SIAM Journal on Control and Optimization, Volume 62, Issue 1, Page 191-219, February 2024. Abstract. We study a stochastically perturbed version of the well-known Krasnoselskii–Mann iteration for computing fixed points of nonexpansive maps in finite dimensional normed spaces. We discuss sufficient conditions on the stochastic noise and stepsizes that guarantee almost sure convergence of the iterates towards a fixed point and derive nonasymptotic error bounds and convergence rates for the fixed-point residuals. Our main results concern the case of a martingale difference noise with variances that can possibly grow unbounded. This supports an application to reinforcement learning for average reward Markov decision processes, for which we establish convergence and asymptotic rates. We also analyze in depth the case where the noise has uniformly bounded variance, obtaining error bounds with explicit computable constants.
{"title":"Stochastic Fixed-Point Iterations for Nonexpansive Maps: Convergence and Error Bounds","authors":"Mario Bravo, Roberto Cominetti","doi":"10.1137/22m1515550","DOIUrl":"https://doi.org/10.1137/22m1515550","url":null,"abstract":"SIAM Journal on Control and Optimization, Volume 62, Issue 1, Page 191-219, February 2024. <br/> Abstract. We study a stochastically perturbed version of the well-known Krasnoselskii–Mann iteration for computing fixed points of nonexpansive maps in finite dimensional normed spaces. We discuss sufficient conditions on the stochastic noise and stepsizes that guarantee almost sure convergence of the iterates towards a fixed point and derive nonasymptotic error bounds and convergence rates for the fixed-point residuals. Our main results concern the case of a martingale difference noise with variances that can possibly grow unbounded. This supports an application to reinforcement learning for average reward Markov decision processes, for which we establish convergence and asymptotic rates. We also analyze in depth the case where the noise has uniformly bounded variance, obtaining error bounds with explicit computable constants.","PeriodicalId":49531,"journal":{"name":"SIAM Journal on Control and Optimization","volume":"22 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2024-01-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139500222","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}
SIAM Journal on Control and Optimization, Volume 62, Issue 1, Page 135-166, February 2024. Abstract. This work uses the entropy-regularized relaxed stochastic control perspective as a principled framework for designing reinforcement learning (RL) algorithms. Herein, an agent interacts with the environment by generating noisy controls distributed according to the optimal relaxed policy. The noisy policies, on the one hand, explore the space and hence facilitate learning, but, on the other hand, they introduce bias by assigning a positive probability to nonoptimal actions. This exploration-exploitation trade-off is determined by the strength of entropy regularization. We study algorithms resulting from two entropy regularization formulations: the exploratory control approach, where entropy is added to the cost objective, and the proximal policy update approach, where entropy penalizes policy divergence between consecutive episodes. We focus on the finite horizon continuous-time linear-quadratic (LQ) RL problem, where a linear dynamics with unknown drift coefficients is controlled subject to quadratic costs. In this setting, both algorithms yield a Gaussian relaxed policy. We quantify the precise difference between the value functions of a Gaussian policy and its noisy evaluation and show that the execution noise must be independent across time. By tuning the frequency of sampling from relaxed policies and the parameter governing the strength of entropy regularization, we prove that the regret, for both learning algorithms, is of the order [math] (up to a logarithmic factor) over [math] episodes, matching the best known result from the literature.
{"title":"Optimal Scheduling of Entropy Regularizer for Continuous-Time Linear-Quadratic Reinforcement Learning","authors":"Lukasz Szpruch, Tanut Treetanthiploet, Yufei Zhang","doi":"10.1137/22m1515744","DOIUrl":"https://doi.org/10.1137/22m1515744","url":null,"abstract":"SIAM Journal on Control and Optimization, Volume 62, Issue 1, Page 135-166, February 2024. <br/> Abstract. This work uses the entropy-regularized relaxed stochastic control perspective as a principled framework for designing reinforcement learning (RL) algorithms. Herein, an agent interacts with the environment by generating noisy controls distributed according to the optimal relaxed policy. The noisy policies, on the one hand, explore the space and hence facilitate learning, but, on the other hand, they introduce bias by assigning a positive probability to nonoptimal actions. This exploration-exploitation trade-off is determined by the strength of entropy regularization. We study algorithms resulting from two entropy regularization formulations: the exploratory control approach, where entropy is added to the cost objective, and the proximal policy update approach, where entropy penalizes policy divergence between consecutive episodes. We focus on the finite horizon continuous-time linear-quadratic (LQ) RL problem, where a linear dynamics with unknown drift coefficients is controlled subject to quadratic costs. In this setting, both algorithms yield a Gaussian relaxed policy. We quantify the precise difference between the value functions of a Gaussian policy and its noisy evaluation and show that the execution noise must be independent across time. By tuning the frequency of sampling from relaxed policies and the parameter governing the strength of entropy regularization, we prove that the regret, for both learning algorithms, is of the order [math] (up to a logarithmic factor) over [math] episodes, matching the best known result from the literature.","PeriodicalId":49531,"journal":{"name":"SIAM Journal on Control and Optimization","volume":"75 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2024-01-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139500602","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}
SIAM Journal on Control and Optimization, Volume 62, Issue 1, Page 167-190, February 2024. Abstract. This work investigates a state estimation problem for linear time-invariant systems based on polarized measurement information from event sensors. To enable estimator design, a new notion of observability, namely, [math]-observability is defined with the precision parameter [math] which relates to the worst-case performance of inferring the initial state, based on which a criterion is developed to test the [math]-observability of discrete-time linear systems. Utilizing multisensor polarity data from event sensors and the implicit information hidden in event-triggering conditions at no-event instants, an iterative event-triggered state estimator is designed to evaluate a set containing all possible values of the state. The proposed estimator is built by outer approximation of intersecting ellipsoids that are predicted from previous state estimates and the ellipsoids inferred from received polarity information of event sensors as well as the event-triggering protocol; the estimated regions of the state derived from multisensor event measurements are fused together, the sizes of which are proved to be asymptotically bounded. Distributed implementation of the estimation algorithm utilizing a two-layer processor network of hierarchy architecture is discussed, and the temporal computational complexity of the algorithm implemented in centralized and distributed ways is analyzed. The efficiency of the proposed event-triggered state estimator is verified by numerical experiments.
{"title":"State Estimation with Event Sensors: Observability Analysis and Multi-sensor Fusion","authors":"Xinhui Liu, Kaikai Zheng, Dawei Shi, Tongwen Chen","doi":"10.1137/22m1539204","DOIUrl":"https://doi.org/10.1137/22m1539204","url":null,"abstract":"SIAM Journal on Control and Optimization, Volume 62, Issue 1, Page 167-190, February 2024. <br/> Abstract. This work investigates a state estimation problem for linear time-invariant systems based on polarized measurement information from event sensors. To enable estimator design, a new notion of observability, namely, [math]-observability is defined with the precision parameter [math] which relates to the worst-case performance of inferring the initial state, based on which a criterion is developed to test the [math]-observability of discrete-time linear systems. Utilizing multisensor polarity data from event sensors and the implicit information hidden in event-triggering conditions at no-event instants, an iterative event-triggered state estimator is designed to evaluate a set containing all possible values of the state. The proposed estimator is built by outer approximation of intersecting ellipsoids that are predicted from previous state estimates and the ellipsoids inferred from received polarity information of event sensors as well as the event-triggering protocol; the estimated regions of the state derived from multisensor event measurements are fused together, the sizes of which are proved to be asymptotically bounded. Distributed implementation of the estimation algorithm utilizing a two-layer processor network of hierarchy architecture is discussed, and the temporal computational complexity of the algorithm implemented in centralized and distributed ways is analyzed. The efficiency of the proposed event-triggered state estimator is verified by numerical experiments.","PeriodicalId":49531,"journal":{"name":"SIAM Journal on Control and Optimization","volume":"1 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2024-01-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139500269","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}
SIAM Journal on Control and Optimization, Volume 62, Issue 1, Page 91-117, February 2024. Abstract. Motivated by a new formulation of the classical dividend problem, we show that Peskir’s maximality principle can be transferred to singular stochastic control problems with two-dimensional degenerate dynamics and absorption along the diagonal of the state space. We construct an optimal control as a Skorokhod reflection along a moving barrier, where the barrier can be computed analytically as the smallest solution to a certain nonlinear ODE. Contrarily to the classical one-dimensional formulation of the dividend problem, our framework produces a nontrivial solution when the firm’s (predividend) equity capital evolves as a geometric Brownian motion. Such a solution is also qualitatively different from the one traditionally obtained for the arithmetic Brownian motion.
{"title":"The Maximality Principle in Singular Control with Absorption and Its Applications to the Dividend Problem","authors":"Tiziano De Angelis, Erik Ekström, Marcus Olofsson","doi":"10.1137/22m152791x","DOIUrl":"https://doi.org/10.1137/22m152791x","url":null,"abstract":"SIAM Journal on Control and Optimization, Volume 62, Issue 1, Page 91-117, February 2024. <br/> Abstract. Motivated by a new formulation of the classical dividend problem, we show that Peskir’s maximality principle can be transferred to singular stochastic control problems with two-dimensional degenerate dynamics and absorption along the diagonal of the state space. We construct an optimal control as a Skorokhod reflection along a moving barrier, where the barrier can be computed analytically as the smallest solution to a certain nonlinear ODE. Contrarily to the classical one-dimensional formulation of the dividend problem, our framework produces a nontrivial solution when the firm’s (predividend) equity capital evolves as a geometric Brownian motion. Such a solution is also qualitatively different from the one traditionally obtained for the arithmetic Brownian motion.","PeriodicalId":49531,"journal":{"name":"SIAM Journal on Control and Optimization","volume":"30 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2024-01-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139463875","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}
SIAM Journal on Control and Optimization, Volume 62, Issue 1, Page 118-134, February 2024. Abstract. Input-to-state stability is one of the most utilizable robust stability properties for nonlinear dynamical systems, while (nearly) fixed-time convergence is a kind of decay for trajectories of disturbance-free systems that is independent in initial conditions. The presence of both these features for a system can be checked by the existence of a proper Lyapunov function. The objective of this work is to provide the conditions for a converse result that (nearly) fixed-time input-to-state stable systems admit a respective Lyapunov function. Similar auxiliary results for uniform finite-time stability and uniform (nearly) fixed-time stability are obtained.
{"title":"On Converse Lyapunov Theorem for Fixed-Time Input-to-State Stability","authors":"Denis Efimov, Andrey Polyakov","doi":"10.1137/22m1497596","DOIUrl":"https://doi.org/10.1137/22m1497596","url":null,"abstract":"SIAM Journal on Control and Optimization, Volume 62, Issue 1, Page 118-134, February 2024. <br/> Abstract. Input-to-state stability is one of the most utilizable robust stability properties for nonlinear dynamical systems, while (nearly) fixed-time convergence is a kind of decay for trajectories of disturbance-free systems that is independent in initial conditions. The presence of both these features for a system can be checked by the existence of a proper Lyapunov function. The objective of this work is to provide the conditions for a converse result that (nearly) fixed-time input-to-state stable systems admit a respective Lyapunov function. Similar auxiliary results for uniform finite-time stability and uniform (nearly) fixed-time stability are obtained.","PeriodicalId":49531,"journal":{"name":"SIAM Journal on Control and Optimization","volume":"8 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2024-01-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139464096","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}
SIAM Journal on Control and Optimization, Volume 62, Issue 1, Page 65-90, February 2024. Abstract. In this paper, we consider a Markov decision process (MDP) with a Borel state space [math], where [math] is an absorbing state (cemetery), and a Borel action space [math]. We consider the space of finite occupation measures restricted on [math] and the extreme points in it. It is possible that some strategies have infinite occupation measures. Nevertheless, we prove that every finite extreme occupation measure is generated by a deterministic stationary strategy. Then, for this MDP, we consider a constrained problem with total undiscounted criteria and [math] constraints, where the cost functions are nonnegative. By assumption, the strategies inducing infinite occupation measures are not optimal. Then our second main result is that, under mild conditions, the solution to this constrained MDP is given by a mixture of no more than [math] occupation measures generated by deterministic stationary strategies.
{"title":"Extreme Occupation Measures in Markov Decision Processes with an Absorbing State","authors":"Alexey Piunovskiy, Yi Zhang","doi":"10.1137/23m1572398","DOIUrl":"https://doi.org/10.1137/23m1572398","url":null,"abstract":"SIAM Journal on Control and Optimization, Volume 62, Issue 1, Page 65-90, February 2024. <br/> Abstract. In this paper, we consider a Markov decision process (MDP) with a Borel state space [math], where [math] is an absorbing state (cemetery), and a Borel action space [math]. We consider the space of finite occupation measures restricted on [math] and the extreme points in it. It is possible that some strategies have infinite occupation measures. Nevertheless, we prove that every finite extreme occupation measure is generated by a deterministic stationary strategy. Then, for this MDP, we consider a constrained problem with total undiscounted criteria and [math] constraints, where the cost functions are nonnegative. By assumption, the strategies inducing infinite occupation measures are not optimal. Then our second main result is that, under mild conditions, the solution to this constrained MDP is given by a mixture of no more than [math] occupation measures generated by deterministic stationary strategies.","PeriodicalId":49531,"journal":{"name":"SIAM Journal on Control and Optimization","volume":"8 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2024-01-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139463902","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}
SIAM Journal on Control and Optimization, Volume 62, Issue 1, Page 42-64, February 2024. Abstract. We construct a marginally stable linear switching system in continuous time, in four dimensions, and with three switching states, which is exponentially stable with respect to constant switching laws and which has a unique Barabanov norm, but such that the Barabanov norm fails to be strictly convex. This resolves a question of Chitour, Gaye, and Mason.
{"title":"An Irreducible Linear Switching System Whose Unique Barabanov Norm Is Not Strictly Convex","authors":"Ian D. Morris","doi":"10.1137/23m1551213","DOIUrl":"https://doi.org/10.1137/23m1551213","url":null,"abstract":"SIAM Journal on Control and Optimization, Volume 62, Issue 1, Page 42-64, February 2024. <br/> Abstract. We construct a marginally stable linear switching system in continuous time, in four dimensions, and with three switching states, which is exponentially stable with respect to constant switching laws and which has a unique Barabanov norm, but such that the Barabanov norm fails to be strictly convex. This resolves a question of Chitour, Gaye, and Mason.","PeriodicalId":49531,"journal":{"name":"SIAM Journal on Control and Optimization","volume":"1 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2024-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139415611","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}
SIAM Journal on Control and Optimization, Volume 62, Issue 1, Page 1-21, February 2024. Abstract. In this paper, adaptive controllers are designed to track a given trajectory for linear and nonlinear systems. No condition on the tracked trajectory, other than continuity and boundedness, is needed to simultaneously ensure exponential convergence to the tracking reference, exponential convergence to the identification of the plant, and robustness to nonparametric uncertainties. To achieve this, the formulation of the excitation condition associated with the identification part of the adaptive scheme is proposed without employing closed-loop signals, allowing the use of a transient enrichment of the reference. The effect of this transient modification is attenuated by using relaxed requirements for the identification, obtained through a generalization of several estimation algorithms found in recent literature that use memory mechanisms. Consequently, no spectral content of the tracked trajectory—a classic requirement in adaptive theory—is needed to guarantee the mentioned features when the proposed scheme is used. A numerical example is given to illustrate the design aspects involved and the distinctive features of the proposed strategy.
{"title":"Relaxed Excitation Conditions for Robust Identification and Adaptive Control Using Estimation with Memory","authors":"Javier Gallegos, Norelys Aguila-Camacho","doi":"10.1137/22m1506183","DOIUrl":"https://doi.org/10.1137/22m1506183","url":null,"abstract":"SIAM Journal on Control and Optimization, Volume 62, Issue 1, Page 1-21, February 2024. <br/> Abstract. In this paper, adaptive controllers are designed to track a given trajectory for linear and nonlinear systems. No condition on the tracked trajectory, other than continuity and boundedness, is needed to simultaneously ensure exponential convergence to the tracking reference, exponential convergence to the identification of the plant, and robustness to nonparametric uncertainties. To achieve this, the formulation of the excitation condition associated with the identification part of the adaptive scheme is proposed without employing closed-loop signals, allowing the use of a transient enrichment of the reference. The effect of this transient modification is attenuated by using relaxed requirements for the identification, obtained through a generalization of several estimation algorithms found in recent literature that use memory mechanisms. Consequently, no spectral content of the tracked trajectory—a classic requirement in adaptive theory—is needed to guarantee the mentioned features when the proposed scheme is used. A numerical example is given to illustrate the design aspects involved and the distinctive features of the proposed strategy.","PeriodicalId":49531,"journal":{"name":"SIAM Journal on Control and Optimization","volume":"6 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2024-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139093039","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}
Felix L. Schwenninger, Alexander A. Wierzba, Hans Zwart
SIAM Journal on Control and Optimization, Volume 62, Issue 1, Page 22-41, February 2024. Abstract. In this paper we consider bounded-input-bounded-output (BIBO) stability of systems described by infinite-dimensional linear state-space representations, filling the so far unattended gap of a formal definition and characterization of BIBO stability in this general case. Furthermore, we provide several sufficient conditions guaranteeing BIBO stability of a particular system and discuss to which extent this property is preserved under additive and multiplicative perturbations of the system.
{"title":"On BIBO Stability of Infinite-Dimensional Linear State-Space Systems","authors":"Felix L. Schwenninger, Alexander A. Wierzba, Hans Zwart","doi":"10.1137/23m1563098","DOIUrl":"https://doi.org/10.1137/23m1563098","url":null,"abstract":"SIAM Journal on Control and Optimization, Volume 62, Issue 1, Page 22-41, February 2024. <br/> Abstract. In this paper we consider bounded-input-bounded-output (BIBO) stability of systems described by infinite-dimensional linear state-space representations, filling the so far unattended gap of a formal definition and characterization of BIBO stability in this general case. Furthermore, we provide several sufficient conditions guaranteeing BIBO stability of a particular system and discuss to which extent this property is preserved under additive and multiplicative perturbations of the system.","PeriodicalId":49531,"journal":{"name":"SIAM Journal on Control and Optimization","volume":"11 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2024-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139093097","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}
SIAM Journal on Control and Optimization, Volume 61, Issue 6, Page 3635-3663, December 2023. Abstract. In this paper, we consider the partial controllability of linear stochastic control systems with terminal constraints. Some necessary and sufficient conditions for this controllability are obtained with the help of backward stochastic differential equations (BSDEs). We establish the equivalence between the controllability of a game-based control system (GBCS), the controllability of a forward backward stochastic differential equation (FBSDE), and the partial controllability of a related stochastic differential equation (SDE) with terminal constraints. By applying our results, we obtain some necessary and sufficient conditions for the controllability of GBCSs with jumps. Then we embed the GBCSs driven only by Brownian motion and deterministic GBCSs into our framework with jumps. Previous results of Zhang and Guo are covered and extended.
{"title":"The Partial Controllability of Linear Stochastic Control Systems with Terminal Constraints and Its Applications to Game-Based Control Systems with Jumps","authors":"Yuanzhuo Song","doi":"10.1137/22m1537114","DOIUrl":"https://doi.org/10.1137/22m1537114","url":null,"abstract":"SIAM Journal on Control and Optimization, Volume 61, Issue 6, Page 3635-3663, December 2023. <br/> Abstract. In this paper, we consider the partial controllability of linear stochastic control systems with terminal constraints. Some necessary and sufficient conditions for this controllability are obtained with the help of backward stochastic differential equations (BSDEs). We establish the equivalence between the controllability of a game-based control system (GBCS), the controllability of a forward backward stochastic differential equation (FBSDE), and the partial controllability of a related stochastic differential equation (SDE) with terminal constraints. By applying our results, we obtain some necessary and sufficient conditions for the controllability of GBCSs with jumps. Then we embed the GBCSs driven only by Brownian motion and deterministic GBCSs into our framework with jumps. Previous results of Zhang and Guo are covered and extended.","PeriodicalId":49531,"journal":{"name":"SIAM Journal on Control and Optimization","volume":"38 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2023-12-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138553796","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}
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