooth problem, which is a generalized equation, is shown to be well-posed under some conditions; then the convergence of the discretized solutions is studied, and the existence of solutions to the continuous-time system is shown as a consequence. Passivity of some operators is pivotal to the analysis. Examples from circuits, mechanics, and switching DAEs illustrate the applicability of the developments.
      Citation: SIAM Journal on Control and Optimization
      PubDate: 2022-07-26T07:00:00Z
      DOI: 10.1137/21M1396101
      Issue No: Vol. 60, No. 4 (2022)
       
  • Robust Mean Field Linear Quadratic Social Control: Open-Loop and
           Closed-Loop Strategies

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      Authors: Yong Liang, Bing-Chang Wang, Huanshui Zhang
      Pages: 2184 - 2213
      Abstract: SIAM Journal on Control and Optimization, Volume 60, Issue 4, Page 2184-2213, August 2022.
      This paper investigates the robust social optimum problem for linear quadratic mean field control systems by the direct approach, where model uncertainty appears in both drift and diffusion terms of each agent. We take a zero-sum game approach by considering local disturbance as the control of an adversarial player. Under centralized information structure, we first obtain the necessary and sufficient condition for the existence of open-loop and closed-loop saddle points, which are characterized by the solvability of forward-backward stochastic differential equations (FBSDEs) and two coupled Riccati equations, respectively. By considering the infinite system, we next design a set of decentralized open-loop strategies based on mean field FBSDEs and obtain closed-loop strategies in terms of two uncoupled Riccati equations. Finally, the performance of the proposed decentralized strategies is analyzed and the efficiency is verified by numerical simulation.
      Citation: SIAM Journal on Control and Optimization
      PubDate: 2022-07-28T07:00:00Z
      DOI: 10.1137/21M1414140
      Issue No: Vol. 60, No. 4 (2022)
       
  • Stabilization by Adaptive Feedback Control for Positive Difference
           Equations with Applications in Pest Management

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      Authors: C. J. Edholm, C. Guiver, R. Rebarber, B. Tenhumberg, S. Townley
      Pages: 2214 - 2245
      Abstract: SIAM Journal on Control and Optimization, Volume 60, Issue 4, Page 2214-2245, August 2022.
      An adaptive feedback control scheme is proposed for stabilizing a class of forced nonlinear positive difference equations. The adaptive scheme is based on so-called high-gain adaptive controllers and contains substantial robustness with respect to model uncertainty as well as with respect to persistent forcing signals, including measurement errors. Our results take advantage of the underlying positive systems structure and ideas from input-to-state stability from nonlinear control theory. Our motivating application is to pest or weed control, and in this context the present work substantially strengthens previous work by the authors. The theory is illustrated with examples.
      Citation: SIAM Journal on Control and Optimization
      PubDate: 2022-07-28T07:00:00Z
      DOI: 10.1137/21M1398240
      Issue No: Vol. 60, No. 4 (2022)
       
  • The Barabanov Norm is Generically Unique, Simple, and Easily Computed

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      Authors: Vladimir Y. Protasov
      Pages: 2246 - 2267
      Abstract: SIAM Journal on Control and Optimization, Volume 60, Issue 4, Page 2246-2267, August 2022.
      We analyze the maximal growth of trajectories of discrete-time linear switching system, i.e., controlled linear systems with the control set being an arbitrary compact set of matrices. This is done by applying the optimal convex Lyapunov function called the Barabanov norm, which provides a very refined analysis of trajectories. Until recently that notion remained rather theoretical apart from special cases. In 2015 N. Guglielmi and M. Zennaro [SIAM J. Matrix Anal. Appl., 36 (2015), pp. 634--655] showed that many systems possess at least one efficiently computed Barabanov norm. In this paper we classify all possible Barabanov norms and prove that, under mild assumptions, which can be verified algorithmically, those norms are unique and are either piecewise-linear or piecewise-quadratic. For some narrow classes of systems, there are more complicated Barabanov norms, but they can still be classified and constructed. Using those results we find all trajectories of the fastest growth. Examples and numerical results are provided.
      Citation: SIAM Journal on Control and Optimization
      PubDate: 2022-07-28T07:00:00Z
      DOI: 10.1137/21M1426821
      Issue No: Vol. 60, No. 4 (2022)
       
  • Global Well-Posedness of the KdV Equation on a Star-Shaped Network and
           Stabilization by Saturated Controllers

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      Authors: Hugo Parada, Emmanuelle Crépeau, Christophe Prieur
      Pages: 2268 - 2296
      Abstract: SIAM Journal on Control and Optimization, Volume 60, Issue 4, Page 2268-2296, August 2022.
      In this work, we deal with the global well-posedness and stability of the linear and nonlinear Korteweg-de Vries equations on a finite star-shaped network by acting with saturated controls. We obtain the global well-posedness by using the Kato smoothing property for the linear case and then using some estimates and a fixed point argument we deal with the nonlinear system. Finally, we obtain the exponential stability using two different kinds of saturation by proving an observability inequality via a contradiction argument.
      Citation: SIAM Journal on Control and Optimization
      PubDate: 2022-08-04T07:00:00Z
      DOI: 10.1137/21M1434581
      Issue No: Vol. 60, No. 4 (2022)
       
  • A Phase-Field Approach to Shape and Topology Optimization of Acoustic
           Waves in Dissipative Media

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      Authors: Harald Garcke, Sourav Mitra, Vanja Nikolić
      Pages: 2297 - 2319
      Abstract: SIAM Journal on Control and Optimization, Volume 60, Issue 4, Page 2297-2319, August 2022.
      We investigate the problem of finding the optimal shape and topology of a system of acoustic lenses in a dissipative medium. The sound propagation is governed by a general semilinear strongly damped wave equation. We introduce a phase-field formulation of this problem through diffuse interfaces between the lenses and the surrounding fluid. The resulting formulation is shown to be well-posed, and we prove that the corresponding optimization problem has a minimizer. By analyzing properties of the reduced objective functional and well-posedness of the adjoint problem, we rigorously derive first-order optimality conditions for this problem. Additionally, we consider the $\Gamma$-limit of the reduced objective functional and in this way establish a relation between the diffuse interface problem and a perimeter-regularized sharp interface shape optimization problem.
      Citation: SIAM Journal on Control and Optimization
      PubDate: 2022-08-08T07:00:00Z
      DOI: 10.1137/21M1449294
      Issue No: Vol. 60, No. 4 (2022)
       
  • The $\mathcal{H}_2$-optimal Control Problem of CSVIU Systems: Discounted,
           Counterdiscounted, and Long-Run Solutions

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      Authors: Joa͂o B. R. do Val, Daniel S. Campos
      Pages: 2320 - 2343
      Abstract: SIAM Journal on Control and Optimization, Volume 60, Issue 4, Page 2320-2343, January 2022.
      The paper deals with stochastic control problems associated with $H_2$ performance indices such as energy or power norms or energy measurements. The control applies to a class of systems for which a stochastic process conveys the underlying uncertainties, known as control and state variation increase uncertainty (CSVIU). These indices allow various emphases, focusing on the transient behavior with the discounted norm to stricter conditions on stability and steady-state mean-square error and convergence rate, using the optimal overtaking criterion. The long-run average power control stands as a midpoint in this respect. A critical advance regards the explicit form of the optimal control law, expressed in two forms. One takes a perturbed affine Riccati-like form of feedback solution; the other comes from a generalized normal equation that arises from the nondifferentiable local optimal problem. They are equivalent, but the former allows optimality and stability, and the latter develops into a search method to attain the optimal law. A detectability notion and a Riccati solution grant stochastic stability from the behavior of the norms. The energy overtaking criterion requires a further constraint on a matrix spectral radius. With these findings, the paper revisits the rising of the inaction solution, a prominent feature of CSVIU models to deal with the uncertainty inherent to poorly known models. Besides the optimal solution, it provides the tools to pursue it.
      Citation: SIAM Journal on Control and Optimization
      PubDate: 2022-08-11T07:00:00Z
      DOI: 10.1137/21M1434593
      Issue No: Vol. 60, No. 4 (2022)
       
  • Observability Estimate for the Wave Equation with Variable Coefficients

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      Authors: Xiaoyu Fu, Zhonghua Liao
      Pages: 2344 - 2372
      Abstract: SIAM Journal on Control and Optimization, Volume 60, Issue 4, Page 2344-2372, January 2022.
      This paper is devoted to a study of an observability estimate for the wave equation with variable coefficients $(h^{jk}(x))_{n\times n}$ ($n\in{{\mathop{\rm l\negthinspace N}}})$. We consider the observation point lying both outside the domain and inside the domain. Based on a Carleman estimate for the ultrahyperbolic operator and a delicate treatment of the observation region, we obtain two observability estimates with explicit observability constants. The key improvements are the waiting time $T$ and the size of the observation region.
      Citation: SIAM Journal on Control and Optimization
      PubDate: 2022-08-11T07:00:00Z
      DOI: 10.1137/21M1468231
      Issue No: Vol. 60, No. 4 (2022)
       
  • Internally Hankel $k$-Positive Systems

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      Authors: Christian Grussler, Thiago Burghi, Somayeh Sojoudi
      Pages: 2373 - 2392
      Abstract: SIAM Journal on Control and Optimization, Volume 60, Issue 4, Page 2373-2392, August 2022.
      There has been an increased interest in the variation diminishing properties of controlled linear time-invariant (LTI) systems and time-varying linear systems without inputs. In controlled LTI systems, these properties have recently been studied from the external perspective of $k$-positive Hankel operators. Such systems have Hankel operators that diminish the number of sign changes (the variation) from past input to future output if the input variation is at most $k-1$. For $k=1$, this coincides with the classical class of externally positive systems. For linear systems without inputs, the focus has been on the internal perspective of $k$-positive state-transition matrices, which diminish the variation of the initial system state. In the LTI case and for $k=1$, this corresponds to the classical class of (unforced) positive systems. This paper bridges the gap between the internal and external perspectives of $k$-positivity by analyzing internally Hankel $k$-positive systems, which we define as state-space LTI systems where controllability and observability operators as well as the state-transition matrix are $k$-positive. We show that the existing notions of external Hankel and internal $k$-positivity are subsumed under internal Hankel $k$-positivity, and we derive tractable conditions for verifying this property in the form of internal positivity of the first $k$ compound systems. As such, this class provides new means to verify external Hankel $k$-positivity, and lays the foundation for future investigations of variation diminishing controlled linear systems. As an application, we use our framework to derive new bounds for the number of over- and undershoots in the step responses of LTI systems. Since our characterization defines a new positive realization problem, we also discuss geometric conditions for the existence of minimal internally Hankel $k$-positive realizations.
      Citation: SIAM Journal on Control and Optimization
      PubDate: 2022-08-16T07:00:00Z
      DOI: 10.1137/21M1404685
      Issue No: Vol. 60, No. 4 (2022)
       
  • Backward Stochastic Volterra Integro-Differential Equations and
           Applications in Optimal Control Problems

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      Authors: Tianxiao Wang
      Pages: 2393 - 2419
      Abstract: SIAM Journal on Control and Optimization, Volume 60, Issue 4, Page 2393-2419, August 2022.
      In this article, a class of backward stochastic Volterra integro-differential equations (BSVIDEs) is introduced and studied. It is worthy mentioning that the proposed BSVIDEs cannot be covered by the existing backward stochastic Volterra integral equations (BSVIEs), and they also have the nice flow property such that Itô's formula becomes quite applicable. It is found that BSVIDEs can provide a neat sufficient condition for the solvability of BSVIEs with generator depending on the \it diagonal value of the solutions. As applications, the optimal control problems in terms of maximum principles and linear quadratic control problems of optimal control for forward stochastic Volterra integro-differential equations are investigated. In contrast with the BSVIEs in current literature, some interesting phenomena and advantages of BSVIDEs are revealed.
      Citation: SIAM Journal on Control and Optimization
      PubDate: 2022-08-16T07:00:00Z
      DOI: 10.1137/20M1371464
      Issue No: Vol. 60, No. 4 (2022)
       
  • Stability and Attractivity Analysis of Uncertain Switched Systems under
           Optimistic Value Criterion

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      Authors: Yadong Shu, Bo Li
      Pages: 2420 - 2439
      Abstract: SIAM Journal on Control and Optimization, Volume 60, Issue 4, Page 2420-2439, August 2022.
      Uncertain switched systems are a significant type of hybrid systems disturbed by subjective uncertainty. Stability and attractivity have been widely investigated, while few results related to property analysis for uncertain switched systems were published before. Therefore, based on optimistic value criterion, stability and attractivity of such systems are proposed and analyzed in this work. By uncertainty theory and the feature of switched systems, corresponding theorems to judge these properties are obtained concerning linear uncertain switched systems in infinite-time horizon. For nonlinear uncertain switched systems, the relationship between stability in optimistic value and stability in measure (or stability in mean) is discussed in depth, and the connection among different attractivities is also revealed. An example about attractivity in optimistic value is provided to illustrate the validness of the results derived.
      Citation: SIAM Journal on Control and Optimization
      PubDate: 2022-08-16T07:00:00Z
      DOI: 10.1137/21M1450343
      Issue No: Vol. 60, No. 4 (2022)
       
  • Slow Decay and Turnpike for Infinite-Horizon Hyperbolic Linear Quadratic
           Problems

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      Authors: Zhong-Jie Han, Enrique Zuazua
      Pages: 2440 - 2468
      Abstract: SIAM Journal on Control and Optimization, Volume 60, Issue 4, Page 2440-2468, August 2022.
      This paper is devoted to analyzing the explicit slow decay rate and turnpike in infinite-horizon linear quadratic optimal control problems for hyperbolic systems. Under suitable weak observability or controllability conditions, lower and upper bounds of the corresponding algebraic Riccati operator are proved. Then based on these two bounds, the explicit slow decay rate of the closed-loop system with Riccati-based optimal feedback control is obtained. The averaged turnpike property for this problem is also further discussed. We then apply these results to LQ optimal control problems constrained to networks of one-dimensional wave equations and also some multidimensional ones with local controls which lack a geometric control condition.
      Citation: SIAM Journal on Control and Optimization
      PubDate: 2022-08-16T07:00:00Z
      DOI: 10.1137/21M1441985
      Issue No: Vol. 60, No. 4 (2022)
       
  • On the Accuracy of the Model Predictive Control Method

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      Authors: Georgi Angelov, Alberto Domínguez Corella, Vladimir M. Veliov
      Pages: 2469 - 2487
      Abstract: SIAM Journal on Control and Optimization, Volume 60, Issue 4, Page 2469-2487, August 2022.
      The paper investigates the accuracy of the model predictive control (MPC) method for finding on-line approximate optimal feedback control for Bolza-type problems on a fixed finite horizon. The predictions for the dynamics, the state measurements, and the solution of the auxiliary open-loop control problems that appear at every step of the MPC method may be inaccurate. The main result provides an error estimate of the MPC-generated solution compared with the optimal open-loop solution of the “ideal” problem, where all predictions and measurements are exact. The technique of proving the estimate involves an extension of the notion of strong metric subregularity of set-valued maps and utilization of a specific new metric in the control space, which makes the proof nonstandard. The result is specialized for two problem classes: coercive problems and affine problems.
      Citation: SIAM Journal on Control and Optimization
      PubDate: 2022-08-16T07:00:00Z
      DOI: 10.1137/21M1460430
      Issue No: Vol. 60, No. 4 (2022)
       
  • 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)
       
 
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