Society for Industrial and Applied Mathematics: SIAM Journal on Control and Optimization: Table of Contents
Table of Contents for SIAM Journal on Control and Optimization. List of articles from both the latest and ahead of print issues.
https://epubs.siam.org/loi/sjcodc?af=R
Society for Industrial and Applied Mathematics: SIAM Journal on Control and Optimization: Table of Contents
Society for Industrial and Applied Mathematics
enUS
SIAM Journal on Control and Optimization
SIAM Journal on Control and Optimization
https://epubs.siam.org/na101/home/literatum/publisher/siam/journals/covergifs/sjcodc/cover.jpg
https://epubs.siam.org/loi/sjcodc?af=R

Stochastic Maximum Principle for Fully Coupled ForwardBackward Stochastic Differential Equations Driven by Subdiffusion
https://epubs.siam.org/doi/abs/10.1137/23M1620168?af=R
SIAM Journal on Control and Optimization, <a href="https://epubs.siam.org/toc/sjcodc/62/5">Volume 62, Issue 5</a>, Page 24332455, October 2024. <br/> Abstract. We study optimal stochastic control problems for fully coupled forwardbackward stochastic differential equations driven by anomalous subdiffusion, which have nontrivial mixed features of deterministic and stochastic controls. Both the stochastic maximum principle (SMP) and sufficient SMP are obtained by using a convex variational method. The paper ends with an application of the main results of this paper to a linear quadratic problem in the subdiffusive setting, which is solved explicitly.
SIAM Journal on Control and Optimization, Volume 62, Issue 5, Page 24332455, October 2024. <br/> Abstract. We study optimal stochastic control problems for fully coupled forwardbackward stochastic differential equations driven by anomalous subdiffusion, which have nontrivial mixed features of deterministic and stochastic controls. Both the stochastic maximum principle (SMP) and sufficient SMP are obtained by using a convex variational method. The paper ends with an application of the main results of this paper to a linear quadratic problem in the subdiffusive setting, which is solved explicitly. <p><img src="https://epubs.siam.org/na101/home/literatum/publisher/siam/journals/covergifs/sjcodc/cover.jpg" alttext="cover image"/></p>
Stochastic Maximum Principle for Fully Coupled ForwardBackward Stochastic Differential Equations Driven by Subdiffusion
10.1137/23M1620168
SIAM Journal on Control and Optimization
20240903T07:00:00Z
© 2024 Society for Industrial and Applied Mathematics
Shuaiqi Zhang
ZhenQing Chen
Stochastic Maximum Principle for Fully Coupled ForwardBackward Stochastic Differential Equations Driven by Subdiffusion
62
5
2433
2455
20241031T07:00:00Z
20241031T07:00:00Z
10.1137/23M1620168
https://epubs.siam.org/doi/abs/10.1137/23M1620168?af=R
© 2024 Society for Industrial and Applied Mathematics

Null Internal Controllability for a Kirchhoff–Love Plate with a CombLike Shaped Structure
https://epubs.siam.org/doi/abs/10.1137/24M1647825?af=R
SIAM Journal on Control and Optimization, <a href="https://epubs.siam.org/toc/sjcodc/62/5">Volume 62, Issue 5</a>, Page 24562474, October 2024. <br/> Abstract. This paper is devoted to studying the null internal controllability of a Kirchoff–Love thin plate with a middle surface having a comblike shaped structure with a large number of thin fingers described by a small positive parameter [math]. It is often impossible to directly approach such a problem numerically, due to the large number of thin fingers. So an asymptotic analysis is needed. In this paper, we first prove that the problem is null controllable at each level [math]. We then prove that the sequence of the respective controls with minimal [math] norm converges, as [math] vanishes, to a limit control function ensuring the optimal null controllability of a degenerate limit problem set in a domain without fingers.
SIAM Journal on Control and Optimization, Volume 62, Issue 5, Page 24562474, October 2024. <br/> Abstract. This paper is devoted to studying the null internal controllability of a Kirchoff–Love thin plate with a middle surface having a comblike shaped structure with a large number of thin fingers described by a small positive parameter [math]. It is often impossible to directly approach such a problem numerically, due to the large number of thin fingers. So an asymptotic analysis is needed. In this paper, we first prove that the problem is null controllable at each level [math]. We then prove that the sequence of the respective controls with minimal [math] norm converges, as [math] vanishes, to a limit control function ensuring the optimal null controllability of a degenerate limit problem set in a domain without fingers. <p><img src="https://epubs.siam.org/na101/home/literatum/publisher/siam/journals/covergifs/sjcodc/cover.jpg" alttext="cover image"/></p>
Null Internal Controllability for a Kirchhoff–Love Plate with a CombLike Shaped Structure
10.1137/24M1647825
SIAM Journal on Control and Optimization
20240904T07:00:00Z
© 2024 Society for Industrial and Applied Mathematics
Umberto De Maio
Antonio Gaudiello
CătălinGeorge Lefter
Null Internal Controllability for a Kirchhoff–Love Plate with a CombLike Shaped Structure
62
5
2456
2474
20241031T07:00:00Z
20241031T07:00:00Z
10.1137/24M1647825
https://epubs.siam.org/doi/abs/10.1137/24M1647825?af=R
© 2024 Society for Industrial and Applied Mathematics

A Tikhonov Theorem for McKean–Vlasov TwoScale Systems and a New Application to Mean Field Optimal Control Problems
https://epubs.siam.org/doi/abs/10.1137/22M1543070?af=R
SIAM Journal on Control and Optimization, <a href="https://epubs.siam.org/toc/sjcodc/62/5">Volume 62, Issue 5</a>, Page 24752505, October 2024. <br/> Abstract. We provide a new version of the Tikhonov theorem for both twoscale forward systems and also twoscale forwardbackward systems of stochastic differential equations, which also covers the McKean–Vlasov case. Differently from what is usually done in the literature, we prove a type of convergence for the “fast” variable, which allows the limiting process to be discontinuous. This is relevant for the second part of the paper, where we present a new application of this theory to the approximation of the solution of mean field control problems. Towards this aim, we construct a twoscale system whose “fast” component converges to the optimal control process, while the “slow” component converges to the optimal state process. The interest in such a procedure is that it allows one to approximate the solution of the control problem, avoiding the usual step of the minimization of the Hamiltonian.
SIAM Journal on Control and Optimization, Volume 62, Issue 5, Page 24752505, October 2024. <br/> Abstract. We provide a new version of the Tikhonov theorem for both twoscale forward systems and also twoscale forwardbackward systems of stochastic differential equations, which also covers the McKean–Vlasov case. Differently from what is usually done in the literature, we prove a type of convergence for the “fast” variable, which allows the limiting process to be discontinuous. This is relevant for the second part of the paper, where we present a new application of this theory to the approximation of the solution of mean field control problems. Towards this aim, we construct a twoscale system whose “fast” component converges to the optimal control process, while the “slow” component converges to the optimal state process. The interest in such a procedure is that it allows one to approximate the solution of the control problem, avoiding the usual step of the minimization of the Hamiltonian. <p><img src="https://epubs.siam.org/na101/home/literatum/publisher/siam/journals/covergifs/sjcodc/cover.jpg" alttext="cover image"/></p>
A Tikhonov Theorem for McKean–Vlasov TwoScale Systems and a New Application to Mean Field Optimal Control Problems
10.1137/22M1543070
SIAM Journal on Control and Optimization
20240904T07:00:00Z
© 2024 Society for Industrial and Applied Mathematics
Matteo Burzoni
Alekos Cecchin
Andrea Cosso
A Tikhonov Theorem for McKean–Vlasov TwoScale Systems and a New Application to Mean Field Optimal Control Problems
62
5
2475
2505
20241031T07:00:00Z
20241031T07:00:00Z
10.1137/22M1543070
https://epubs.siam.org/doi/abs/10.1137/22M1543070?af=R
© 2024 Society for Industrial and Applied Mathematics

An Optimal Spectral Inequality for Degenerate Operators
https://epubs.siam.org/doi/abs/10.1137/23M1605211?af=R
SIAM Journal on Control and Optimization, <a href="https://epubs.siam.org/toc/sjcodc/62/5">Volume 62, Issue 5</a>, Page 25062528, October 2024. <br/> Abstract. In this paper we establish a Lebeau–Robbiano spectral inequality for a degenerate onedimensional elliptic operator, with an optimal dependency with the frequency parameter. The proof relies on a combination of uniform local Carleman estimates away from the degeneracy and a moment method adapted for a degenerate elliptic operator. We also provide an application to the nullcontrollability on a measurable set in time for the associated degenerate heat equation.
SIAM Journal on Control and Optimization, Volume 62, Issue 5, Page 25062528, October 2024. <br/> Abstract. In this paper we establish a Lebeau–Robbiano spectral inequality for a degenerate onedimensional elliptic operator, with an optimal dependency with the frequency parameter. The proof relies on a combination of uniform local Carleman estimates away from the degeneracy and a moment method adapted for a degenerate elliptic operator. We also provide an application to the nullcontrollability on a measurable set in time for the associated degenerate heat equation. <p><img src="https://epubs.siam.org/na101/home/literatum/publisher/siam/journals/covergifs/sjcodc/cover.jpg" alttext="cover image"/></p>
An Optimal Spectral Inequality for Degenerate Operators
10.1137/23M1605211
SIAM Journal on Control and Optimization
20240905T07:00:00Z
© 2024 R. Buffe, K. D. Phung, and A. Slimani
Rémi Buffe
Kim Dang Phung
Amine Slimani
An Optimal Spectral Inequality for Degenerate Operators
62
5
2506
2528
20241031T07:00:00Z
20241031T07:00:00Z
10.1137/23M1605211
https://epubs.siam.org/doi/abs/10.1137/23M1605211?af=R
© 2024 R. Buffe, K. D. Phung, and A. Slimani

Logarithmic Regret Bounds for ContinuousTime AverageReward Markov Decision Processes
https://epubs.siam.org/doi/abs/10.1137/23M1584101?af=R
SIAM Journal on Control and Optimization, <a href="https://epubs.siam.org/toc/sjcodc/62/5">Volume 62, Issue 5</a>, Page 25292556, October 2024. <br/> Abstract. We consider reinforcement learning for continuoustime Markov decision processes (MDPs) in the infinitehorizon, averagereward setting. In contrast to discretetime MDPs, a continuoustime process moves to a state and stays there for a random holding time after an action is taken. With unknown transition probabilities and rates of exponential holding times, we derive instancedependent regret lower bounds that are logarithmic in the time horizon. Moreover, we design a learning algorithm and establish a finitetime regret bound that achieves the logarithmic growth rate. Our analysis builds upon upper confidence reinforcement learning, a delicate estimation of the mean holding times, and stochastic comparison of point processes.
SIAM Journal on Control and Optimization, Volume 62, Issue 5, Page 25292556, October 2024. <br/> Abstract. We consider reinforcement learning for continuoustime Markov decision processes (MDPs) in the infinitehorizon, averagereward setting. In contrast to discretetime MDPs, a continuoustime process moves to a state and stays there for a random holding time after an action is taken. With unknown transition probabilities and rates of exponential holding times, we derive instancedependent regret lower bounds that are logarithmic in the time horizon. Moreover, we design a learning algorithm and establish a finitetime regret bound that achieves the logarithmic growth rate. Our analysis builds upon upper confidence reinforcement learning, a delicate estimation of the mean holding times, and stochastic comparison of point processes. <p><img src="https://epubs.siam.org/na101/home/literatum/publisher/siam/journals/covergifs/sjcodc/cover.jpg" alttext="cover image"/></p>
Logarithmic Regret Bounds for ContinuousTime AverageReward Markov Decision Processes
10.1137/23M1584101
SIAM Journal on Control and Optimization
20240910T07:00:00Z
© 2024 Society for Industrial and Applied Mathematics
Xuefeng Gao
Xun Yu Zhou
Logarithmic Regret Bounds for ContinuousTime AverageReward Markov Decision Processes
62
5
2529
2556
20241031T07:00:00Z
20241031T07:00:00Z
10.1137/23M1584101
https://epubs.siam.org/doi/abs/10.1137/23M1584101?af=R
© 2024 Society for Industrial and Applied Mathematics

Backward Stochastic Differential Equations with Conditional Reflection and Related Recursive Optimal Control Problems
https://epubs.siam.org/doi/abs/10.1137/22M1534985?af=R
SIAM Journal on Control and Optimization, <a href="https://epubs.siam.org/toc/sjcodc/62/5">Volume 62, Issue 5</a>, Page 25572589, October 2024. <br/> Abstract. We introduce a new type of reflected backward stochastic differential equations (BSDEs) for which the reflection constraint is imposed on its main solution component, denoted as [math] by convention, but in terms of its conditional expectation [math] on a general subfiltration [math]. We thus term such a equation as conditionally reflected BSDE (for short, conditional RBSDE). Conditional RBSDE subsumes classical RBSDE with a pointwise reflection barrier and the recently developed BSDE with a mean reflection constraint as its two special and extreme cases: they exactly correspond to [math] being the full filtration to represent complete information and the degenerated filtration to deterministic scenario, respectively. For conditional RBSDE, we obtain its existence and uniqueness under mild conditions by combining the Snell envelope method with the Skorokhod lemma. We also discuss its connection, in the case of a linear driver, to a class of optimal stopping problems in the presence of partial information. As a byproduct, a new version of the comparison theorem is obtained. With the help of this connection, we study weak formulations of a class of optimal control problems with reflected recursive functionals by characterizing the related optimal solution and value. Moreover, in the special case of recursive functionals being RBSDE with pointwise reflections, we study the strong formulations of related stochastic backward recursive control and zerosum games, both in a nonMarkovian framework, that are of their own interests and have not been fully explored by existing literature yet.
SIAM Journal on Control and Optimization, Volume 62, Issue 5, Page 25572589, October 2024. <br/> Abstract. We introduce a new type of reflected backward stochastic differential equations (BSDEs) for which the reflection constraint is imposed on its main solution component, denoted as [math] by convention, but in terms of its conditional expectation [math] on a general subfiltration [math]. We thus term such a equation as conditionally reflected BSDE (for short, conditional RBSDE). Conditional RBSDE subsumes classical RBSDE with a pointwise reflection barrier and the recently developed BSDE with a mean reflection constraint as its two special and extreme cases: they exactly correspond to [math] being the full filtration to represent complete information and the degenerated filtration to deterministic scenario, respectively. For conditional RBSDE, we obtain its existence and uniqueness under mild conditions by combining the Snell envelope method with the Skorokhod lemma. We also discuss its connection, in the case of a linear driver, to a class of optimal stopping problems in the presence of partial information. As a byproduct, a new version of the comparison theorem is obtained. With the help of this connection, we study weak formulations of a class of optimal control problems with reflected recursive functionals by characterizing the related optimal solution and value. Moreover, in the special case of recursive functionals being RBSDE with pointwise reflections, we study the strong formulations of related stochastic backward recursive control and zerosum games, both in a nonMarkovian framework, that are of their own interests and have not been fully explored by existing literature yet. <p><img src="https://epubs.siam.org/na101/home/literatum/publisher/siam/journals/covergifs/sjcodc/cover.jpg" alttext="cover image"/></p>
Backward Stochastic Differential Equations with Conditional Reflection and Related Recursive Optimal Control Problems
10.1137/22M1534985
SIAM Journal on Control and Optimization
20240910T07:00:00Z
© 2024 Society for Industrial and Applied Mathematics
Ying Hu
Jianhui Huang
Wenqiang Li
Backward Stochastic Differential Equations with Conditional Reflection and Related Recursive Optimal Control Problems
62
5
2557
2589
20241031T07:00:00Z
20241031T07:00:00Z
10.1137/22M1534985
https://epubs.siam.org/doi/abs/10.1137/22M1534985?af=R
© 2024 Society for Industrial and Applied Mathematics

Optimal Ratcheting of Dividend Payout Under Brownian Motion Surplus
https://epubs.siam.org/doi/abs/10.1137/23M159250X?af=R
SIAM Journal on Control and Optimization, <a href="https://epubs.siam.org/toc/sjcodc/62/5">Volume 62, Issue 5</a>, Page 25902620, October 2024. <br/> Abstract. This paper is concerned with a longstanding optimal dividend payout problem subject to the socalled ratcheting constraint, that is, the dividend payout rate shall be nondecreasing over time and is thus selfpathdependent. The surplus process is modeled by a drifted Brownian motion process and the aim is to find the optimal dividend ratcheting strategy to maximize the expectation of the total discounted dividend payouts until the ruin time. Due to the selfpathdependent control constraint, the standard control theory cannot be directly applied to tackle the problem. The related Hamilton–Jacobi–Bellman (HJB) equation is a new type of variational inequality. In the literature, it is only shown to have a viscosity solution, which is not strong enough to guarantee the existence of an optimal dividend ratcheting strategy. This paper proposes a novel partial differential equation method to study the HJB equation. We not only prove the existence and uniqueness of the solution in some stronger functional space, but also prove the strict monotonicity, boundedness, and [math]smoothness of the dividend ratcheting free boundary. Based on these results, we eventually derive an optimal dividend ratcheting strategy, and thus solve the open problem completely. Economically speaking, we find that if the surplus volatility is above an explicit threshold, then one should pay dividends at the maximum rate, regardless of the surplus level. Otherwise, by contrast, the optimal dividend ratcheting strategy relies on the surplus level and one should only ratchet up the dividend payout rate when the surplus level touches the dividend ratcheting free boundary. Moreover, our numerical results suggest that one should invest in those companies with stable dividend payout strategies since their income rates should be higher and volatility rates smaller.
SIAM Journal on Control and Optimization, Volume 62, Issue 5, Page 25902620, October 2024. <br/> Abstract. This paper is concerned with a longstanding optimal dividend payout problem subject to the socalled ratcheting constraint, that is, the dividend payout rate shall be nondecreasing over time and is thus selfpathdependent. The surplus process is modeled by a drifted Brownian motion process and the aim is to find the optimal dividend ratcheting strategy to maximize the expectation of the total discounted dividend payouts until the ruin time. Due to the selfpathdependent control constraint, the standard control theory cannot be directly applied to tackle the problem. The related Hamilton–Jacobi–Bellman (HJB) equation is a new type of variational inequality. In the literature, it is only shown to have a viscosity solution, which is not strong enough to guarantee the existence of an optimal dividend ratcheting strategy. This paper proposes a novel partial differential equation method to study the HJB equation. We not only prove the existence and uniqueness of the solution in some stronger functional space, but also prove the strict monotonicity, boundedness, and [math]smoothness of the dividend ratcheting free boundary. Based on these results, we eventually derive an optimal dividend ratcheting strategy, and thus solve the open problem completely. Economically speaking, we find that if the surplus volatility is above an explicit threshold, then one should pay dividends at the maximum rate, regardless of the surplus level. Otherwise, by contrast, the optimal dividend ratcheting strategy relies on the surplus level and one should only ratchet up the dividend payout rate when the surplus level touches the dividend ratcheting free boundary. Moreover, our numerical results suggest that one should invest in those companies with stable dividend payout strategies since their income rates should be higher and volatility rates smaller. <p><img src="https://epubs.siam.org/na101/home/literatum/publisher/siam/journals/covergifs/sjcodc/cover.jpg" alttext="cover image"/></p>
Optimal Ratcheting of Dividend Payout Under Brownian Motion Surplus
10.1137/23M159250X
SIAM Journal on Control and Optimization
20240910T07:00:00Z
© 2024 Society for Industrial and Applied Mathematics
Chonghu Guan
Zuo Quan Xu
Optimal Ratcheting of Dividend Payout Under Brownian Motion Surplus
62
5
2590
2620
20241031T07:00:00Z
20241031T07:00:00Z
10.1137/23M159250X
https://epubs.siam.org/doi/abs/10.1137/23M159250X?af=R
© 2024 Society for Industrial and Applied Mathematics

Controlled Martingale Problems and Their Markov Mimics
https://epubs.siam.org/doi/abs/10.1137/23M1598428?af=R
SIAM Journal on Control and Optimization, <a href="https://epubs.siam.org/toc/sjcodc/62/5">Volume 62, Issue 5</a>, Page 26212638, October 2024. <br/> Abstract. In this article we prove under suitable assumptions that the marginals of any solution to a relaxed controlled martingale problem on a Polish space [math] can be mimicked by a Markovian solution of a Markovrelaxed controlled martingale problem. We also show how such ‘`Markov mimics’’ can be obtained by relative entropy minimization. We provide many examples where the above results can be applied.
SIAM Journal on Control and Optimization, Volume 62, Issue 5, Page 26212638, October 2024. <br/> Abstract. In this article we prove under suitable assumptions that the marginals of any solution to a relaxed controlled martingale problem on a Polish space [math] can be mimicked by a Markovian solution of a Markovrelaxed controlled martingale problem. We also show how such ‘`Markov mimics’’ can be obtained by relative entropy minimization. We provide many examples where the above results can be applied. <p><img src="https://epubs.siam.org/na101/home/literatum/publisher/siam/journals/covergifs/sjcodc/cover.jpg" alttext="cover image"/></p>
Controlled Martingale Problems and Their Markov Mimics
10.1137/23M1598428
SIAM Journal on Control and Optimization
20240916T07:00:00Z
© 2024 Society for Industrial and Applied Mathematics
Siva Athreya
Vivek S. Borkar
Nitya Gadhiwala
Controlled Martingale Problems and Their Markov Mimics
62
5
2621
2638
20241031T07:00:00Z
20241031T07:00:00Z
10.1137/23M1598428
https://epubs.siam.org/doi/abs/10.1137/23M1598428?af=R
© 2024 Society for Industrial and Applied Mathematics

Average Submodularity of Maximizing Anticoordination in Network Games
https://epubs.siam.org/doi/abs/10.1137/22M1506614?af=R
SIAM Journal on Control and Optimization, <a href="https://epubs.siam.org/toc/sjcodc/62/5">Volume 62, Issue 5</a>, Page 26392663, October 2024. <br/> Abstract. We consider the control of decentralized learning dynamics for agents in an anticoordination network game. In the anticoordination network game, there is a preferred action in the absence of neighbors’ actions, and the utility an agent receives from the preferred action decreases as more of its neighbors select the preferred action, potentially causing the agent to select a less desirable action. The decentralized dynamics that are based on the synchronous bestresponse dynamics converge for the considered payoffs. Given a convergent action profile, we measure anticoordination by the number of edges in the underlying graph that have at least one agent in either end of the edge not taking the preferred action. A designer wants to find an optimal set of agents to control under a finite budget in order to achieve maximum anticoordination (MAC) on game convergence as a result of the dynamics. We show that the MAC is submodular in expectation over all realizations of the payoff interaction constants in bipartite networks. The proof relies on characterizing wellbehavedness of MAC instances for bipartite networks, and designing a coupling between the dynamics and another distribution preserving selection protocol, for which we can show the diminishing returns property. Utilizing this result, we obtain a performance guarantee for the greedy optimization of MAC. Finally, we provide a computational study to show the effectiveness of greedy node selection strategies to solve MAC on general bipartite networks.
SIAM Journal on Control and Optimization, Volume 62, Issue 5, Page 26392663, October 2024. <br/> Abstract. We consider the control of decentralized learning dynamics for agents in an anticoordination network game. In the anticoordination network game, there is a preferred action in the absence of neighbors’ actions, and the utility an agent receives from the preferred action decreases as more of its neighbors select the preferred action, potentially causing the agent to select a less desirable action. The decentralized dynamics that are based on the synchronous bestresponse dynamics converge for the considered payoffs. Given a convergent action profile, we measure anticoordination by the number of edges in the underlying graph that have at least one agent in either end of the edge not taking the preferred action. A designer wants to find an optimal set of agents to control under a finite budget in order to achieve maximum anticoordination (MAC) on game convergence as a result of the dynamics. We show that the MAC is submodular in expectation over all realizations of the payoff interaction constants in bipartite networks. The proof relies on characterizing wellbehavedness of MAC instances for bipartite networks, and designing a coupling between the dynamics and another distribution preserving selection protocol, for which we can show the diminishing returns property. Utilizing this result, we obtain a performance guarantee for the greedy optimization of MAC. Finally, we provide a computational study to show the effectiveness of greedy node selection strategies to solve MAC on general bipartite networks. <p><img src="https://epubs.siam.org/na101/home/literatum/publisher/siam/journals/covergifs/sjcodc/cover.jpg" alttext="cover image"/></p>
Average Submodularity of Maximizing Anticoordination in Network Games
10.1137/22M1506614
SIAM Journal on Control and Optimization
20240920T07:00:00Z
© 2024 Society for Industrial and Applied Mathematics
Soham Das
Ceyhun Eksin
Average Submodularity of Maximizing Anticoordination in Network Games
62
5
2639
2663
20241031T07:00:00Z
20241031T07:00:00Z
10.1137/22M1506614
https://epubs.siam.org/doi/abs/10.1137/22M1506614?af=R
© 2024 Society for Industrial and Applied Mathematics

Unbiased Parameter Estimation for Partially Observed Diffusions
https://epubs.siam.org/doi/abs/10.1137/23M160298X?af=R
SIAM Journal on Control and Optimization, <a href="https://epubs.siam.org/toc/sjcodc/62/5">Volume 62, Issue 5</a>, Page 26642694, October 2024. <br/> Abstract. In this article we consider the estimation of static parameters for a partially observed diffusion process with discretetime observations over a fixed time interval. In particular, we assume that one must timediscretize the partially observed diffusion process and work with the model with bias and consider maximizing the resulting loglikelihood. Using a novel double randomization scheme, based upon Markovian stochastic approximation we develop a new method to, in principle, unbiasedly estimate the static parameters, that is, to obtain the maximum likelihood estimator with no time discretization bias. Under appropriate mathematical assumptions we prove that our estimator is unbiased and investigate the method in several numerical examples, showing that it can empirically outperform the unbiased method in [J. Heng, J. Houssineau, and A. Jasra, J. Mach. Learn. Res., 25 (2024)].
SIAM Journal on Control and Optimization, Volume 62, Issue 5, Page 26642694, October 2024. <br/> Abstract. In this article we consider the estimation of static parameters for a partially observed diffusion process with discretetime observations over a fixed time interval. In particular, we assume that one must timediscretize the partially observed diffusion process and work with the model with bias and consider maximizing the resulting loglikelihood. Using a novel double randomization scheme, based upon Markovian stochastic approximation we develop a new method to, in principle, unbiasedly estimate the static parameters, that is, to obtain the maximum likelihood estimator with no time discretization bias. Under appropriate mathematical assumptions we prove that our estimator is unbiased and investigate the method in several numerical examples, showing that it can empirically outperform the unbiased method in [J. Heng, J. Houssineau, and A. Jasra, J. Mach. Learn. Res., 25 (2024)]. <p><img src="https://epubs.siam.org/na101/home/literatum/publisher/siam/journals/covergifs/sjcodc/cover.jpg" alttext="cover image"/></p>
Unbiased Parameter Estimation for Partially Observed Diffusions
10.1137/23M160298X
SIAM Journal on Control and Optimization
20240927T07:00:00Z
© 2024 Society for Industrial and Applied Mathematics
Elsiddig Awadelkarim
Ajay Jasra
Hamza Ruzayqat
Unbiased Parameter Estimation for Partially Observed Diffusions
62
5
2664
2694
20241031T07:00:00Z
20241031T07:00:00Z
10.1137/23M160298X
https://epubs.siam.org/doi/abs/10.1137/23M160298X?af=R
© 2024 Society for Industrial and Applied Mathematics

Multiple Lyapunov Functions and Memory: A Symbolic Dynamics Approach to Systems and Control
https://epubs.siam.org/doi/abs/10.1137/23M1589244?af=R
SIAM Journal on Control and Optimization, <a href="https://epubs.siam.org/toc/sjcodc/62/5">Volume 62, Issue 5</a>, Page 26952722, October 2024. <br/> Abstract. We propose a novel framework for the Lyapunov analysis of an important class of hybrid systems, inspired by the theory of symbolic dynamics and earlier results on the restricted class of switched systems. This new framework allows us to leverage language theory tools in order to provide a universal characterization of Lyapunov stability for this class of systems. We establish, in particular, a formal connection between multiple Lyapunov functions and techniques based on memorization and/or prediction of the discrete part of the state. This allows us to provide an equivalent (single) Lyapunov function, for any given multipleLyapunov criterion. By leveraging our languagetheoretic formalism, a new class of stability conditions is then obtained when considering both memory and future values of the state in a joint fashion, providing new numerical schemes that outperform existing technique. Our techniques are then illustrated on numerical examples.
SIAM Journal on Control and Optimization, Volume 62, Issue 5, Page 26952722, October 2024. <br/> Abstract. We propose a novel framework for the Lyapunov analysis of an important class of hybrid systems, inspired by the theory of symbolic dynamics and earlier results on the restricted class of switched systems. This new framework allows us to leverage language theory tools in order to provide a universal characterization of Lyapunov stability for this class of systems. We establish, in particular, a formal connection between multiple Lyapunov functions and techniques based on memorization and/or prediction of the discrete part of the state. This allows us to provide an equivalent (single) Lyapunov function, for any given multipleLyapunov criterion. By leveraging our languagetheoretic formalism, a new class of stability conditions is then obtained when considering both memory and future values of the state in a joint fashion, providing new numerical schemes that outperform existing technique. Our techniques are then illustrated on numerical examples. <p><img src="https://epubs.siam.org/na101/home/literatum/publisher/siam/journals/covergifs/sjcodc/cover.jpg" alttext="cover image"/></p>
Multiple Lyapunov Functions and Memory: A Symbolic Dynamics Approach to Systems and Control
10.1137/23M1589244
SIAM Journal on Control and Optimization
20240930T07:00:00Z
© 2024 Society for Industrial and Applied Mathematics
Matteo Della Rossa
Raphaël M. Jungers
Multiple Lyapunov Functions and Memory: A Symbolic Dynamics Approach to Systems and Control
62
5
2695
2722
20241031T07:00:00Z
20241031T07:00:00Z
10.1137/23M1589244
https://epubs.siam.org/doi/abs/10.1137/23M1589244?af=R
© 2024 Society for Industrial and Applied Mathematics

Further on Pinning Synchronization of Dynamical Networks with Coupling Delay
https://epubs.siam.org/doi/abs/10.1137/23M1578085?af=R
SIAM Journal on Control and Optimization, <a href="https://epubs.siam.org/toc/sjcodc/62/4">Volume 62, Issue 4</a>, Page 19331952, August 2024. <br/> Abstract. Though extensively studied, the longstanding pinning synchronization problem of dynamical networks with coupling delay has not been well solved until now. In this paper, we further investigate this problem. By proposing a system of functional differential inequalities, we derive synchronization criteria for dynamical networks with coupling delay under linear pinning control, where the threshold of the admissible delay and the control gain threshold are estimated. Since the estimated control gain threshold could be very large when the delay draws close to the delay threshold, we also use the adaptive pinning control scheme to avoid control gain estimation. Pinning synchronization criteria of networks under adaptive control are derived and the delay threshold is given. This is the first time that general coupling delay has been addressed in the field of pinning control. Finally, two numerical examples are presented to validate the theoretical results.
SIAM Journal on Control and Optimization, Volume 62, Issue 4, Page 19331952, August 2024. <br/> Abstract. Though extensively studied, the longstanding pinning synchronization problem of dynamical networks with coupling delay has not been well solved until now. In this paper, we further investigate this problem. By proposing a system of functional differential inequalities, we derive synchronization criteria for dynamical networks with coupling delay under linear pinning control, where the threshold of the admissible delay and the control gain threshold are estimated. Since the estimated control gain threshold could be very large when the delay draws close to the delay threshold, we also use the adaptive pinning control scheme to avoid control gain estimation. Pinning synchronization criteria of networks under adaptive control are derived and the delay threshold is given. This is the first time that general coupling delay has been addressed in the field of pinning control. Finally, two numerical examples are presented to validate the theoretical results. <p><img src="https://epubs.siam.org/na101/home/literatum/publisher/siam/journals/covergifs/sjcodc/cover.jpg" alttext="cover image"/></p>
Further on Pinning Synchronization of Dynamical Networks with Coupling Delay
10.1137/23M1578085
SIAM Journal on Control and Optimization
20240703T07:00:00Z
© 2024 Society for Industrial and Applied Mathematics
Shuaibing Zhu
Jinhu Lü
Further on Pinning Synchronization of Dynamical Networks with Coupling Delay
62
4
1933
1952
20240831T07:00:00Z
20240831T07:00:00Z
10.1137/23M1578085
https://epubs.siam.org/doi/abs/10.1137/23M1578085?af=R
© 2024 Society for Industrial and Applied Mathematics

On the Exact Boundary Controllability of Semilinear Wave Equations
https://epubs.siam.org/doi/abs/10.1137/23M1586598?af=R
SIAM Journal on Control and Optimization, <a href="https://epubs.siam.org/toc/sjcodc/62/4">Volume 62, Issue 4</a>, Page 19531976, August 2024. <br/> Abstract. We address the exact boundary controllability of the semilinear wave equation [math] posed over a bounded domain [math] of [math]. Assuming that [math] is continuous and satisfies the condition [math] for some [math] small enough and some [math] in [math], we apply the Schauder fixed point theorem to prove the uniform controllability for initial data in [math]. Then, assuming that [math] is in [math] and satisfies the condition [math], we apply the Banach fixed point theorem and exhibit a strongly convergent sequence to a statecontrol pair for the semilinear equation.
SIAM Journal on Control and Optimization, Volume 62, Issue 4, Page 19531976, August 2024. <br/> Abstract. We address the exact boundary controllability of the semilinear wave equation [math] posed over a bounded domain [math] of [math]. Assuming that [math] is continuous and satisfies the condition [math] for some [math] small enough and some [math] in [math], we apply the Schauder fixed point theorem to prove the uniform controllability for initial data in [math]. Then, assuming that [math] is in [math] and satisfies the condition [math], we apply the Banach fixed point theorem and exhibit a strongly convergent sequence to a statecontrol pair for the semilinear equation. <p><img src="https://epubs.siam.org/na101/home/literatum/publisher/siam/journals/covergifs/sjcodc/cover.jpg" alttext="cover image"/></p>
On the Exact Boundary Controllability of Semilinear Wave Equations
10.1137/23M1586598
SIAM Journal on Control and Optimization
20240703T07:00:00Z
© 2024 Society for Industrial and Applied Mathematics
Sue Claret
Jérôme Lemoine
Arnaud Münch
On the Exact Boundary Controllability of Semilinear Wave Equations
62
4
1953
1976
20240831T07:00:00Z
20240831T07:00:00Z
10.1137/23M1586598
https://epubs.siam.org/doi/abs/10.1137/23M1586598?af=R
© 2024 Society for Industrial and Applied Mathematics

Controlling a Vlasov–Poisson Plasma by a ParticleinCell Method Based on a Monte Carlo Framework
https://epubs.siam.org/doi/abs/10.1137/23M1563852?af=R
SIAM Journal on Control and Optimization, <a href="https://epubs.siam.org/toc/sjcodc/62/4">Volume 62, Issue 4</a>, Page 19772011, August 2024. <br/> Abstract. The Vlasov–Poisson system describes the time evolution of a plasma in the socalled collisionless regime. The investigation of a hightemperature plasma that is influenced by an exterior magnetic field is one of the most significant aspects of thermonuclear fusion research. In this paper, we formulate and analyze a kinetic optimal control problem for the Vlasov–Poisson system where the control is represented by an external magnetic field. The main goal of such optimal control problems is to confine the plasma to a certain region in phase space. We first investigate the optimal control problem in terms of mathematical analysis, i.e., we show the existence of at least one global minimizer and rigorously derive a firstorder necessary optimality condition for local minimizers by the adjoint approach. Then we build a Monte Carlo framework to solve the state equations as well as the adjoint equations by means of a particleincell method, and we apply a nonlinear conjugate gradient method to solve the optimization problem. Eventually, we present numerical experiments that successfully validate our optimization framework.
SIAM Journal on Control and Optimization, Volume 62, Issue 4, Page 19772011, August 2024. <br/> Abstract. The Vlasov–Poisson system describes the time evolution of a plasma in the socalled collisionless regime. The investigation of a hightemperature plasma that is influenced by an exterior magnetic field is one of the most significant aspects of thermonuclear fusion research. In this paper, we formulate and analyze a kinetic optimal control problem for the Vlasov–Poisson system where the control is represented by an external magnetic field. The main goal of such optimal control problems is to confine the plasma to a certain region in phase space. We first investigate the optimal control problem in terms of mathematical analysis, i.e., we show the existence of at least one global minimizer and rigorously derive a firstorder necessary optimality condition for local minimizers by the adjoint approach. Then we build a Monte Carlo framework to solve the state equations as well as the adjoint equations by means of a particleincell method, and we apply a nonlinear conjugate gradient method to solve the optimization problem. Eventually, we present numerical experiments that successfully validate our optimization framework. <p><img src="https://epubs.siam.org/na101/home/literatum/publisher/siam/journals/covergifs/sjcodc/cover.jpg" alttext="cover image"/></p>
Controlling a Vlasov–Poisson Plasma by a ParticleinCell Method Based on a Monte Carlo Framework
10.1137/23M1563852
SIAM Journal on Control and Optimization
20240710T07:00:00Z
© 2024 Society for Industrial and Applied Mathematics
Jan Bartsch
Patrik Knopf
Stefania Scheurer
Jörg Weber
Controlling a Vlasov–Poisson Plasma by a ParticleinCell Method Based on a Monte Carlo Framework
62
4
1977
2011
20240831T07:00:00Z
20240831T07:00:00Z
10.1137/23M1563852
https://epubs.siam.org/doi/abs/10.1137/23M1563852?af=R
© 2024 Society for Industrial and Applied Mathematics

Optimal Impulsive Control for Time Delay Systems
https://epubs.siam.org/doi/abs/10.1137/24M1632450?af=R
SIAM Journal on Control and Optimization, <a href="https://epubs.siam.org/toc/sjcodc/62/4">Volume 62, Issue 4</a>, Page 20122035, August 2024. <br/> Abstract. We introduce discontinuous solutions to nonlinear impulsive control systems with state time delays in the dynamics and derive necessary optimality conditions in the form of a maximum principle for associated optimal control problems. In the case without delays, if the measure control is scalar valued, the corresponding discontinuous state trajectory, understood as a limit of classical state trajectories for absolutely continuous controls approximating the measure, is unique. For vectorvalued measure controls, however, the limiting trajectory is not unique and a full description of the control must include additional “attached” controls affecting instantaneous state evolution at a discontinuity. For impulsive control systems with time delays we reveal a new phenomenon, namely, that the limiting state trajectory resulting from different approximations of a given measure control needs not to be unique, even in the scalar case. Correspondingly, our framework allows for additional attached controls, even though the measure control is scalar valued.
SIAM Journal on Control and Optimization, Volume 62, Issue 4, Page 20122035, August 2024. <br/> Abstract. We introduce discontinuous solutions to nonlinear impulsive control systems with state time delays in the dynamics and derive necessary optimality conditions in the form of a maximum principle for associated optimal control problems. In the case without delays, if the measure control is scalar valued, the corresponding discontinuous state trajectory, understood as a limit of classical state trajectories for absolutely continuous controls approximating the measure, is unique. For vectorvalued measure controls, however, the limiting trajectory is not unique and a full description of the control must include additional “attached” controls affecting instantaneous state evolution at a discontinuity. For impulsive control systems with time delays we reveal a new phenomenon, namely, that the limiting state trajectory resulting from different approximations of a given measure control needs not to be unique, even in the scalar case. Correspondingly, our framework allows for additional attached controls, even though the measure control is scalar valued. <p><img src="https://epubs.siam.org/na101/home/literatum/publisher/siam/journals/covergifs/sjcodc/cover.jpg" alttext="cover image"/></p>
Optimal Impulsive Control for Time Delay Systems
10.1137/24M1632450
SIAM Journal on Control and Optimization
20240710T07:00:00Z
© 2024 Society for Industrial and Applied Mathematics
Giovanni Fusco
Monica Motta
Richard Vinter
Optimal Impulsive Control for Time Delay Systems
62
4
2012
2035
20240831T07:00:00Z
20240831T07:00:00Z
10.1137/24M1632450
https://epubs.siam.org/doi/abs/10.1137/24M1632450?af=R
© 2024 Society for Industrial and Applied Mathematics

Gradient Flows for Regularized Stochastic Control Problems
https://epubs.siam.org/doi/abs/10.1137/20M1373645?af=R
SIAM Journal on Control and Optimization, <a href="https://epubs.siam.org/toc/sjcodc/62/4">Volume 62, Issue 4</a>, Page 20362070, August 2024. <br/> Abstract. This paper studies stochastic control problems with the action space taken to be probability measures, with the objective penalized by the relative entropy. We identify a suitable metric space on which we construct a gradient flow for the measurevalued control process, in the set of admissible controls, along which the cost functional is guaranteed to decrease. It is shown that any invariant measure of this gradient flow satisfies the Pontryagin optimality principle. If the problem we work with is sufficiently convex, the gradient flow converges exponentially fast. Furthermore, the optimal measurevalued control process admits a Bayesian interpretation, which means that one can incorporate prior knowledge when solving such stochastic control problems. This work is motivated by a desire to extend the theoretical underpinning for the convergence of stochastic gradient type algorithms widely employed in the reinforcement learning community to solve control problems.
SIAM Journal on Control and Optimization, Volume 62, Issue 4, Page 20362070, August 2024. <br/> Abstract. This paper studies stochastic control problems with the action space taken to be probability measures, with the objective penalized by the relative entropy. We identify a suitable metric space on which we construct a gradient flow for the measurevalued control process, in the set of admissible controls, along which the cost functional is guaranteed to decrease. It is shown that any invariant measure of this gradient flow satisfies the Pontryagin optimality principle. If the problem we work with is sufficiently convex, the gradient flow converges exponentially fast. Furthermore, the optimal measurevalued control process admits a Bayesian interpretation, which means that one can incorporate prior knowledge when solving such stochastic control problems. This work is motivated by a desire to extend the theoretical underpinning for the convergence of stochastic gradient type algorithms widely employed in the reinforcement learning community to solve control problems. <p><img src="https://epubs.siam.org/na101/home/literatum/publisher/siam/journals/covergifs/sjcodc/cover.jpg" alttext="cover image"/></p>
Gradient Flows for Regularized Stochastic Control Problems
10.1137/20M1373645
SIAM Journal on Control and Optimization
20240710T07:00:00Z
© 2024 Society for Industrial and Applied Mathematics
David Šiška
Łukasz Szpruch
Gradient Flows for Regularized Stochastic Control Problems
62
4
2036
2070
20240831T07:00:00Z
20240831T07:00:00Z
10.1137/20M1373645
https://epubs.siam.org/doi/abs/10.1137/20M1373645?af=R
© 2024 Society for Industrial and Applied Mathematics

Robust Funnel Model Predictive Control for Output Tracking with Prescribed Performance
https://epubs.siam.org/doi/abs/10.1137/23M1551195?af=R
SIAM Journal on Control and Optimization, <a href="https://epubs.siam.org/toc/sjcodc/62/4">Volume 62, Issue 4</a>, Page 20712097, August 2024. <br/> Abstract. We propose a novel robust Model Predictive Control (MPC) scheme for nonlinear multiinput multioutput systems of relative degree one with stable internal dynamics. The proposed algorithm is a combination of funnel MPC, i.e., MPC with a particular stage cost, and the modelfree adaptive funnel controller. The new robust funnel MPC scheme guarantees output tracking of reference signals within prescribed performance bounds—even in the presence of unknown disturbances and a structural modelplant mismatch. We show initial and recursive feasibility of the proposed control scheme without imposing terminal conditions or any requirements on the prediction horizon. Moreover, we allow for model updates at runtime. To this end, we propose a proper initialization strategy, which ensures that recursive feasibility is preserved. Finally, we validate the performance of the proposed robust MPC scheme by simulations.
SIAM Journal on Control and Optimization, Volume 62, Issue 4, Page 20712097, August 2024. <br/> Abstract. We propose a novel robust Model Predictive Control (MPC) scheme for nonlinear multiinput multioutput systems of relative degree one with stable internal dynamics. The proposed algorithm is a combination of funnel MPC, i.e., MPC with a particular stage cost, and the modelfree adaptive funnel controller. The new robust funnel MPC scheme guarantees output tracking of reference signals within prescribed performance bounds—even in the presence of unknown disturbances and a structural modelplant mismatch. We show initial and recursive feasibility of the proposed control scheme without imposing terminal conditions or any requirements on the prediction horizon. Moreover, we allow for model updates at runtime. To this end, we propose a proper initialization strategy, which ensures that recursive feasibility is preserved. Finally, we validate the performance of the proposed robust MPC scheme by simulations. <p><img src="https://epubs.siam.org/na101/home/literatum/publisher/siam/journals/covergifs/sjcodc/cover.jpg" alttext="cover image"/></p>
Robust Funnel Model Predictive Control for Output Tracking with Prescribed Performance
10.1137/23M1551195
SIAM Journal on Control and Optimization
20240712T07:00:00Z
© 2024 Society for Industrial and Applied Mathematics
Thomas Berger
Dario Dennstädt
Lukas Lanza
Karl Worthmann
Robust Funnel Model Predictive Control for Output Tracking with Prescribed Performance
62
4
2071
2097
20240831T07:00:00Z
20240831T07:00:00Z
10.1137/23M1551195
https://epubs.siam.org/doi/abs/10.1137/23M1551195?af=R
© 2024 Society for Industrial and Applied Mathematics

Existence of Optimal Pairs for Optimal Control Problems with States Constrained to Riemannian Manifolds
https://epubs.siam.org/doi/abs/10.1137/23M1584095?af=R
SIAM Journal on Control and Optimization, <a href="https://epubs.siam.org/toc/sjcodc/62/4">Volume 62, Issue 4</a>, Page 20982114, August 2024. <br/> Abstract. In this paper, we investigate the existence of optimal pairs for optimal control problems with their states constrained pointwise to Riemannian manifolds. For this purpose, by means of the Riemannian geometric tool, we introduce a crucial Cesaritype property, which is an extension of the classical Cesari property (see Definition 3.3, p. 51 in [L. D. Berkovitz, Optimal Control Theory, Appl. Math. Sci. 12, SpringerVerlag, New York, Heidelberg, 1974]) from the setting of Euclidean spaces to that of Riemannian manifolds. Moreover, we show the efficiency of our result by a concrete example.
SIAM Journal on Control and Optimization, Volume 62, Issue 4, Page 20982114, August 2024. <br/> Abstract. In this paper, we investigate the existence of optimal pairs for optimal control problems with their states constrained pointwise to Riemannian manifolds. For this purpose, by means of the Riemannian geometric tool, we introduce a crucial Cesaritype property, which is an extension of the classical Cesari property (see Definition 3.3, p. 51 in [L. D. Berkovitz, Optimal Control Theory, Appl. Math. Sci. 12, SpringerVerlag, New York, Heidelberg, 1974]) from the setting of Euclidean spaces to that of Riemannian manifolds. Moreover, we show the efficiency of our result by a concrete example. <p><img src="https://epubs.siam.org/na101/home/literatum/publisher/siam/journals/covergifs/sjcodc/cover.jpg" alttext="cover image"/></p>
Existence of Optimal Pairs for Optimal Control Problems with States Constrained to Riemannian Manifolds
10.1137/23M1584095
SIAM Journal on Control and Optimization
20240712T07:00:00Z
© 2024 Society for Industrial and Applied Mathematics
Li Deng
Xu Zhang
Existence of Optimal Pairs for Optimal Control Problems with States Constrained to Riemannian Manifolds
62
4
2098
2114
20240831T07:00:00Z
20240831T07:00:00Z
10.1137/23M1584095
https://epubs.siam.org/doi/abs/10.1137/23M1584095?af=R
© 2024 Society for Industrial and Applied Mathematics

RiskSensitive Average Markov Decision Processes in General Spaces
https://epubs.siam.org/doi/abs/10.1137/23M156118X?af=R
SIAM Journal on Control and Optimization, <a href="https://epubs.siam.org/toc/sjcodc/62/4">Volume 62, Issue 4</a>, Page 21152147, August 2024. <br/> Abstract. In this paper we study discretetime Markov decision processes with Borel state and action spaces under the risksensitive average cost criterion. The cost function can be unbounded. We introduce a new kernel and prove the quasicompactness of the kernel from which the multiplicative Poisson equation is derived. Moreover, we develop a new approach to show the existence of a solution to the risksensitive average cost optimality equation and obtain the existence of an optimal deterministic stationary policy. Furthermore, we give two examples to illustrate our results.
SIAM Journal on Control and Optimization, Volume 62, Issue 4, Page 21152147, August 2024. <br/> Abstract. In this paper we study discretetime Markov decision processes with Borel state and action spaces under the risksensitive average cost criterion. The cost function can be unbounded. We introduce a new kernel and prove the quasicompactness of the kernel from which the multiplicative Poisson equation is derived. Moreover, we develop a new approach to show the existence of a solution to the risksensitive average cost optimality equation and obtain the existence of an optimal deterministic stationary policy. Furthermore, we give two examples to illustrate our results. <p><img src="https://epubs.siam.org/na101/home/literatum/publisher/siam/journals/covergifs/sjcodc/cover.jpg" alttext="cover image"/></p>
RiskSensitive Average Markov Decision Processes in General Spaces
10.1137/23M156118X
SIAM Journal on Control and Optimization
20240712T07:00:00Z
© 2024 Society for Industrial and Applied Mathematics
Xian Chen
Qingda Wei
RiskSensitive Average Markov Decision Processes in General Spaces
62
4
2115
2147
20240831T07:00:00Z
20240831T07:00:00Z
10.1137/23M156118X
https://epubs.siam.org/doi/abs/10.1137/23M156118X?af=R
© 2024 Society for Industrial and Applied Mathematics

On Markov Perfect Equilibria in Discounted Stochastic ARAT Games
https://epubs.siam.org/doi/abs/10.1137/23M1592365?af=R
SIAM Journal on Control and Optimization, <a href="https://epubs.siam.org/toc/sjcodc/62/4">Volume 62, Issue 4</a>, Page 21482175, August 2024. <br/> Abstract. In this paper, we study discounted stochastic games with an additive rewards and transitions ([math]) structure. We assume that the transition probabilities are dominated by some probability measures on a countably generated measurable state space and are norm continuous in actions of the players. We prove the existence of Markov perfect equilibria in which the players can use randomization on two pure actions in each state. When the state space is countable, then we show that there exists a pure Markov perfect equilibrium. Assuming additionally that the transition probabilities have no conditional atoms, we establish some existence results on pure Markov perfect equilibria for [math] games with uncountable state space using a version of Lyapunov’s theorem for conditional expectation of correspondences due to Dynkin and Evstigneev. We also include a wideranging discussion on equilibria for discounted stochastic games with a general state space.
SIAM Journal on Control and Optimization, Volume 62, Issue 4, Page 21482175, August 2024. <br/> Abstract. In this paper, we study discounted stochastic games with an additive rewards and transitions ([math]) structure. We assume that the transition probabilities are dominated by some probability measures on a countably generated measurable state space and are norm continuous in actions of the players. We prove the existence of Markov perfect equilibria in which the players can use randomization on two pure actions in each state. When the state space is countable, then we show that there exists a pure Markov perfect equilibrium. Assuming additionally that the transition probabilities have no conditional atoms, we establish some existence results on pure Markov perfect equilibria for [math] games with uncountable state space using a version of Lyapunov’s theorem for conditional expectation of correspondences due to Dynkin and Evstigneev. We also include a wideranging discussion on equilibria for discounted stochastic games with a general state space. <p><img src="https://epubs.siam.org/na101/home/literatum/publisher/siam/journals/covergifs/sjcodc/cover.jpg" alttext="cover image"/></p>
On Markov Perfect Equilibria in Discounted Stochastic ARAT Games
10.1137/23M1592365
SIAM Journal on Control and Optimization
20240716T07:00:00Z
© 2024 Society for Industrial and Applied Mathematics
Anna Jaśkiewicz
Andrzej S. Nowak
On Markov Perfect Equilibria in Discounted Stochastic ARAT Games
62
4
2148
2175
20240831T07:00:00Z
20240831T07:00:00Z
10.1137/23M1592365
https://epubs.siam.org/doi/abs/10.1137/23M1592365?af=R
© 2024 Society for Industrial and Applied Mathematics

GraphStructured Tensor Optimization for Nonlinear Density Control and Mean Field Games
https://epubs.siam.org/doi/abs/10.1137/23M1571587?af=R
SIAM Journal on Control and Optimization, <a href="https://epubs.siam.org/toc/sjcodc/62/4">Volume 62, Issue 4</a>, Page 21762202, August 2024. <br/> Abstract. In this work we develop a numerical method for solving a type of convex graphstructured tensor optimization problem. This type of problem, which can be seen as a generalization of multimarginal optimal transport problems with graphstructured costs, appears in many applications. Examples are unbalanced optimal transport and multispecies potential mean field games, where the latter is a class of nonlinear density control problems. The method we develop is based on coordinate ascent in a Lagrangian dual, and under mild assumptions we prove that the algorithm converges globally. Moreover, under a set of stricter assumptions, the algorithm converges Rlinearly. To perform the coordinate ascent steps one has to compute projections of the tensor, and doing so by brute force is in general not computationally feasible. Nevertheless, for certain graph structures it is possible to derive efficient methods for computing these projections, and here we specifically consider the graph structure that occurs in multispecies potential mean field games. We also illustrate the methodology on a numerical example from this problem class.
SIAM Journal on Control and Optimization, Volume 62, Issue 4, Page 21762202, August 2024. <br/> Abstract. In this work we develop a numerical method for solving a type of convex graphstructured tensor optimization problem. This type of problem, which can be seen as a generalization of multimarginal optimal transport problems with graphstructured costs, appears in many applications. Examples are unbalanced optimal transport and multispecies potential mean field games, where the latter is a class of nonlinear density control problems. The method we develop is based on coordinate ascent in a Lagrangian dual, and under mild assumptions we prove that the algorithm converges globally. Moreover, under a set of stricter assumptions, the algorithm converges Rlinearly. To perform the coordinate ascent steps one has to compute projections of the tensor, and doing so by brute force is in general not computationally feasible. Nevertheless, for certain graph structures it is possible to derive efficient methods for computing these projections, and here we specifically consider the graph structure that occurs in multispecies potential mean field games. We also illustrate the methodology on a numerical example from this problem class. <p><img src="https://epubs.siam.org/na101/home/literatum/publisher/siam/journals/covergifs/sjcodc/cover.jpg" alttext="cover image"/></p>
GraphStructured Tensor Optimization for Nonlinear Density Control and Mean Field Games
10.1137/23M1571587
SIAM Journal on Control and Optimization
20240716T07:00:00Z
© 2024 Society for Industrial and Applied Mathematics
Axel Ringh
Isabel Haasler
Yongxin Chen
Johan Karlsson
GraphStructured Tensor Optimization for Nonlinear Density Control and Mean Field Games
62
4
2176
2202
20240831T07:00:00Z
20240831T07:00:00Z
10.1137/23M1571587
https://epubs.siam.org/doi/abs/10.1137/23M1571587?af=R
© 2024 Society for Industrial and Applied Mathematics

ZeroSum Stopper Versus SingularController Games with Constrained Control Directions
https://epubs.siam.org/doi/abs/10.1137/23M1579558?af=R
SIAM Journal on Control and Optimization, <a href="https://epubs.siam.org/toc/sjcodc/62/4">Volume 62, Issue 4</a>, Page 22032228, August 2024. <br/> Abstract. We consider a class of zerosum stopper versus singularcontroller games in which the controller can only act on a subset [math] of the [math] coordinates of a controlled diffusion. Due to the constraint on the control directions these games fall outside the framework of recently studied variational methods. In this paper we develop an approximation procedure, based on [math]stability estimates for the controlled diffusion process and almost sure convergence of suitable stopping times. That allows us to prove existence of the game’s value and to obtain an optimal strategy for the stopper under continuity and growth conditions on the payoff functions. This class of games is a natural extension of (singleagent) singular control problems, studied in the literature, with similar constraints on the admissible controls.
SIAM Journal on Control and Optimization, Volume 62, Issue 4, Page 22032228, August 2024. <br/> Abstract. We consider a class of zerosum stopper versus singularcontroller games in which the controller can only act on a subset [math] of the [math] coordinates of a controlled diffusion. Due to the constraint on the control directions these games fall outside the framework of recently studied variational methods. In this paper we develop an approximation procedure, based on [math]stability estimates for the controlled diffusion process and almost sure convergence of suitable stopping times. That allows us to prove existence of the game’s value and to obtain an optimal strategy for the stopper under continuity and growth conditions on the payoff functions. This class of games is a natural extension of (singleagent) singular control problems, studied in the literature, with similar constraints on the admissible controls. <p><img src="https://epubs.siam.org/na101/home/literatum/publisher/siam/journals/covergifs/sjcodc/cover.jpg" alttext="cover image"/></p>
ZeroSum Stopper Versus SingularController Games with Constrained Control Directions
10.1137/23M1579558
SIAM Journal on Control and Optimization
20240719T07:00:00Z
© 2024 Society for Industrial and Applied Mathematics
Andrea Bovo
Tiziano De Angelis
Jan Palczewski
ZeroSum Stopper Versus SingularController Games with Constrained Control Directions
62
4
2203
2228
20240831T07:00:00Z
20240831T07:00:00Z
10.1137/23M1579558
https://epubs.siam.org/doi/abs/10.1137/23M1579558?af=R
© 2024 Society for Industrial and Applied Mathematics

Deep Relaxation of Controlled Stochastic Gradient Descent via Singular Perturbations
https://epubs.siam.org/doi/abs/10.1137/23M1544878?af=R
SIAM Journal on Control and Optimization, <a href="https://epubs.siam.org/toc/sjcodc/62/4">Volume 62, Issue 4</a>, Page 22292253, August 2024. <br/> Abstract. We consider a singularly perturbed system of stochastic differential equations proposed by Chaudhari et al. (Res. Math. Sci. 2018) to approximate the entropic gradient descent in the optimization of deep neural networks via homogenization. We embed it in a much larger class of twoscale stochastic control problems and rely on convergence results for Hamilton–Jacobi–Bellman equations with unbounded data proved recently by ourselves (ESAIM Control Optim. Calc. Var. 2023). We show that the limit of the value functions is itself the value function of an effective control problem with extended controls and that the trajectories of the perturbed system converge in a suitable sense to the trajectories of the limiting effective control system. These rigorous results improve the understanding of the convergence of the algorithms used by Chaudhari et al., as well as of their possible extensions where some tuning parameters are modeled as dynamic controls.
SIAM Journal on Control and Optimization, Volume 62, Issue 4, Page 22292253, August 2024. <br/> Abstract. We consider a singularly perturbed system of stochastic differential equations proposed by Chaudhari et al. (Res. Math. Sci. 2018) to approximate the entropic gradient descent in the optimization of deep neural networks via homogenization. We embed it in a much larger class of twoscale stochastic control problems and rely on convergence results for Hamilton–Jacobi–Bellman equations with unbounded data proved recently by ourselves (ESAIM Control Optim. Calc. Var. 2023). We show that the limit of the value functions is itself the value function of an effective control problem with extended controls and that the trajectories of the perturbed system converge in a suitable sense to the trajectories of the limiting effective control system. These rigorous results improve the understanding of the convergence of the algorithms used by Chaudhari et al., as well as of their possible extensions where some tuning parameters are modeled as dynamic controls. <p><img src="https://epubs.siam.org/na101/home/literatum/publisher/siam/journals/covergifs/sjcodc/cover.jpg" alttext="cover image"/></p>
Deep Relaxation of Controlled Stochastic Gradient Descent via Singular Perturbations
10.1137/23M1544878
SIAM Journal on Control and Optimization
20240724T07:00:00Z
© 2024 Society for Industrial and Applied Mathematics
Martino Bardi
Hicham Kouhkouh
Deep Relaxation of Controlled Stochastic Gradient Descent via Singular Perturbations
62
4
2229
2253
20240831T07:00:00Z
20240831T07:00:00Z
10.1137/23M1544878
https://epubs.siam.org/doi/abs/10.1137/23M1544878?af=R
© 2024 Society for Industrial and Applied Mathematics

DualGain Function Based PrescribedTime Output Feedback Control Nonlinear TimeDelay Systems
https://epubs.siam.org/doi/abs/10.1137/23M1556496?af=R
SIAM Journal on Control and Optimization, <a href="https://epubs.siam.org/toc/sjcodc/62/4">Volume 62, Issue 4</a>, Page 22542272, August 2024. <br/> Abstract. This paper investigates the prescribedtime output feedback stabilization problem for a class of nonlinear timedelay systems. First, a novel dualgain function is put forward by exploiting the dynamic gain and the timevarying gain function to design the reducedorder observer for reconstructing unavailable states. Then, by utilizing the Lyapunov–Krasovskii functional and state variables of the reducedorder observer, a new prescribedtime controller is presented based on the nonscaling design framework. Since no state scaling is required in controller design process under this framework, our control strategy is simpler and can greatly reduce the computational burden. Further, compared with the previous prescribedtime stabilization results, our designed controller acts on the entire time domain, not just a limited time interval. Based on our proposed stability criterion, it is proved that the controller can render that all system state variables converge to the origin within the prescribed time. Finally, a numerical example is provided to illustrate the effectiveness of the proposed control strategy.
SIAM Journal on Control and Optimization, Volume 62, Issue 4, Page 22542272, August 2024. <br/> Abstract. This paper investigates the prescribedtime output feedback stabilization problem for a class of nonlinear timedelay systems. First, a novel dualgain function is put forward by exploiting the dynamic gain and the timevarying gain function to design the reducedorder observer for reconstructing unavailable states. Then, by utilizing the Lyapunov–Krasovskii functional and state variables of the reducedorder observer, a new prescribedtime controller is presented based on the nonscaling design framework. Since no state scaling is required in controller design process under this framework, our control strategy is simpler and can greatly reduce the computational burden. Further, compared with the previous prescribedtime stabilization results, our designed controller acts on the entire time domain, not just a limited time interval. Based on our proposed stability criterion, it is proved that the controller can render that all system state variables converge to the origin within the prescribed time. Finally, a numerical example is provided to illustrate the effectiveness of the proposed control strategy. <p><img src="https://epubs.siam.org/na101/home/literatum/publisher/siam/journals/covergifs/sjcodc/cover.jpg" alttext="cover image"/></p>
DualGain Function Based PrescribedTime Output Feedback Control Nonlinear TimeDelay Systems
10.1137/23M1556496
SIAM Journal on Control and Optimization
20240805T07:00:00Z
© 2024 Society for Industrial and Applied Mathematics
Pengju Ning
Sergey N. Dashkovskiy
Changchun Hua
Kuo Li
DualGain Function Based PrescribedTime Output Feedback Control Nonlinear TimeDelay Systems
62
4
2254
2272
20240831T07:00:00Z
20240831T07:00:00Z
10.1137/23M1556496
https://epubs.siam.org/doi/abs/10.1137/23M1556496?af=R
© 2024 Society for Industrial and Applied Mathematics

An Observer for Pipeline Flow with Hydrogen Blending in Gas Networks: Exponential Synchronization
https://epubs.siam.org/doi/abs/10.1137/23M1563840?af=R
SIAM Journal on Control and Optimization, <a href="https://epubs.siam.org/toc/sjcodc/62/4">Volume 62, Issue 4</a>, Page 22732296, August 2024. <br/> Abstract. We consider a state estimation problem for gas flows in pipeline networks where hydrogen is blended into the natural gas. The flow is modeled by the quasilinear isothermal Euler equations coupled to an advection equation on a graph. The flow through the vertices where the pipes are connected is governed by algebraic node conditions. The state is approximated by an observer system that uses nodal measurements. We prove that the state of the observer system converges to the original system state exponentially fast in the [math]norm if the measurements are exact. If measurement errors are present we show that the observer state approximates the original system state up to an error that is proportional to the maximal measurement error. The proof of the synchronization result uses Lyapunov functions with exponential weights.
SIAM Journal on Control and Optimization, Volume 62, Issue 4, Page 22732296, August 2024. <br/> Abstract. We consider a state estimation problem for gas flows in pipeline networks where hydrogen is blended into the natural gas. The flow is modeled by the quasilinear isothermal Euler equations coupled to an advection equation on a graph. The flow through the vertices where the pipes are connected is governed by algebraic node conditions. The state is approximated by an observer system that uses nodal measurements. We prove that the state of the observer system converges to the original system state exponentially fast in the [math]norm if the measurements are exact. If measurement errors are present we show that the observer state approximates the original system state up to an error that is proportional to the maximal measurement error. The proof of the synchronization result uses Lyapunov functions with exponential weights. <p><img src="https://epubs.siam.org/na101/home/literatum/publisher/siam/journals/covergifs/sjcodc/cover.jpg" alttext="cover image"/></p>
An Observer for Pipeline Flow with Hydrogen Blending in Gas Networks: Exponential Synchronization
10.1137/23M1563840
SIAM Journal on Control and Optimization
20240807T07:00:00Z
© 2024 Society for Industrial and Applied Mathematics
Martin Gugat
Jan Giesselmann
An Observer for Pipeline Flow with Hydrogen Blending in Gas Networks: Exponential Synchronization
62
4
2273
2296
20240831T07:00:00Z
20240831T07:00:00Z
10.1137/23M1563840
https://epubs.siam.org/doi/abs/10.1137/23M1563840?af=R
© 2024 Society for Industrial and Applied Mathematics

The Unconditional Consensus Control through Leadership for the Delayed Hegselmann–Krause Model
https://epubs.siam.org/doi/abs/10.1137/23M1588858?af=R
SIAM Journal on Control and Optimization, <a href="https://epubs.siam.org/toc/sjcodc/62/4">Volume 62, Issue 4</a>, Page 22972318, August 2024. <br/> Abstract. We consider the Hegselmann–Krause opinion formation model with leadership and time delay, which is a generalization of the model studied by Wongkaew, Caponigro, and Borzi [Math. Models Methods Appl. Sci., 25 (2015), pp. 565–585], dealing with the control strategies without time delay effect. Numerical simulations suggest that the consensus can still emerge asymptotically in the opinion evolution flow under the leader’s control even when the time delay is large. However, rigorous theoretical analysis for such consensus dynamics still lacks a complete understanding. In this paper, we present an iterated framework for the consensus control behavior for the delayed Hegselmann–Krause model with leadership, without any restriction on the length of the time delay. After that, we design a simple control strategy which can steer all agents to any target opinion and give a theoretical proof of its validity. Numerical simulations are performed to confirm theoretical results.
SIAM Journal on Control and Optimization, Volume 62, Issue 4, Page 22972318, August 2024. <br/> Abstract. We consider the Hegselmann–Krause opinion formation model with leadership and time delay, which is a generalization of the model studied by Wongkaew, Caponigro, and Borzi [Math. Models Methods Appl. Sci., 25 (2015), pp. 565–585], dealing with the control strategies without time delay effect. Numerical simulations suggest that the consensus can still emerge asymptotically in the opinion evolution flow under the leader’s control even when the time delay is large. However, rigorous theoretical analysis for such consensus dynamics still lacks a complete understanding. In this paper, we present an iterated framework for the consensus control behavior for the delayed Hegselmann–Krause model with leadership, without any restriction on the length of the time delay. After that, we design a simple control strategy which can steer all agents to any target opinion and give a theoretical proof of its validity. Numerical simulations are performed to confirm theoretical results. <p><img src="https://epubs.siam.org/na101/home/literatum/publisher/siam/journals/covergifs/sjcodc/cover.jpg" alttext="cover image"/></p>
The Unconditional Consensus Control through Leadership for the Delayed Hegselmann–Krause Model
10.1137/23M1588858
SIAM Journal on Control and Optimization
20240808T07:00:00Z
© 2024 Society for Industrial and Applied Mathematics
Linglong Du
Jianwen Zhu
Feng Xie
The Unconditional Consensus Control through Leadership for the Delayed Hegselmann–Krause Model
62
4
2297
2318
20240831T07:00:00Z
20240831T07:00:00Z
10.1137/23M1588858
https://epubs.siam.org/doi/abs/10.1137/23M1588858?af=R
© 2024 Society for Industrial and Applied Mathematics

Sharp Equilibria for TimeInconsistent MeanField Stopping Games
https://epubs.siam.org/doi/abs/10.1137/23M1625512?af=R
SIAM Journal on Control and Optimization, <a href="https://epubs.siam.org/toc/sjcodc/62/4">Volume 62, Issue 4</a>, Page 23192345, August 2024. <br/> Abstract. We investigate timeinconsistent meanfield stopping games under nonexponential discounting in discrete time. At the intrapersonal level, each player plays against her future selves as a result of the time inconsistency caused by nonexponential discounting. At the interpersonal level, she plays against other players due to players’ interaction via the proportion of players that have stopped. We look for sharp meanfield equilibria (MFEs), such that given other players’ stopping policies, the representative player’s strategy not only is an intrapersonal equilibrium, but also an optimal one among all such intrapersonal equilibria. We analyze two classes of examples. The first one is on timeinconsistent bankrun models, and we construct an (optimal) sharp MFE by a monotone iteration scheme. The second one has a Markovian setup and no common noise, and we show the existence of a sharp MFE based on the Tikhonov fixedpoint theorem.
SIAM Journal on Control and Optimization, Volume 62, Issue 4, Page 23192345, August 2024. <br/> Abstract. We investigate timeinconsistent meanfield stopping games under nonexponential discounting in discrete time. At the intrapersonal level, each player plays against her future selves as a result of the time inconsistency caused by nonexponential discounting. At the interpersonal level, she plays against other players due to players’ interaction via the proportion of players that have stopped. We look for sharp meanfield equilibria (MFEs), such that given other players’ stopping policies, the representative player’s strategy not only is an intrapersonal equilibrium, but also an optimal one among all such intrapersonal equilibria. We analyze two classes of examples. The first one is on timeinconsistent bankrun models, and we construct an (optimal) sharp MFE by a monotone iteration scheme. The second one has a Markovian setup and no common noise, and we show the existence of a sharp MFE based on the Tikhonov fixedpoint theorem. <p><img src="https://epubs.siam.org/na101/home/literatum/publisher/siam/journals/covergifs/sjcodc/cover.jpg" alttext="cover image"/></p>
Sharp Equilibria for TimeInconsistent MeanField Stopping Games
10.1137/23M1625512
SIAM Journal on Control and Optimization
20240808T07:00:00Z
© 2024 Society for Industrial and Applied Mathematics
Ziyuan Wang
Zhou Zhou
Sharp Equilibria for TimeInconsistent MeanField Stopping Games
62
4
2319
2345
20240831T07:00:00Z
20240831T07:00:00Z
10.1137/23M1625512
https://epubs.siam.org/doi/abs/10.1137/23M1625512?af=R
© 2024 Society for Industrial and Applied Mathematics

Constituting an Extension of Lyapunov’s Direct Method
https://epubs.siam.org/doi/abs/10.1137/23M1595242?af=R
SIAM Journal on Control and Optimization, <a href="https://epubs.siam.org/toc/sjcodc/62/4">Volume 62, Issue 4</a>, Page 23462366, August 2024. <br/> Abstract. This paper investigates new sufficient conditions for the stability, asymptotic stability, and global asymptotic stability of nonlinear autonomous systems, specifically in cases where the first derivative of the Lyapunov function candidate may have both positive and negative values on its domain. The main contribution of this approach is the introduction of a new auxiliary function that relaxes the stability conditions, allowing the first derivative of the Lyapunov function candidate to be less than or equal to a nonnegative function. The suggested auxiliary function should be integrable within our first theorem. Meanwhile, our first corollary presents a technique that simplifies the task by establishing specific conditions related to differential inequalities. This weaker condition in the proposed results enables the establishment of stability properties in cases where the Lyapunov function candidate is not well chosen or finding a Lyapunov function is not straightforward. Additionally, it is proven that the original Lyapunov method for autonomous systems is a special case of our first theorem. Furthermore, it is demonstrated that assumptions in previous studies, such as Matrosov’s theorem or results on higherorder derivatives of the Lyapunov function, guarantee the existence of our auxiliary function. Finally, lemmas are provided to construct these auxiliary functions, and examples are presented to demonstrate the effectiveness of this approach. This work will contribute to the development of stability analysis techniques for nonlinear autonomous systems.
SIAM Journal on Control and Optimization, Volume 62, Issue 4, Page 23462366, August 2024. <br/> Abstract. This paper investigates new sufficient conditions for the stability, asymptotic stability, and global asymptotic stability of nonlinear autonomous systems, specifically in cases where the first derivative of the Lyapunov function candidate may have both positive and negative values on its domain. The main contribution of this approach is the introduction of a new auxiliary function that relaxes the stability conditions, allowing the first derivative of the Lyapunov function candidate to be less than or equal to a nonnegative function. The suggested auxiliary function should be integrable within our first theorem. Meanwhile, our first corollary presents a technique that simplifies the task by establishing specific conditions related to differential inequalities. This weaker condition in the proposed results enables the establishment of stability properties in cases where the Lyapunov function candidate is not well chosen or finding a Lyapunov function is not straightforward. Additionally, it is proven that the original Lyapunov method for autonomous systems is a special case of our first theorem. Furthermore, it is demonstrated that assumptions in previous studies, such as Matrosov’s theorem or results on higherorder derivatives of the Lyapunov function, guarantee the existence of our auxiliary function. Finally, lemmas are provided to construct these auxiliary functions, and examples are presented to demonstrate the effectiveness of this approach. This work will contribute to the development of stability analysis techniques for nonlinear autonomous systems. <p><img src="https://epubs.siam.org/na101/home/literatum/publisher/siam/journals/covergifs/sjcodc/cover.jpg" alttext="cover image"/></p>
Constituting an Extension of Lyapunov’s Direct Method
10.1137/23M1595242
SIAM Journal on Control and Optimization
20240812T07:00:00Z
© 2024 Society for Industrial and Applied Mathematics
M. Akbarian
N. Pariz
A. Heydari
Constituting an Extension of Lyapunov’s Direct Method
62
4
2346
2366
20240831T07:00:00Z
20240831T07:00:00Z
10.1137/23M1595242
https://epubs.siam.org/doi/abs/10.1137/23M1595242?af=R
© 2024 Society for Industrial and Applied Mathematics

On Borkar and Young Relaxed Control Topologies and Continuous Dependence of Invariant Measures on Control Policy
https://epubs.siam.org/doi/abs/10.1137/23M1571940?af=R
SIAM Journal on Control and Optimization, <a href="https://epubs.siam.org/toc/sjcodc/62/4">Volume 62, Issue 4</a>, Page 23672386, August 2024. <br/> Abstract. In deterministic and stochastic control theory, relaxed or randomized control policies allow for versatile mathematical analysis (on continuity, compactness, convexity, and approximations) to be applicable with no artificial restrictions on the classes of control policies considered, leading to very general existence results on optimal measurable policies under various setups and information structures. On relaxed controls, two studied topologies are the Young and Borkar (weak[math]) topologies on spaces of functions from a state/measurement space to the space of probability measures on control action spaces; the former via a weak convergence topology on probability measures on a product space with a fixed marginal on the input (state) space, and the latter via a weak[math] topology on randomized policies viewed as maps from states/measurements to the space of signed measures with bounded variation. We establish implication and equivalence conditions between the Young and Borkar topologies on control policies. We then show that, under some conditions, for a controlled Markov chain with standard Borel spaces the invariant measure is weakly continuous on the space of stationary control policies defined by either of these topologies. An implication is nearoptimality of quantized stationary policies in state and actions or continuous stationary and deterministic policies for average cost control under two sets of continuity conditions (with either weak continuity in the stateaction pair or strong continuity in the action for each state) on transition kernels.
SIAM Journal on Control and Optimization, Volume 62, Issue 4, Page 23672386, August 2024. <br/> Abstract. In deterministic and stochastic control theory, relaxed or randomized control policies allow for versatile mathematical analysis (on continuity, compactness, convexity, and approximations) to be applicable with no artificial restrictions on the classes of control policies considered, leading to very general existence results on optimal measurable policies under various setups and information structures. On relaxed controls, two studied topologies are the Young and Borkar (weak[math]) topologies on spaces of functions from a state/measurement space to the space of probability measures on control action spaces; the former via a weak convergence topology on probability measures on a product space with a fixed marginal on the input (state) space, and the latter via a weak[math] topology on randomized policies viewed as maps from states/measurements to the space of signed measures with bounded variation. We establish implication and equivalence conditions between the Young and Borkar topologies on control policies. We then show that, under some conditions, for a controlled Markov chain with standard Borel spaces the invariant measure is weakly continuous on the space of stationary control policies defined by either of these topologies. An implication is nearoptimality of quantized stationary policies in state and actions or continuous stationary and deterministic policies for average cost control under two sets of continuity conditions (with either weak continuity in the stateaction pair or strong continuity in the action for each state) on transition kernels. <p><img src="https://epubs.siam.org/na101/home/literatum/publisher/siam/journals/covergifs/sjcodc/cover.jpg" alttext="cover image"/></p>
On Borkar and Young Relaxed Control Topologies and Continuous Dependence of Invariant Measures on Control Policy
10.1137/23M1571940
SIAM Journal on Control and Optimization
20240812T07:00:00Z
© 2024 Society for Industrial and Applied Mathematics
Serdar Yüksel
On Borkar and Young Relaxed Control Topologies and Continuous Dependence of Invariant Measures on Control Policy
62
4
2367
2386
20240831T07:00:00Z
20240831T07:00:00Z
10.1137/23M1571940
https://epubs.siam.org/doi/abs/10.1137/23M1571940?af=R
© 2024 Society for Industrial and Applied Mathematics

Chain Controllability of Linear Control Systems
https://epubs.siam.org/doi/abs/10.1137/23M1626347?af=R
SIAM Journal on Control and Optimization, <a href="https://epubs.siam.org/toc/sjcodc/62/4">Volume 62, Issue 4</a>, Page 23872411, August 2024. <br/> Abstract. For linear control systems with bounded control range, chain controllability properties are analyzed. It is shown that there exists a unique chain control set and that it equals the sum of the control set around the origin and the center Lyapunov space of the homogeneous part. For the proof, the linear control system is extended to a bilinear control system on an augmented state space. This system induces a control system on projective space. For the associated control flow, attractorrepeller decompositions are used to show that the control system on projective space has a unique chain control set that is not contained in the equator. It is given by the image of the chain control set of the original linear control system.
SIAM Journal on Control and Optimization, Volume 62, Issue 4, Page 23872411, August 2024. <br/> Abstract. For linear control systems with bounded control range, chain controllability properties are analyzed. It is shown that there exists a unique chain control set and that it equals the sum of the control set around the origin and the center Lyapunov space of the homogeneous part. For the proof, the linear control system is extended to a bilinear control system on an augmented state space. This system induces a control system on projective space. For the associated control flow, attractorrepeller decompositions are used to show that the control system on projective space has a unique chain control set that is not contained in the equator. It is given by the image of the chain control set of the original linear control system. <p><img src="https://epubs.siam.org/na101/home/literatum/publisher/siam/journals/covergifs/sjcodc/cover.jpg" alttext="cover image"/></p>
Chain Controllability of Linear Control Systems
10.1137/23M1626347
SIAM Journal on Control and Optimization
20240819T07:00:00Z
© 2024 Society for Industrial and Applied Mathematics
Fritz Colonius
Alexandre J. Santana
Eduardo C. Viscovini
Chain Controllability of Linear Control Systems
62
4
2387
2411
20240831T07:00:00Z
20240831T07:00:00Z
10.1137/23M1626347
https://epubs.siam.org/doi/abs/10.1137/23M1626347?af=R
© 2024 Society for Industrial and Applied Mathematics

The Hybrid Maximum Principle for Optimal Control Problems with Spatially Heterogeneous Dynamics is a Consequence of a Pontryagin Maximum Principle for [math]Local Solutions
https://epubs.siam.org/doi/abs/10.1137/23M155311X?af=R
SIAM Journal on Control and Optimization, <a href="https://epubs.siam.org/toc/sjcodc/62/4">Volume 62, Issue 4</a>, Page 24122432, August 2024. <br/> Abstract. The title of the present work is a nod to the paper “The hybrid maximum principle is a consequence of Pontryagin maximum principle” by Dmitruk and Kaganovich [Systems Control Lett., 57 (2008), pp. 964–970]. We investigate a similar framework of hybrid optimal control problems that is also different from Dmitruk and Kaganovich’s. Precisely, we consider a general control system that is described by a differential equation involving a spatially heterogeneous dynamics. In that context, the sequence of dynamics followed by the trajectory and the corresponding switching times are fully constrained by the state position. We prove with an explicit counterexample that the augmentation technique used by Dmitruk and Kaganovich cannot be fully applied to our setting, but we show that it can be adapted by introducing a new notion of local solution to classical optimal control problems and by establishing a corresponding Pontryagin maximum principle. Thanks to this method, we derive a hybrid maximum principle adapted to our setting, with a simple proof that does not require any technical tools (such as implicit function arguments) to handle the dynamical discontinuities.
SIAM Journal on Control and Optimization, Volume 62, Issue 4, Page 24122432, August 2024. <br/> Abstract. The title of the present work is a nod to the paper “The hybrid maximum principle is a consequence of Pontryagin maximum principle” by Dmitruk and Kaganovich [Systems Control Lett., 57 (2008), pp. 964–970]. We investigate a similar framework of hybrid optimal control problems that is also different from Dmitruk and Kaganovich’s. Precisely, we consider a general control system that is described by a differential equation involving a spatially heterogeneous dynamics. In that context, the sequence of dynamics followed by the trajectory and the corresponding switching times are fully constrained by the state position. We prove with an explicit counterexample that the augmentation technique used by Dmitruk and Kaganovich cannot be fully applied to our setting, but we show that it can be adapted by introducing a new notion of local solution to classical optimal control problems and by establishing a corresponding Pontryagin maximum principle. Thanks to this method, we derive a hybrid maximum principle adapted to our setting, with a simple proof that does not require any technical tools (such as implicit function arguments) to handle the dynamical discontinuities. <p><img src="https://epubs.siam.org/na101/home/literatum/publisher/siam/journals/covergifs/sjcodc/cover.jpg" alttext="cover image"/></p>
The Hybrid Maximum Principle for Optimal Control Problems with Spatially Heterogeneous Dynamics is a Consequence of a Pontryagin Maximum Principle for [math]Local Solutions
10.1137/23M155311X
SIAM Journal on Control and Optimization
20240821T07:00:00Z
© 2024 Society for Industrial and Applied Mathematics
Térence Bayen
Anas Bouali
Loïc Bourdin
The Hybrid Maximum Principle for Optimal Control Problems with Spatially Heterogeneous Dynamics is a Consequence of a Pontryagin Maximum Principle for [math]Local Solutions
62
4
2412
2432
20240831T07:00:00Z
20240831T07:00:00Z
10.1137/23M155311X
https://epubs.siam.org/doi/abs/10.1137/23M155311X?af=R
© 2024 Society for Industrial and Applied Mathematics

Local Exact Controllability of the OneDimensional Nonlinear Schrödinger Equation in the Case of Dirichlet Boundary Conditions
https://epubs.siam.org/doi/abs/10.1137/23M1556034?af=R
SIAM Journal on Control and Optimization, Ahead of Print. <br/> Abstract. We consider the onedimensional nonlinear Schrödinger equation with bilinear control. In the present paper, we study its local exact controllability near the ground state in the case of Dirichlet boundary conditions. To establish the controllability of the linearized equation, we use a bilinear control acting through four directions: three Fourier modes and one generic direction. The Fourier modes are appropriately chosen so that they satisfy a saturation property. These modes allow one to control approximately the linearzied Schrödinger equation. Then we show that the reachable set for the linearized equation is closed. This is achieved by representing the solution operator as a sum of two linear continuous mappings: one is surjective (here the control in generic direction is used) and the other is compact. A mapping with dense and closed image is surjective, so we conclude that the linearized Schrödinger equation is exactly controllable. The local exact controllability of the nonlinear equation then follows by the inverse mapping theorem.
SIAM Journal on Control and Optimization, Ahead of Print. <br/> Abstract. We consider the onedimensional nonlinear Schrödinger equation with bilinear control. In the present paper, we study its local exact controllability near the ground state in the case of Dirichlet boundary conditions. To establish the controllability of the linearized equation, we use a bilinear control acting through four directions: three Fourier modes and one generic direction. The Fourier modes are appropriately chosen so that they satisfy a saturation property. These modes allow one to control approximately the linearzied Schrödinger equation. Then we show that the reachable set for the linearized equation is closed. This is achieved by representing the solution operator as a sum of two linear continuous mappings: one is surjective (here the control in generic direction is used) and the other is compact. A mapping with dense and closed image is surjective, so we conclude that the linearized Schrödinger equation is exactly controllable. The local exact controllability of the nonlinear equation then follows by the inverse mapping theorem. <p><img src="https://epubs.siam.org/na101/home/literatum/publisher/siam/journals/covergifs/sjcodc/cover.jpg" alttext="cover image"/></p>
Local Exact Controllability of the OneDimensional Nonlinear Schrödinger Equation in the Case of Dirichlet Boundary Conditions
10.1137/23M1556034
SIAM Journal on Control and Optimization
20240913T07:00:00Z
© 2024 Society for Industrial and Applied Mathematics
Alessandro Duca
Vahagn Nersesyan
Local Exact Controllability of the OneDimensional Nonlinear Schrödinger Equation in the Case of Dirichlet Boundary Conditions
S20
S36
10.1137/23M1556034
https://epubs.siam.org/doi/abs/10.1137/23M1556034?af=R
© 2024 Society for Industrial and Applied Mathematics

Switching Controls for Conservative Bilinear Quantum Systems with Discrete Spectrum
https://epubs.siam.org/doi/abs/10.1137/23M1588494?af=R
SIAM Journal on Control and Optimization, Ahead of Print. <br/>Abstract. We analyze attainable sets of singleinput bilinear conservative systems with piecewise constant controls. Under the assumption that the ambient space admits a Hilbert basis made of eigenvectors of the drift operator, we show that the closure of the attainable set does not depend on the set of admissible controls, provided the controls can take at least two or three values.
SIAM Journal on Control and Optimization, Ahead of Print. <br/>Abstract. We analyze attainable sets of singleinput bilinear conservative systems with piecewise constant controls. Under the assumption that the ambient space admits a Hilbert basis made of eigenvectors of the drift operator, we show that the closure of the attainable set does not depend on the set of admissible controls, provided the controls can take at least two or three values. <p><img src="https://epubs.siam.org/na101/home/literatum/publisher/siam/journals/covergifs/sjcodc/cover.jpg" alttext="cover image"/></p>
Switching Controls for Conservative Bilinear Quantum Systems with Discrete Spectrum
10.1137/23M1588494
SIAM Journal on Control and Optimization
20240507T07:00:00Z
© 2024 Society for Industrial and Applied Mathematics
Nabile Boussaïd
Marco Caponigro
Thomas Chambrion
Switching Controls for Conservative Bilinear Quantum Systems with Discrete Spectrum
S1
S19
10.1137/23M1588494
https://epubs.siam.org/doi/abs/10.1137/23M1588494?af=R
© 2024 Society for Industrial and Applied Mathematics