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Optimal Control Duality and the Douglas–Rachford Algorithm 最优控制对偶性和道格拉斯-拉赫福德算法
IF 2.2 2区 数学
SIAM Journal on Control and Optimization Pub Date : 2024-02-12 DOI: 10.1137/23m1558549
Regina S. Burachik, Bethany I. Caldwell, C. Yalçin Kaya, Walaa M. Moursi
{"title":"Optimal Control Duality and the Douglas–Rachford Algorithm","authors":"Regina S. Burachik, Bethany I. Caldwell, C. Yalçin Kaya, Walaa M. Moursi","doi":"10.1137/23m1558549","DOIUrl":"https://doi.org/10.1137/23m1558549","url":null,"abstract":"SIAM Journal on Control and Optimization, Volume 62, Issue 1, Page 680-698, February 2024. <br/> Abstract. We explore the relationship between the dual of a weighted minimum-energy control problem, a special case of linear-quadratic optimal control problems, and the Douglas–Rachford (DR) algorithm. We obtain an expression for the fixed point of the DR operator as applied to solving the optimal control problem, which in turn devises a certificate of optimality that can be employed for numerical verification. The fixed point and the optimality check are illustrated in two example optimal control problems.","PeriodicalId":49531,"journal":{"name":"SIAM Journal on Control and Optimization","volume":"53 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2024-02-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139758464","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Primal-Dual Regression Approach for Markov Decision Processes with General State and Action Spaces 具有一般状态和行动空间的马尔可夫决策过程的原始-双重回归方法
IF 2.2 2区 数学
SIAM Journal on Control and Optimization Pub Date : 2024-02-12 DOI: 10.1137/22m1526010
Denis Belomestny, John Schoenmakers
{"title":"Primal-Dual Regression Approach for Markov Decision Processes with General State and Action Spaces","authors":"Denis Belomestny, John Schoenmakers","doi":"10.1137/22m1526010","DOIUrl":"https://doi.org/10.1137/22m1526010","url":null,"abstract":"SIAM Journal on Control and Optimization, Volume 62, Issue 1, Page 650-679, February 2024. <br/> Abstract. We develop a regression-based primal-dual martingale approach for solving discrete time, finite-horizon MDPs. The state and action spaces may be finite or infinite (but regular enough) subsets of Euclidean space. Consequently, our method allows for the construction of tight upper and lower-biased approximations of the value functions, providing precise estimates of the optimal policy. Importantly, we prove error bounds for the estimated duality gap featuring polynomial dependence on the time horizon. Additionally, we observe sublinear dependence of the stochastic part of the error on the cardinality/dimension of the state and action spaces. From a computational perspective, our proposed method is efficient. Unlike typical duality-based methods for optimal control problems in the literature, the Monte Carlo procedures involved here do not require nested simulations.","PeriodicalId":49531,"journal":{"name":"SIAM Journal on Control and Optimization","volume":"5 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2024-02-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139758454","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A Stability Result for a Degenerate Beam Equation 退化梁方程的稳定结果
IF 2.2 2区 数学
SIAM Journal on Control and Optimization Pub Date : 2024-02-09 DOI: 10.1137/23m1565668
Alessandro Camasta, Genni Fragnelli
{"title":"A Stability Result for a Degenerate Beam Equation","authors":"Alessandro Camasta, Genni Fragnelli","doi":"10.1137/23m1565668","DOIUrl":"https://doi.org/10.1137/23m1565668","url":null,"abstract":"SIAM Journal on Control and Optimization, Volume 62, Issue 1, Page 630-649, February 2024. <br/> Abstract. We consider a beam equation in the presence of a leading degenerate operator which is not in divergence form. We impose clamped conditions where the degeneracy occurs and dissipative conditions at the other endpoint. We provide some conditions for the uniform exponential decay of solutions for the associated problem.","PeriodicalId":49531,"journal":{"name":"SIAM Journal on Control and Optimization","volume":"92 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2024-02-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139758463","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Optimal Control and Signaling Strategies of Control-Coding Capacity of General Decision Models: Applications to Gaussian Models and Decentralized Strategies 一般决策模型控制编码能力的最佳控制和信号策略：高斯模型和分散策略的应用
IF 2.2 2区 数学
SIAM Journal on Control and Optimization Pub Date : 2024-02-08 DOI: 10.1137/22m1518700
Charalambos D. Charalambous, Christos K. Kourtellaris, Ioannis Tzortzis
{"title":"Optimal Control and Signaling Strategies of Control-Coding Capacity of General Decision Models: Applications to Gaussian Models and Decentralized Strategies","authors":"Charalambos D. Charalambous, Christos K. Kourtellaris, Ioannis Tzortzis","doi":"10.1137/22m1518700","DOIUrl":"https://doi.org/10.1137/22m1518700","url":null,"abstract":"SIAM Journal on Control and Optimization, Volume 62, Issue 1, Page 600-629, February 2024. <br/> Abstract. We investigate the control-coding (CC) capacity of general dynamical decision models (DMs) that involve nonlinear filtering, which is absent in the specific DMs investigated in [C. K. Kourtellaris and C. D. Charalambous, IEEE Trans. Inform. Theory, 64 (2018), pp. 4962–4992]. We derive characterizations of CC capacity and we show their equivalence to extremum problems of maximizing the information theoretic measure of directed information from the input process to the output process of the DM over randomized strategies. Due to the generality of the DMs, the CC capacity is shown to be equivalent to partially observable Markov decision problems, contrary to the DMs in the above mentioned paper, which give rise to fully observable Markov decision problems. Subsequently, the CC capacity is transformed, using nonlinear filtering theory, to fully observable Markov decision problems. For the application example of a Gaussian DM with past dependence on inputs and outputs, we prove a decentralized separation principle that states optimal inputs are Gaussian and consist of (i) a control, (ii) an estimation, and (iii) an information transmission part, which interact in a specific order. The optimal control and estimation parts are related to linear-quadratic Gaussian stochastic optimal control problems with partial information. Various degenerated cases are discussed, including examples from the above mentioned paper, which do not involve estimation.","PeriodicalId":49531,"journal":{"name":"SIAM Journal on Control and Optimization","volume":"10 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2024-02-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139758434","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Exact Controllability for a Refined Stochastic Wave Equation 精炼随机波方程的精确可控性
IF 2.2 2区 数学
SIAM Journal on Control and Optimization Pub Date : 2024-02-07 DOI: 10.1137/22m1537680
Zhonghua Liao, Qi Lü
{"title":"Exact Controllability for a Refined Stochastic Wave Equation","authors":"Zhonghua Liao, Qi Lü","doi":"10.1137/22m1537680","DOIUrl":"https://doi.org/10.1137/22m1537680","url":null,"abstract":"SIAM Journal on Control and Optimization, Volume 62, Issue 1, Page 563-580, February 2024. <br/> Abstract. In this paper, we obtain the exact controllability for a refined stochastic wave equation with three controls by establishing a novel Carleman estimate for a backward hyperbolic-like operator. Compared with the known result [Q. Lü and X Zhang, Mathematical Control Theory for Stochastic Partial Differential Equations, Springer, Cham, Switzerland, 2021], the novelty of this paper is twofold: (1) Our model contains the effects in the drift terms when we put controls directly in the diffusion terms, which is more sensible for practical applications; (2) We provide an explicit description of the waiting time which is sharp in the case of dimension one and is independent of the coefficents of lower terms.","PeriodicalId":49531,"journal":{"name":"SIAM Journal on Control and Optimization","volume":"168 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2024-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139758534","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Stability of Abstract Interconnected Systems with a Possibly Unstable Component 带有可能不稳定成分的抽象互联系统的稳定性
IF 2.2 2区 数学
SIAM Journal on Control and Optimization Pub Date : 2024-02-07 DOI: 10.1137/23m1572350
Ivan Atamas, Sergey Dashkovskiy, Vitalii Slynko
{"title":"Stability of Abstract Interconnected Systems with a Possibly Unstable Component","authors":"Ivan Atamas, Sergey Dashkovskiy, Vitalii Slynko","doi":"10.1137/23m1572350","DOIUrl":"https://doi.org/10.1137/23m1572350","url":null,"abstract":"SIAM Journal on Control and Optimization, Volume 62, Issue 1, Page 581-599, February 2024. <br/> Abstract. We consider an interconnection of a one-dimensional ODE and an infinite dimensional abstract differential equation in view of the asymptotic stability. Sufficient stability conditions are obtained under the assumption that the whole system is positive with respect to the Minkowski cone. The decoupled ODE subsystem is not required to be stable. We illustrate our results by means of examples demonstrating the advantages of the developed approach over the existing results. As well we compare our results with the known small-gain theory.","PeriodicalId":49531,"journal":{"name":"SIAM Journal on Control and Optimization","volume":"96 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2024-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139758453","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Exact Controllability and Stabilization for Linear Dispersive PDE’s on the Two-Dimensional Torus 二维环面上线性分散 PDE 的精确可控性和稳定性
IF 2.2 2区 数学
SIAM Journal on Control and Optimization Pub Date : 2024-02-07 DOI: 10.1137/22m1529361
Francisco J. Vielma-Leal, Ademir Pastor
{"title":"Exact Controllability and Stabilization for Linear Dispersive PDE’s on the Two-Dimensional Torus","authors":"Francisco J. Vielma-Leal, Ademir Pastor","doi":"10.1137/22m1529361","DOIUrl":"https://doi.org/10.1137/22m1529361","url":null,"abstract":"SIAM Journal on Control and Optimization, Volume 62, Issue 1, Page 539-562, February 2024. <br/> Abstract. The moment method is used to prove the exact controllability of a wide class of bidimensional linear dispersive PDE’s posed on the two-dimensional torus [math]. The control function is considered to be acting on a small vertical and horizontal strip of the torus. Our results apply to several well-known models including some bidimesional extensions of the Benajamin–Ono and Korteweg–de Vries equations. As a by product, the exponential stabilizability with any given decay rate is also established in the Sobolev space [math], with [math], by constructing an appropriated feedback control law.","PeriodicalId":49531,"journal":{"name":"SIAM Journal on Control and Optimization","volume":"96 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2024-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139758351","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The Global Maximum Principle for Optimal Control of Partially Observed Stochastic Systems Driven by Fractional Brownian Motion 分数布朗运动驱动的部分观测随机系统最优控制的全局最大原则
IF 2.2 2区 数学
SIAM Journal on Control and Optimization Pub Date : 2024-02-06 DOI: 10.1137/22m1543203
Yueyang Zheng, Yaozhong Hu
{"title":"The Global Maximum Principle for Optimal Control of Partially Observed Stochastic Systems Driven by Fractional Brownian Motion","authors":"Yueyang Zheng, Yaozhong Hu","doi":"10.1137/22m1543203","DOIUrl":"https://doi.org/10.1137/22m1543203","url":null,"abstract":"SIAM Journal on Control and Optimization, Volume 62, Issue 1, Page 509-538, February 2024. <br/> Abstract. In this paper we study the stochastic control problem of a partially observed (multidimensional) stochastic system driven by both Brownian motions and fractional Brownian motions. In the absence of the powerful tool of Girsanov transformation, we introduce and study new stochastic processes which are used to transform the original problem to a “classical one”. The adjoint backward stochastic differential equations and the necessary condition satisfied by the optimal control (maximum principle) are obtained.","PeriodicalId":49531,"journal":{"name":"SIAM Journal on Control and Optimization","volume":"18 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2024-02-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139758462","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Admissibility and Observability of Jeffreys Type of Overdamped Second Order Linear Systems 杰弗里斯型过阻尼二阶线性系统的可接受性和可观测性
IF 2.2 2区 数学
SIAM Journal on Control and Optimization Pub Date : 2024-02-02 DOI: 10.1137/22m1511680
Jian-Hua Chen, Xian-Feng Zhao, Hua-Cheng Zhou
{"title":"Admissibility and Observability of Jeffreys Type of Overdamped Second Order Linear Systems","authors":"Jian-Hua Chen, Xian-Feng Zhao, Hua-Cheng Zhou","doi":"10.1137/22m1511680","DOIUrl":"https://doi.org/10.1137/22m1511680","url":null,"abstract":"SIAM Journal on Control and Optimization, Volume 62, Issue 1, Page 466-486, February 2024. <br/> Abstract. We study Jeffreys-type overdamped second order linear systems with observed outputs in the setting of Hilbert spaces. The state equation comes from an overdamped second order linear partial differential equation which is wave-like but was proposed to describe heat conduction. It results from adopting the Jeffreys law of constitutive relation for heat flux, rather than the usual Fourier law. Sufficient conditions for infinite-time admissibility of the system observation operator and system observability are obtained. In the general case, we obtain the infinite-time admissibility from that of the first order Cauchy system, which is done by employing the Hardy space approach. In the special case when the operator in the state equation is negative definite, we derive the infinite-time admissibility and system observability using a semigroup approach. Illustrative examples are given.","PeriodicalId":49531,"journal":{"name":"SIAM Journal on Control and Optimization","volume":"19 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2024-02-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139666348","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The Nonlocal Kelvin Principle and the Dual Approach to Nonlocal Control in the Conduction Coefficients 非局部开尔文原理和传导系数非局部控制的双重方法
IF 2.2 2区 数学
SIAM Journal on Control and Optimization Pub Date : 2024-02-02 DOI: 10.1137/22m1522127
Anton Evgrafov, José C. Bellido
{"title":"The Nonlocal Kelvin Principle and the Dual Approach to Nonlocal Control in the Conduction Coefficients","authors":"Anton Evgrafov, José C. Bellido","doi":"10.1137/22m1522127","DOIUrl":"https://doi.org/10.1137/22m1522127","url":null,"abstract":"SIAM Journal on Control and Optimization, Volume 62, Issue 1, Page 487-508, February 2024. <br/> Abstract. We explore the dual approach to nonlocal optimal control in the coefficients, specifically for a classical min-max problem which in this study is associated with a nonlocal scalar diffusion equation. We reformulate the optimal control problem utilizing a dual variational principle, which is expressed in terms of nonlocal two-point fluxes. We introduce the proper functional space framework to deal with this formulation and establish its well-posedness. The key ingredient is the inf-sup (Ladyzhenskaya–Babuška–Brezzi) condition, which holds uniformly with respect to small nonlocal horizons. As a by-product of this fact, we are able to prove convergence of nonlocal optimal control problems toward their local counterparts in a straightforward fashion.","PeriodicalId":49531,"journal":{"name":"SIAM Journal on Control and Optimization","volume":"19 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2024-02-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139666311","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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