Optimal control for multistage uncertain random dynamic systems with multiple time delays

Chen, Xin; Zhu, Yuanguo

doi:10.1016/j.isatra.2022.02.016

Cited by 13 publications

(11 citation statements)

References 27 publications

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“…Compared with the general optimal control problem, we obtain the analytical expression for the optimal control (14) of the optimal control problem (13). This type of optimal control ( 14) is easy to implement compared to some optimal controls and has a wide range of applications [25], [27].…”

Section: Bang-bang Problem Of Optimal Control Modelmentioning

confidence: 99%

“…Then Liu [20] presented the operational laws of uncertain random variables. In recent years, considerable related works have been researched [21], [22], [23], [24], [25].…”

Section: Introductionmentioning

confidence: 99%

“…This paper further develops optimal control theory and considers an uncertain random optimal control including uncertainty and randomness. This work provides theoretical support for dynamic optimization and decision-making when the system is disturbed by uncertainty and randomness in production life and other fields [25]. The second contribution is to get recurrence equations that turn the uncertain random optimal control problem into a much easier problem.…”

Section: Introductionmentioning

confidence: 99%

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Optimal Control for a Multistage Uncertain Random System

Chen

Jin

2023

IEEE Access

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Chance theory is a mathematical methodology for modelling complex systems including both uncertainty and randomness. Based on chance theory, this paper introduces the optimal control model for a multistage uncertain random system. For solving such a model, recurrence equations are presented via Bellman's principle. With the aid of recurrence equations, the bang-bang problem of optimal control model and indefinite linear quadratic (LQ) problem of optimal control model are studied. Meanwhile, the exact solutions of such problems are presented. Furthermore, numerical examples are provided on the proposed theorems to show the effectiveness of our results. INDEX TERMSChance theory, bang-bang control, indefinite LQ control, uncertain random system, constrained difference equation.

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Section: Bang-bang Problem Of Optimal Control Modelmentioning

confidence: 99%

“…Then Liu [20] presented the operational laws of uncertain random variables. In recent years, considerable related works have been researched [21], [22], [23], [24], [25].…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Optimal Control for a Multistage Uncertain Random System

Chen

Jin

2023

IEEE Access

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“…[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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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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“…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 multistage uncertain random dynamic systems with multiple time delays

Cited by 13 publications

References 27 publications

Optimal Control for a Multistage Uncertain Random System

Optimal Control for a Multistage Uncertain Random System

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

Linear quadratic control for multiple time‐delayed uncertain random systems

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