Optimal control for uncertain random continuous-time systems

Chen, Xin; Zhu, Yuanguo; Bo, Li

doi:10.1080/02331934.2021.2017429

Cited by 9 publications

(5 citation statements)

References 46 publications

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“…20,24 The equations of optimality presented in Sections 4 and 6 are generalization of that in References 20 and 24, respectively. Compared with Chen et al, 33 random matrices and multiple Liu processes are introduced into an optimal control problem, which might be better applicable to handling difficult circumstances having many diverse indeterminate factors.…”

Section: Introductionmentioning

confidence: 99%

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Optimal control and zero‐sum game subject to differential equations with Liu processes and random matrices

Chen,

Zhu

2024

Optim Control Appl Methods

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This paper presents a differential equation including both random matrices and a Liu process. Then we demonstrate that the solution to this equation exists and is unique. Under the framework of chance theory, problems of optimal control and two‐person zero‐sum game subject to differential equations are considered. An equation of optimality is provided for solving a problem of optimal control. Then equilibrium equations are proposed to identify the saddle‐point of a two‐person zero‐sum game problem. As an extension, we generalize the obtained results to the problems subject to differential equations including both random matrices and multiple Liu processes. Finally, we utilize the acquired theoretical results to analyze a portfolio selection game problem.

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Section: Introductionmentioning

confidence: 99%

“…[28][29][30][31] Qin 32 showed that using chance theory can effectively solve a portfolio selection problem having uncertainty together with randomness. Subsequently, optimal control problems [33][34][35] with both uncertainty and randomness were constructed by exerting chance theory.…”

Section: Introductionmentioning

confidence: 99%

Optimal control and zero‐sum game subject to differential equations with Liu processes and random matrices

Chen,

Zhu

2024

Optim Control Appl Methods

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“…Time delays represent a common occurrence in dynamic systems, and the study of these delays is vital for comprehending and controlling system behavior. Recent advancements in chance theory and uncertain stochastic optimal control [31][32][33][34] have significantly enhanced the analysis and control of such intricate systems. In this paper, we employ stochastic and uncertain difference equations to elucidate the behavior of time-delayed uncertain stochastic systems.…”

Section: Introductionmentioning

confidence: 99%

“…In complex environments, there may be various sources of noises, and the combined use of both stochastic and uncertain systems might better reflect the comprehensive characteristics of a complex system 4,30 . References 32 and 34 studied optimal control problems of uncertain stochastic systems including both stochastic systems and uncertain systems. Zero‐sum game can be regarded as an extension of optimal control problem.…”

Section: Introductionmentioning

confidence: 99%

Linear quadratic zero‐sum game for time‐delayed uncertain stochastic systems

Chen,

Yuan,

Yuan

et al. 2024

Optim Control Appl Methods

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SummaryThis study focuses on the analysis of a linear quadratic zero‐sum game (LQZSG) for time‐delayed uncertain stochastic systems. To begin, we introduce a general time‐delayed zero‐sum game. Employing an algebraic transformation method, we transform the time‐delayed zero‐sum game into an equivalent uncertain random zero‐sum game without time delay. Subsequently, we present equilibrium equations that streamline the transformation of the uncertain random zero‐sum game into problems solvable as deterministic difference equations. We then investigate the LQZSG involving a linear time‐delayed uncertain stochastic system with a quadratic objective function. Within this framework, we provide a unified framework for solving this type of game and obtaining the analytic expression for the saddle‐point equilibrium of the LQZSG. Additionally, we present a numerical example and a counter‐terrorism economic game to illustrate the applicability of our findings.

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“…These systems can be found in a number of contexts, including game problems [24], portfolio selection [25], and reliability analysis [26]. Chance theory is a useful technique for dealing with uncertain random control problems [27][28][29][30].…”

Section: Introductionmentioning

confidence: 99%

Linear quadratic control for multiple time‐delayed uncertain random systems

Chen

Zhu

2023

Asian Journal of Control

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This study focuses on time‐delayed linear quadratic control problems (LQCPs). Firstly, a general time‐delayed control problem for a linear time‐varying system is investigated. This problem is equivalent to an optimization problem without time delays, and corresponding recurrence equations are proposed accordingly. Furthermore, based on recurrence equations and chance theory, two different types of LQCPs are researched, where the control weighting matrices are positive definite and indefinite, respectively. Exact solutions for the optimal results of these LQCPs are provided. Finally, numerical examples are provided to demonstrate the findings.

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Optimal control for uncertain random continuous-time systems

Cited by 9 publications

References 46 publications

Optimal control and zero‐sum game subject to differential equations with Liu processes and random matrices

Optimal control and zero‐sum game subject to differential equations with Liu processes and random matrices

Linear quadratic zero‐sum game for time‐delayed uncertain stochastic systems

Linear quadratic control for multiple time‐delayed uncertain random systems

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