JournalTOCs

SIAM Journal on Control and Optimization
Journal Prestige (SJR): 1.399

Citation Impact (citeScore): 2
Number of Followers: 21

Hybrid journal (It can contain Open Access articles)
ISSN (Print) 0363-0129 - ISSN (Online) 1095-7138
Published by Society for Industrial and Applied Mathematics

[17 journals]

Stochastic Stabilization of Neutral Stochastic Delay Systems Based on
Discrete Observations
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  Authors: Fangzhe Wan, Xueyan Zhao, Feiqi Deng, Peilin Yu, Xiongding Liu
  Pages: 3259 - 3279
  Abstract: SIAM Journal on Control and Optimization, Volume 61, Issue 6, Page 3259-3279, December 2023.
  Abstract. This paper addresses the problem of stochastic stabilization for the neutral stochastic delay systems (NSDSs) based on discrete observations. Specifically, we design sampled-data based controllers (SDBCs) to stabilize NSDSs. To conquer the difficulties caused by the neutral term and stochastic stabilization, we introduce a new nominal system. By using the Lyapunov function method, we discuss the stability of the nominal system and provide a stability criterion. For the part of SDBC design, there are two methods: the lifting technique method (LTM) and the input delay method (IDM). The LTM is more effective for linear delay-free systems, but there is little research on the LTM for nonlinear stochastic delay systems. In this research, we combine the LTM with the equivalence technique for NSDSs, resulting in improved results. Additionally, to overcome the difficulty caused by LTM, we propose a series of mathematical tools, such as Gronwall’s inequality of the discrete version. We compared our method with the IDM presented in X. Mao, IEEE Trans. Automat. Control, 61 (2016), pp. 1619–1624., and our method performs better. Finally, to showcase the efficiency and correctness of our proposed approach, we provide an application.
  Citation: SIAM Journal on Control and Optimization
  PubDate: 2023-11-03T07:00:00Z
  DOI: 10.1137/22M1470918
  Issue No: Vol. 61, No. 6 (2023)
Second-Order Hamilton–Jacobi PDE Problems and Certain Related
First-Order Problems, Part 1: Approximation
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  Authors: William M. McEneaney, Peter M. Dower, Tao Wang
  Pages: 3280 - 3315
  Abstract: SIAM Journal on Control and Optimization, Volume 61, Issue 6, Page 3280-3315, December 2023.
  Abstract. A class of nonlinear, stochastic staticization control problems (including minimization problems with smooth, convex, coercive payoffs) driven by diffusion dynamics with constant diffusion coefficient is considered. The nonlinearities are addressed through stat duality. The second-order Hamilton–Jacobi partial differential equation (HJ PDE) is converted into a first-order HJ PDE in the dual variable, which, however, contains a correction term. Approximations to the correction term are indicated. A numerical example is included.
  Citation: SIAM Journal on Control and Optimization
  PubDate: 2023-11-06T08:00:00Z
  DOI: 10.1137/21M1450057
  Issue No: Vol. 61, No. 6 (2023)
Exact Controllability of the Vortex System by Means of a Single Vortex
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  Authors: Justine Dorsz, Olivier Glass
  Pages: 3316 - 3340
  Abstract: SIAM Journal on Control and Optimization, Volume 61, Issue 6, Page 3316-3340, December 2023.
  Abstract. In this paper, we investigate the controllability of the point vortex system by means of a single vortex. The point vortex system is a well-known simplified model for the incompressible Euler equation, where the vorticity is concentrated in a finite number of Dirac masses. We use one of the vortices as a control and prove that by suitably choosing its trajectory, we can drive all other vortices to a given prescribed position in arbitrary time.
  Citation: SIAM Journal on Control and Optimization
  PubDate: 2023-11-07T08:00:00Z
  DOI: 10.1137/22M1509710
  Issue No: Vol. 61, No. 6 (2023)
An Algebraic Convergence Rate for the Optimal Control of
McKean–Vlasov Dynamics
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  Authors: Pierre Cardaliaguet, Samuel Daudin, Joe Jackson, Panagiotis E. Souganidis
  Pages: 3341 - 3369
  Abstract: SIAM Journal on Control and Optimization, Volume 61, Issue 6, Page 3341-3369, December 2023.
  Abstract. We establish an algebraic rate of convergence of the value functions of [math]-particle stochastic control problems towards the value function of the corresponding McKean–Vlasov problem, also known as mean field control. The rate is obtained in the presence of both idiosyncratic and common noises and in a setting where the value function for the McKean–Vlasov problem need not be smooth. Our approach relies crucially on uniform in [math] Lipschitz and semiconcavity estimates for the [math]-particle value functions as well as a certain concentration inequality.
  Citation: SIAM Journal on Control and Optimization
  PubDate: 2023-11-09T08:00:00Z
  DOI: 10.1137/22M1486789
  Issue No: Vol. 61, No. 6 (2023)
An Optimal Control Problem with Terminal Stochastic Linear Complementarity
Constraints
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  Authors: Jianfeng Luo, Xiaojun Chen
  Pages: 3370 - 3389
  Abstract: SIAM Journal on Control and Optimization, Volume 61, Issue 6, Page 3370-3389, December 2023.
  Abstract. In this paper, we investigate an optimal control problem with a crucial ODE constraint involving a terminal stochastic LCP and its discrete approximation using the relaxation, the sample average approximation (SAA), and the implicit Euler time-stepping scheme. We show the existence of feasible solutions and optimal solutions to the optimal control problem and its discrete approximation under the condition that the expectation of the stochastic matrix in the stochastic LCP is a Z-matrix or an adequate matrix. Moreover, we prove that the solution sequence generated by the discrete approximation converges to a solution of the original optimal control problem with probability 1 by the repeated limits in the order of [math], [math] and [math], where [math] is the relaxation parameter, [math] is the sample size, and [math] is the mesh size. We also provide asymptotics of the SAA optimal value and error bounds of the time-stepping method. A numerical example is used to illustrate the existence of optimal solutions, the discretization scheme, and error estimation.
  Citation: SIAM Journal on Control and Optimization
  PubDate: 2023-11-14T08:00:00Z
  DOI: 10.1137/22M151594X
  Issue No: Vol. 61, No. 6 (2023)
Interior Point Methods in Optimal Control Problems of Affine Systems:
Convergence Results and Solving Algorithms
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  Authors: Paul Malisani
  Pages: 3390 - 3414
  Abstract: SIAM Journal on Control and Optimization, Volume 61, Issue 6, Page 3390-3414, December 2023.
  Abstract. This paper presents an interior point method for pure state and mixed-constraint optimal control problems for dynamics, mixed constraints, and cost function all affine in the control variable. This method relies on resolving a sequence of two-point boundary value problems of differential and algebraic equations. This paper establishes a convergence result for primal and dual variables of the optimal control problem. A primal and a primal-dual solving algorithm are presented, and a challenging numerical example is treated for illustration.
  Citation: SIAM Journal on Control and Optimization
  PubDate: 2023-11-15T08:00:00Z
  DOI: 10.1137/23M1561233
  Issue No: Vol. 61, No. 6 (2023)
On Integer Optimal Control with Total Variation Regularization on
Multidimensional Domains
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  Authors: Paul Manns, Annika Schiemann
  Pages: 3415 - 3441
  Abstract: SIAM Journal on Control and Optimization, Volume 61, Issue 6, Page 3415-3441, December 2023.
  Abstract. We consider optimal control problems with integer-valued controls and a total variation regularization penalty in the objective on domains of dimension two or higher. The penalty yields that the feasible set is sequentially closed in the weak-[math] topology and closed in the strict topology in the space of functions of bounded variation. In turn, we derive first-order optimality conditions of the optimal control problem as well as trust-region subproblems with partially linearized model functions using local variations of the level sets of the feasible control functions. We also prove that a recently proposed function space trust-region algorithm—sequential linear integer programming—produces sequences of iterates whose limits are first-order optimal points.
  Citation: SIAM Journal on Control and Optimization
  PubDate: 2023-11-15T08:00:00Z
  DOI: 10.1137/22M152116X
  Issue No: Vol. 61, No. 6 (2023)
Mean-Field Approximations for Stochastic Population Processes with
Heterogeneous Interactions
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  Authors: Anirudh Sridhar, Soummya Kar
  Pages: 3442 - 3466
  Abstract: SIAM Journal on Control and Optimization, Volume 61, Issue 6, Page 3442-3466, December 2023.
  Abstract. This paper studies a general class of stochastic population processes in which agents interact with one another over a network. Agents update their behaviors in a random and decentralized manner according to a policy that depends only on the agent’s current state and an estimate of the macroscopic population state, given by a weighted average of the neighboring states. When the number of agents is large and the network is a complete graph (has all-to-all information access), the macroscopic behavior of the population can be well-approximated by a set of deterministic differential equations called a mean-field approximation. For incomplete networks such characterizations remained previously unclear, i.e., in general whether a suitable mean-field approximation exists for the macroscopic behavior of the population. The paper addresses this gap by establishing a generic theory describing when various mean-field approximations are accurate for arbitrary interaction structures. Our results are threefold. Letting [math] be the matrix describing agent interactions, we first show that a simple mean-field approximation that incorrectly assumes a homogeneous interaction structure is accurate provided [math] has a large spectral gap. Second, we show that a more complex mean-field approximation which takes into account agent interactions is accurate as long as the Frobenius norm of [math] is small. Finally, we compare the predictions of the two mean-field approximations through simulations, highlighting cases where using mean-field approximations that assume a homogeneous interaction structure can lead to inaccurate qualitative and quantitative predictions.
  Citation: SIAM Journal on Control and Optimization
  PubDate: 2023-11-16T08:00:00Z
  DOI: 10.1137/22M1488922
  Issue No: Vol. 61, No. 6 (2023)
Maximum Principle for Optimal Control of Stochastic Evolution Equations
with Recursive Utilities
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  Authors: Guomin Liu, Shanjian Tang
  Pages: 3467 - 3500
  Abstract: SIAM Journal on Control and Optimization, Volume 61, Issue 6, Page 3467-3500, December 2023.
  Abstract. We consider the optimal control problem of stochastic evolution equations in a Hilbert space under a recursive utility, which is described as the solution of a backward stochastic differential equation (BSDE). A very general maximum principle is given for the optimal control, allowing the control domain to not be convex and the generator of the BSDE to vary with the second unknown variable [math]. The associated second-order adjoint process is characterized as a unique solution of a conditionally expected operator-valued backward stochastic integral equation.
  Citation: SIAM Journal on Control and Optimization
  PubDate: 2023-11-17T08:00:00Z
  DOI: 10.1137/21M1467249
  Issue No: Vol. 61, No. 6 (2023)
Exact Controllability for a Schrödinger Equation with Dynamic
Boundary Conditions
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  Authors: Alberto Mercado, Roberto Morales
  Pages: 3501 - 3525
  Abstract: SIAM Journal on Control and Optimization, Volume 61, Issue 6, Page 3501-3525, December 2023.
  Abstract. In this paper, we study the controllability of a Schrödinger equation with mixed boundary conditions on disjoint subsets of the boundary: dynamic boundary condition of Wentzell type and Dirichlet boundary condition. The main result of this article is given by new Carleman estimates for the associated adjoint system, where the weight function is constructed specially adapted to the geometry of the domain. Using these estimates, we prove the exact controllability of the system with a boundary control acting only in the part of the boundary where the Dirichlet condition is imposed. Also, we obtain a distributed exact controllability result for the system.
  Citation: SIAM Journal on Control and Optimization
  PubDate: 2023-11-17T08:00:00Z
  DOI: 10.1137/21M1439407
  Issue No: Vol. 61, No. 6 (2023)
Nonparametric Adaptive Robust Control under Model Uncertainty
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  Authors: Erhan Bayraktar, Tao Chen
  Pages: 2737 - 2760
  Abstract: SIAM Journal on Control and Optimization, Volume 61, Issue 5, Page 2737-2760, October 2023.
  Abstract. We consider a discrete time stochastic Markovian control problem under model uncertainty. Such uncertainty comes not only from the fact that the true probability law of the underlying stochastic process is unknown, but also from the fact that the parametric family of probability distributions to which the true law belongs is unknown. We propose a nonparametric adaptive robust control methodology to deal with such a problem. Our approach hinges on the following building concepts: first, using the adaptive robust paradigm to incorporate online learning and uncertainty reduction into the robust control problem; second, learning the unknown probability law through the empirical distribution, and representing uncertainty reduction in terms of a sequence of Wasserstein balls around the empirical distribution; third, using Lagrangian duality to convert the optimization over Wasserstein balls to a scalar optimization problem, and adopting a machine learning technique to achieve efficient computation of the optimal control. We illustrate our methodology by considering a utility maximization problem. Numerical comparisons show that the nonparametric adaptive robust control approach is preferable to the traditional robust frameworks.
  Citation: SIAM Journal on Control and Optimization
  PubDate: 2023-09-12T07:00:00Z
  DOI: 10.1137/22M1481609
  Issue No: Vol. 61, No. 5 (2023)
The Exact Boundary Controllability of Nodal Profile for Entropy Solutions
to 1-D Quasilinear Hyperbolic Systems of Conservation Laws with Linearly
Degenerate Negative (Resp., Positive) Characteristic Fields
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  Authors: Tatsien Li, Lei Yu
  Pages: 2761 - 2776
  Abstract: SIAM Journal on Control and Optimization, Volume 61, Issue 5, Page 2761-2776, October 2023.
  Abstract. We consider the exact boundary controllability of nodal profile for entropy solutions to 1-D quasilinear hyperbolic systems of conservation laws [math] under the assumption that all negative (resp., positive) characteristic fields are linearly degenerate. We prove that for small initial-boundary data, if the total variations of the nodal profile and the boundary data given at [math] (resp., [math]) are sufficiently small, then there exists a time [math] and boundary controls at [math] (resp., [math]), such that the corresponding mixed initial-boundary value problem admits a unique entropy solution as the limit of front tracking approximate solutions, which takes the given nodal profile at the boundary [math] (resp., [math]) from a time larger than [math] to infinity. Moreover, if the nodal profile decays to zero when [math], then the entropy solution, together with the boundary control, possesses the same decay rate as the nodal profile.
  Citation: SIAM Journal on Control and Optimization
  PubDate: 2023-09-13T07:00:00Z
  DOI: 10.1137/21M1395946
  Issue No: Vol. 61, No. 5 (2023)
Choquet Regularization for Continuous-Time Reinforcement Learning
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  Authors: Xia Han, Ruodu Wang, Xun Yu Zhou
  Pages: 2777 - 2801
  Abstract: SIAM Journal on Control and Optimization, Volume 61, Issue 5, Page 2777-2801, October 2023.
  Abstract. We propose Choquet regularizers to measure and manage the level of exploration for reinforcement learning (RL) and reformulate the continuous-time entropy-regularized RL problem of H. Wang, T. Zariphopoulou, and X. Zhou [J. Mach. Learn. Res., 21 (2020), pp. 1–34] in which we replace the differential entropy used for regularization with a Choquet regularizer. We derive the Hamilton–Jacobi–Bellman equation of the problem and solve it explicitly in the linear-quadratic (LQ) case via maximizing statically a mean-variance constrained Choquet regularizer. Under the LQ setting, we derive explicit optimal distributions for several specific Choquet regularizers and conversely identify the Choquet regularizers that generate a number of broadly used exploratory samplers, such as [math]-greedy, exponential, uniform, and Gaussian.
  Citation: SIAM Journal on Control and Optimization
  PubDate: 2023-09-14T07:00:00Z
  DOI: 10.1137/22M1524734
  Issue No: Vol. 61, No. 5 (2023)
Optimal Control of Parabolic Equations – A Spectral Calculus Based
Approach
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  Authors: Luka Grubišić, Martin Lazar, Ivica Nakić, Martin Tautenhahn
  Pages: 2802 - 2825
  Abstract: SIAM Journal on Control and Optimization, Volume 61, Issue 5, Page 2802-2825, October 2023.
  Abstract. In this paper we consider a constrained parabolic optimal control problem. The cost functional is quadratic and it combines the distance of the trajectory of the system from the desired evolution profile together with the cost of a control. The constraint is given by a term measuring the distance between the final state and the desired state towards which the solution should be steered. The control enters the system through the initial condition. We present a geometric analysis of this problem and provide a closed-form expression for the solution. This approach allows us to present the sensitivity analysis of this problem based on the resolvent estimates for the generator of the system. The numerical implementation is performed by exploring efficient rational Krylov approximation techniques that allow us to approximate a complex function of an operator by a series of linear problems. Our method does not depend on the actual choice of discretization. The main approximation task is to construct an efficient rational approximation of a generalized exponential function. It is well known that this class of functions allows exponentially convergent rational approximations, which, combined with the sensitivity analysis of the closed form solution, allows us to present a robust numerical method. Several case studies are presented to illustrate our results.
  Citation: SIAM Journal on Control and Optimization
  PubDate: 2023-09-19T07:00:00Z
  DOI: 10.1137/21M1449762
  Issue No: Vol. 61, No. 5 (2023)
On Gradient Flows Initialized near Maxima
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  Authors: Mohamed-Ali Belabbas
  Pages: 2826 - 2848
  Abstract: SIAM Journal on Control and Optimization, Volume 61, Issue 5, Page 2826-2848, October 2023.
  Abstract. Let [math] be a closed Riemannian manifold, and let [math] be a smooth function on [math]. We show the following holds generically for the function [math]: for each maximum [math] of [math], there exist two minima, denoted by [math] and [math], so that the gradient flow initialized at a random point close to [math] converges to either [math] or [math] with high probability. The statement also holds for [math] fixed and a generic metric [math] on [math]. We conclude by associating to a generic pair [math] what we call its max-min graph, which captures the relation between minima and maxima derived in the main result.
  Citation: SIAM Journal on Control and Optimization
  PubDate: 2023-09-19T07:00:00Z
  DOI: 10.1137/21M1450756
  Issue No: Vol. 61, No. 5 (2023)
Lyapunov Stabilization for Nonlocal Traffic Flow Models
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  Authors: Jan Friedrich, Simone Göttlich, Michael Herty
  Pages: 2849 - 2875
  Abstract: SIAM Journal on Control and Optimization, Volume 61, Issue 5, Page 2849-2875, October 2023.
  Abstract. Using a nonlocal second-order traffic flow model we present an approach to control the dynamics toward a steady state. The system is controlled by the leading vehicle driving at a prescribed velocity and also determines the steady state. Thereby, we consider both the microscopic (trajectory based) and macroscopic (density based) scales. We show that the fixed point of the microscopic traffic flow model is (locally) asymptotically stable for any kernel function. To obtain global stabilization, we present Lyapunov functions for both the microscopic and the macroscopic scale and compute the explicit rates at which the vehicles influenced by the nonlocality tend toward the stationary solution. We obtain stabilization results for a constant kernel function and arbitrary initial data or concave kernels and monotone initial data. In particular, the stabilization is exponential in time. Numerical examples demonstrate the theoretical results.
  Citation: SIAM Journal on Control and Optimization
  PubDate: 2023-09-20T07:00:00Z
  DOI: 10.1137/22M152181X
  Issue No: Vol. 61, No. 5 (2023)
Deflating Subspace Approach to UIO Design and Application to
Fault-Tolerant Control
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  Authors: Jovan D. Stefanovski
  Pages: 2876 - 2901
  Abstract: SIAM Journal on Control and Optimization, Volume 61, Issue 5, Page 2876-2901, October 2023.
  Abstract. A deflating subspace approach is applied to the unknown input observer (UIO) design. The associated matrix pencil (MP) to the transfer matrix from the unknown input to the measured output is arbitrary. A unique necessary and sufficient condition is given, in terms of a proper stable left-deflating subspace (PSL-DS) of the MP. For the class of plants such that UIO exists, a UIO-based controller design is presented, based on obtaining a constant coefficient matrix that is a part of the controller, instead of a rational controller matrix. Then the design is applied to a fault-tolerant control (FTC). Illustrative examples are presented.
  Citation: SIAM Journal on Control and Optimization
  PubDate: 2023-09-22T07:00:00Z
  DOI: 10.1137/22M1535619
  Issue No: Vol. 61, No. 5 (2023)
Weak Energy Shaping for Stochastic Controlled Port-Hamiltonian Systems
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  Authors: Francesco Cordoni, Luca Di Persio, Riccardo Muradore
  Pages: 2902 - 2926
  Abstract: SIAM Journal on Control and Optimization, Volume 61, Issue 5, Page 2902-2926, October 2023.
  Abstract. The present work addresses the problem of energy shaping for stochastic port-Hamiltonian systems. Energy shaping is a powerful technique that allows one to systematically find feedback laws to shape the Hamiltonian of a controlled system so that, under a general passivity condition, it converges to a desired configuration. Energy shaping has been recently generalized to consider stochastic port-Hamiltonian systems. Nonetheless, the resulting theory presents several limitations so that relevant examples, such as the additive noise case, are immediately ruled out from the possible use of energy shaping. In the current paper we continue the investigation of the properties of a weak notion of passivity for a stochastic system and derive a weak notion of convergence for the controlled system. Such weak notion of passivity is strictly related to the existence and uniqueness of an invariant measure for the system so that the theory developed has a purely probabilistic flavor. We will show how all the relevant results of energy shaping can be recover under the proposed weak setting.
  Citation: SIAM Journal on Control and Optimization
  PubDate: 2023-09-25T07:00:00Z
  DOI: 10.1137/22M1482585
  Issue No: Vol. 61, No. 5 (2023)
Relative Controllability of Quaternion Differential Equations with Delay
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  Authors: Teng Fu, Kit Ian Kou, Jinrong Wang
  Pages: 2927 - 2952
  Abstract: SIAM Journal on Control and Optimization, Volume 61, Issue 5, Page 2927-2952, October 2023.
  Abstract. The main focus of this study is on the relative controllability of linear and semilinear quaternion differential equations with delay. The Gram criterion and the rank criterion for the relative controllability of linear quaternion differential equations (LQDEs) with pure delay are presented by the delayed quaternion Gram matrix and the maximal right linearly independent group, respectively. Furthermore, a pure delay-based minimal norm control of LQDEs is achieved. For LQDEs with delay, we provide a necessary and sufficient condition for relative controllability and eliminate the requirement for permutation matrices. The relative controllability requirement for semi-LQDEs (SLQDEs) is then established using the Krasnoselskii’s fixed point theorem. Some examples are given to illustrate our theoretical results.
  Citation: SIAM Journal on Control and Optimization
  PubDate: 2023-09-26T07:00:00Z
  DOI: 10.1137/23M1544684
  Issue No: Vol. 61, No. 5 (2023)
Global Optimization via Schrödinger–Föllmer Diffusion
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  Authors: Yin Dai, Yuling Jiao, Lican Kang, Xiliang Lu, Jerry Zhijian Yang
  Pages: 2953 - 2980
  Abstract: SIAM Journal on Control and Optimization, Volume 61, Issue 5, Page 2953-2980, October 2023.
  Abstract. We study the problem of approximately finding global minimizers of [math] via sampling from a probability distribution [math] with density [math] with respect to the Lebesgue measure for [math] small enough. We analyze a sampler based on the Euler–Maruyama discretization of the Schrödinger–Föllmer diffusion processes with stochastic approximation under appropriate assumptions on the step size [math] and the potential [math]. We prove that the output of the proposed sampler is an approximate global minimizer of [math] with high probability at cost of sampling [math] standard normal random variables. Numerical studies illustrate the effectiveness of the proposed method and its superiority to the Langevin method.
  Citation: SIAM Journal on Control and Optimization
  PubDate: 2023-09-28T07:00:00Z
  DOI: 10.1137/22M1477738
  Issue No: Vol. 61, No. 5 (2023)
Global Carleman Estimate and State Observation Problem for
Ginzburg–Landau Equation
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  Authors: Fangfang Dou, Xiaoyu Fu, Zhonghua Liao, Xiaomin Zhu
  Pages: 2981 - 2996
  Abstract: SIAM Journal on Control and Optimization, Volume 61, Issue 5, Page 2981-2996, October 2023.
  Abstract. In this paper, we prove a global Carleman estimate for the complex Ginzburg–Landau operator with a cubic nonlinear term in a bounded domain of [math]. As applications, we study state observation problems for the Ginzburg–Landau equation.
  Citation: SIAM Journal on Control and Optimization
  PubDate: 2023-10-04T07:00:00Z
  DOI: 10.1137/22M1522516
  Issue No: Vol. 61, No. 5 (2023)
The de Finetti Problem with Uncertain Competition
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  Authors: Erik Ekström, Alessandro Milazzo, Marcus Olofsson
  Pages: 2997 - 3017
  Abstract: SIAM Journal on Control and Optimization, Volume 61, Issue 5, Page 2997-3017, October 2023.
  Abstract. We consider a resource extraction problem which extends the classical de Finetti problem for a Wiener process to include the case when a competitor, who is equipped with the ability to extract all the remaining resources in one piece, may exist. This situation is modeled as a nonzero-sum controller-and-stopper game with incomplete information. For this stochastic game we provide a Nash equilibrium with an explicit structure. In equilibrium, the agent and the competitor use singular strategies in such a way that a two-dimensional process, which represents available resources and the filtering estimate of active competition, reflects in a specific direction along a given boundary.
  Citation: SIAM Journal on Control and Optimization
  PubDate: 2023-10-16T07:00:00Z
  DOI: 10.1137/22M1524849
  Issue No: Vol. 61, No. 5 (2023)
Nonuniform Observability for Moving Horizon Estimation and Stability with
Respect to Additive Perturbation
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  Authors: Emilien Flayac, Iman Shames
  Pages: 3018 - 3050
  Abstract: SIAM Journal on Control and Optimization, Volume 61, Issue 5, Page 3018-3050, October 2023.
  Abstract. This paper formalizes the concepts of weakly and weakly regularly persistent input trajectory as well as their link to the observability Grammian and the existence and uniqueness of solutions of moving horizon estimation (MHE) problems. Additionally, thanks to a new time-uniform implicit function theorem, these notions are proved to imply the stability of MHE solutions with respect to small additive perturbation in the measurements and in the dynamics, both uniformly and nonuniformly in time. Finally, examples and counterexamples of weakly persistent and weakly regularly persistent input trajectories are given in the case of 2D bearing-only navigation.
  Citation: SIAM Journal on Control and Optimization
  PubDate: 2023-10-17T07:00:00Z
  DOI: 10.1137/22M1475132
  Issue No: Vol. 61, No. 5 (2023)
Stability of Continuous Time Linear Systems with Bounded Switching
Intervals
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  Authors: Vladimir Yu. Protasov, Rinat Kamalov
  Pages: 3051 - 3075
  Abstract: SIAM Journal on Control and Optimization, Volume 61, Issue 5, Page 3051-3075, October 2023.
  Abstract. We address the stability problem for linear switching systems with mode-dependent restrictions on the switching intervals. Their lengths can be bounded both from below (the guaranteed dwell-time) and from above (the maximal time of a single mode). The presence of upper bounds makes this problem quite different from the classical case. For instance, a stable system can now consist of unstable matrices, it may not possess Lyapunov functions, etc. We introduce the concept of a convex Lyapunov multifunction with discrete monotonicity. Its existence, as well as the existence of invariant norms, are proved. We also establish a modified Berger–Wang formula over periodizable switching laws. Those results provide a method of computation of the Lyapunov exponent with an arbitrary precision. Its efficiency is shown in numerical examples.
  Citation: SIAM Journal on Control and Optimization
  PubDate: 2023-10-18T07:00:00Z
  DOI: 10.1137/22M1529579
  Issue No: Vol. 61, No. 5 (2023)
Two-Sided Singular Control of an Inventory with Unknown Demand Trend
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  Authors: Salvatore Federico, Giorgio Ferrari, Neofytos Rodosthenous
  Pages: 3076 - 3101
  Abstract: SIAM Journal on Control and Optimization, Volume 61, Issue 5, Page 3076-3101, October 2023.
  Abstract. We study the problem of optimally managing an inventory with unknown demand trend. Our formulation leads to a stochastic control problem under partial observation, in which a Brownian motion with nonobservable drift can be singularly controlled in both an upward and downward direction. We first derive the equivalent separated problem under full information, with state-space components given by the Brownian motion and the filtering estimate of its unknown drift, and we then completely solve this latter problem. Our approach uses the transition among three different but equivalent problem formulations, links between two-dimensional bounded-variation stochastic control problems and games of optimal stopping, and probabilistic methods in combination with refined viscosity theory arguments. We show substantial regularity of (a transformed version of) the value function, we construct an optimal control rule, and we show that the free boundaries delineating (transformed) action and inaction regions are bounded globally Lipschitz continuous functions. To our knowledge this is the first time that such a problem has been solved in the literature.
  Citation: SIAM Journal on Control and Optimization
  PubDate: 2023-10-18T07:00:00Z
  DOI: 10.1137/21M1442115
  Issue No: Vol. 61, No. 5 (2023)
Isomorphism Properties of Optimality and Equilibrium Solutions Under
Equivalent Information Structure Transformations: Stochastic Dynamic Games
and Teams
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  Authors: Sina Sanjari, Tamer Basar, Serdar Yuksel
  Pages: 3102 - 3130
  Abstract: SIAM Journal on Control and Optimization, Volume 61, Issue 5, Page 3102-3130, October 2023.
  Abstract. Static reduction of information structures is a method that is commonly adopted in stochastic control, team theory, and game theory. One approach entails change of measure arguments, which has been crucial for stochastic analysis and has been an effective method for establishing existence and approximation results for optimal policies. Another approach entails utilization of invertibility properties of measurements, with further generalizations of equivalent information structure reductions being possible. In this paper, we demonstrate the limitations of such approaches for a wide class of stochastic dynamic games and teams, and present a systematic classification of static reductions for which both positive and negative results on equivalence properties of equilibrium solutions can be obtained: (i) those that are policy-independent, (ii) those that are policy-dependent, and (iii) a third type that we will refer to as static measurements with control-sharing reduction (where the measurements are static although control actions are shared according to the partially nested information structure). For the first type, we show that there is a bijection between Nash equilibrium policies under the original information structure and their policy-independent static reductions, and establish sufficient conditions under which stationary solutions are also isomorphic between these information structures. For the second type, however, we show that there is generally no isomorphism between Nash equilibrium (or stationary) solutions under the original information structure and their policy-dependent static reductions. Sufficient conditions (on the cost functions and policies) are obtained to establish such an isomorphism relationship between Nash equilibria of dynamic non-zero-sum games and their policy-dependent static reductions. For zero-sum games and teams, these sufficient conditions can be further relaxed. In view of the equivalence between policies for dynamic games and their static reductions, and closed-loop and open-loop policies, we also present three classes of multistage games and teams with partially nested information structures, where we establish connections between closed-loop, open-loop, and control-sharing Nash and saddle point equilibria. By taking into account a playerwise concept of equilibrium, we introduce two further classes of “playerwise” static reductions: (i) independent data reduction under which the policy-independent reduction holds through players and time, and (ii) playerwise (partially) nested independent reduction under which measurements are independent through players but (partially) nested through time for each player.
  Citation: SIAM Journal on Control and Optimization
  PubDate: 2023-10-19T07:00:00Z
  DOI: 10.1137/22M1521936
  Issue No: Vol. 61, No. 5 (2023)
On the Approximability of Koopman-Based Operator Lyapunov Equations
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  Authors: Tobias Breiten, Bernhard Höveler
  Pages: 3131 - 3155
  Abstract: SIAM Journal on Control and Optimization, Volume 61, Issue 5, Page 3131-3155, October 2023.
  Abstract. Lyapunov functions play a vital role in the context of control theory for nonlinear dynamical systems. Besides their classical use for stability analysis, Lyapunov functions also arise in iterative schemes for computing optimal feedback laws such as the well-known policy iteration. In this manuscript, the focus is on the Lyapunov function of a nonlinear autonomous finite-dimensional dynamical system which will be rewritten as an infinite-dimensional linear system using the Koopman or composition operator. Since this infinite-dimensional system has the structure of a weak-* continuous semigroup, in a specially weighted [math]-space one can establish a connection between the solution of an operator Lyapunov equation and the desired Lyapunov function. It will be shown that the solution to this operator equation attains a rapid eigenvalue decay which justifies finite rank approximations with numerical methods. The potential benefit for numerical computations will be demonstrated with two short examples.
  Citation: SIAM Journal on Control and Optimization
  PubDate: 2023-10-19T07:00:00Z
  DOI: 10.1137/23M1552693
  Issue No: Vol. 61, No. 5 (2023)
An Optimal Control Problem Subject to Strong Solutions of
Chemotaxis-Consumption Models
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  Authors: Francisco Guillén-González, André Luiz Corrêa Vianna Filho
  Pages: 3156 - 3182
  Abstract: SIAM Journal on Control and Optimization, Volume 61, Issue 5, Page 3156-3182, October 2023.
  Abstract. We consider a bilinear optimal control problem associated to the following chemotaxis-consumption model in a bounded domain [math] during a time interval [math]: [math], with [math], endowed with isolated boundary conditions and initial conditions for [math], [math] being the cell density, [math] the chemical concentration, and [math] the bilinear control acting in a subdomain [math]. The existence of weak solutions [math] to this model given [math], for some [math], has been proved in [F. Guillén-González and A. L. Corrêa Vianna Filho, Optimal Control Related to Weak Solutions of a Chemotaxis-Consumption Model, https://arxiv.org/abs/2211.14612, 2022]. In this paper, we study a related optimal control problem in the strong solution setting. First, imposing the regularity criterion [math] ([math]) for a given weak solution, we prove existence and uniqueness of global-in-time strong solutions. Then, the existence of a global optimal solution can be deduced. Finally, using a Lagrange multipliers theorem, we establish first order optimality conditions for any local optimal solution, proving existence, uniqueness, and regularity of the associated Lagrange multipliers.
  Citation: SIAM Journal on Control and Optimization
  PubDate: 2023-10-20T07:00:00Z
  DOI: 10.1137/23M1553637
  Issue No: Vol. 61, No. 5 (2023)
Adaptive Optimal Control of Linear Discrete-Time Networked Control Systems
with Two-Channel Stochastic Dropouts
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  Authors: Yi Jiang, Weinan Gao, Ci Chen, Tianyou Chai, Frank L. Lewis
  Pages: 3183 - 3208
  Abstract: SIAM Journal on Control and Optimization, Volume 61, Issue 5, Page 3183-3208, October 2023.
  Abstract. This paper investigates the adaptive optimal control problem and proposes fundamentally novel non-model-based approaches for linear discrete-time networked control systems (NCSs) with both sensor and actuator two-channel stochastic dropouts by using directly the data transmitted via communication networks. First, we formulate a modified algebraic Riccati equation parameterized by the system dynamics and the network-induced packet dropouts probabilities, whose solvability is related to a critical arrival probability. To deal with this problem, two model-based reinforcement learning algorithms, policy iteration (PI) and value iteration (VI), are designed with their convergence proofs. To enable the application for NCSs with unknown system dynamics, two novel online PI and VI algorithms are designed. These algorithms develop a new theoretical framework to solve the Bellman function with stochastic dropouts by using directly the data transmitted via networks. Furthermore, a bilevel learning algorithm is proposed to approximate the critical arrival probability. Last but not least, an extension of the developed online VI algorithm is presented for stochastic systems with both unmeasurable noises and stochastic dropouts.
  Citation: SIAM Journal on Control and Optimization
  PubDate: 2023-10-24T07:00:00Z
  DOI: 10.1137/21M1438797
  Issue No: Vol. 61, No. 5 (2023)
Vector Control Lyapunov and Barrier Functions for Safe Stabilization of
Interconnected Systems
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  Authors: Wei Ren, Jingjie Li, Junlin Xiong, Xi-Ming Sun
  Pages: 3209 - 3233
  Abstract: SIAM Journal on Control and Optimization, Volume 61, Issue 5, Page 3209-3233, October 2023.
  Abstract. In this paper, we investigate the safety and stabilization problems of interconnected nonlinear systems. In particular, different subsystems may involve potentially conflicting control objectives and distributed safety constraints. For this purpose, we first propose a novel vector control Lyapunov function (VCLF) to deal with the stabilization problem and vector control barrier functions (VCBFs) to resolve the safety problem. Both VCLF and VCBFs not only extend the control Lyapunov function and control barrier function from the scalar case to the vector case, but also allow for the decentralized controller design to reduce the conservatism caused by the existing methods based on scalar control functions. To address the safety and stabilization problems simultaneously, the proposed VCLF and VCBF are combined into a quadratic programming, which is in a decentralized manner and results in a decentralized optimization-based control approach. The decentralized controllers are derived explicitly in a closed form, which facilitates the analysis and shows the simultaneous guarantee of the safety and stabilization objectives. Finally, the derived results are illustrated via an example from the formation control problem of multirobot systems.
  Citation: SIAM Journal on Control and Optimization
  PubDate: 2023-10-25T07:00:00Z
  DOI: 10.1137/22M1530422
  Issue No: Vol. 61, No. 5 (2023)
Kullback–Leibler-Quadratic Optimal Control
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  Authors: Neil Cammardella, Ana Bušić, Sean P. Meyn
  Pages: 3234 - 3258
  Abstract: SIAM Journal on Control and Optimization, Volume 61, Issue 5, Page 3234-3258, October 2023.
  Abstract. This paper presents approaches to mean-field control, motivated by distributed control of multiagent systems. Control solutions are based on a convex optimization problem, whose domain is a convex set of probability mass functions (pmfs). The main contributions follow: (1) Kullback–Leibler-quadratic (KLQ) optimal control is a special case in which the objective function is composed of a control cost in the form of Kullback–Leibler divergence between a candidate pmf and the nominal, plus a quadratic cost on the sequence of marginals. Theory in this paper extends prior work on deterministic control systems, establishing that the optimal solution is an exponential tilting of the nominal pmf. Transform techniques are introduced to reduce complexity of the KLQ solution, motivated by the need to consider time horizons that are much longer than the intersampling times required for reliable control. (2) Infinite-horizon KLQ leads to a state feedback control solution with attractive properties. It can be expressed as state feedback, in which the state is the sequence of marginal pmfs, or an open loop solution is obtained that is more easily computed. (3) Numerical experiments are surveyed in an application of distributed control of residential loads to provide grid services, similar to utility-scale battery storage. The results show that KLQ optimal control enables the aggregate power consumption of a collection of flexible loads to track a time-varying reference signal, while simultaneously ensuring each individual load satisfies its own quality of service constraints.
  Citation: SIAM Journal on Control and Optimization
  PubDate: 2023-10-25T07:00:00Z
  DOI: 10.1137/21M1433654
  Issue No: Vol. 61, No. 5 (2023)