Mixed zero-sum game based dynamic event-triggered optimal control of multi-input nonlinear system with safety constraints

IF 3.8 2区数学 Q1 MATHEMATICS, APPLIED

Communications in Nonlinear Science and Numerical Simulation Pub Date : 2025-09-28 DOI:10.1016/j.cnsns.2025.109376

Chunbin Qin , Zhongwei Wang , Suyang Hou , Mingyu Pang , Guanghui Wang , Ying Wang , Jishi Zhang , Xin Wang

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引用次数: 0

Abstract

This paper investigates the optimal safe control problem for mixed zero-sum game (MZS)-based multi-input nonlinear systems under dynamic event-triggered control with safety constraints. First, by employing a barrier-function-based system transformation methodology, the safety-constrained MZS game problem is converted into an equivalent system formulation, thereby ensuring persistent satisfaction of safety constraints throughout system operation. Secondly, a new dynamic event-triggered control is proposed for the multi-input MZS game system to reduce the system’s resource consumption. Furthermore, solving the Hamilton-Jacobi-Bellman (HJB) equation associated with the mixed zero-sum game (MZS) allows determination of the system’s optimal control strategy. Moreover, a critic neural network algorithm based on the experience replay is proposed to more efficiently approximate the optimal control strategy. Finally, the single-link robotic arm is employed to confirm the feasibility of the suggested method.

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基于混合零和博弈的安全约束多输入非线性系统动态事件触发最优控制

研究了具有安全约束的动态事件触发控制下基于混合零和博弈的多输入非线性系统的最优安全控制问题。首先，采用基于障碍函数的系统转换方法，将安全约束的MZS博弈问题转化为等效的系统公式，从而保证在整个系统运行过程中安全约束的持续满足。其次，针对多输入MZS游戏系统，提出了一种新的动态事件触发控制方法，以降低系统的资源消耗。此外，通过求解与混合零和博弈（MZS）相关的Hamilton-Jacobi-Bellman （HJB）方程，可以确定系统的最优控制策略。在此基础上，提出了一种基于经验回放的评价神经网络算法，以更有效地逼近最优控制策略。最后，以单连杆机械臂为例，验证了所提方法的可行性。

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来源期刊

Communications in Nonlinear Science and Numerical Simulation MATHEMATICS, APPLIED-MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

CiteScore

6.80

自引率

7.70%

发文量

378

审稿时长

78 days

期刊介绍： The journal publishes original research findings on experimental observation, mathematical modeling, theoretical analysis and numerical simulation, for more accurate description, better prediction or novel application, of nonlinear phenomena in science and engineering. It offers a venue for researchers to make rapid exchange of ideas and techniques in nonlinear science and complexity. The submission of manuscripts with cross-disciplinary approaches in nonlinear science and complexity is particularly encouraged. Topics of interest: Nonlinear differential or delay equations, Lie group analysis and asymptotic methods, Discontinuous systems, Fractals, Fractional calculus and dynamics, Nonlinear effects in quantum mechanics, Nonlinear stochastic processes, Experimental nonlinear science, Time-series and signal analysis, Computational methods and simulations in nonlinear science and engineering, Control of dynamical systems, Synchronization, Lyapunov analysis, High-dimensional chaos and turbulence, Chaos in Hamiltonian systems, Integrable systems and solitons, Collective behavior in many-body systems, Biological physics and networks, Nonlinear mechanical systems, Complex systems and complexity. No length limitation for contributions is set, but only concisely written manuscripts are published. Brief papers are published on the basis of Rapid Communications. Discussions of previously published papers are welcome.