预定性能约束下非线性博弈系统的最优事件触发控制

Optimal Event-Triggered Control for Nonlinear Game Systems with Prescribed Performance Constraints

摘要

针对动态未知的非线性零和博弈系统，提出一种基于预定性能约束的最优事件触发控制方法，在降低计算资源的条件下实现系统动态未知的预定性能控制。首先，引入预定性能函数，将受约束的系统控制问题转化为等效的无约束最优控制问题；其次，基于离策略（off policy）数据迭代机制，结合多项式拟合技术与积分强化学习（Integral Reinforcement Learning, IRL）方法，在纯数据驱动的控制律求解框架下推导出无模型迭代控制策略，解决系统动态未知带来的求解困难问题。同时，本文设计了一种基于博弈理论的事件触发机制，首先，通过将事件采样误差与控制策略建模为零和博弈，有效降低了采样数量，从而减少计算负担；然后，采用单评价神经网络逼近最优控制解，利用设计的策略更新网络权值；最后，通过理论分析和仿真验证说明了方法的收敛性和有效性。

Abstract

This paper proposes an optimal event-triggering control method based on prescribed performance constraints for nonlinear zero-sum game systems with unknown dynamics, achieving prescribed performance control for systems with unknown dynamics under reduced computational resources. First, by introducing a prescribed performance function, the constrained system control problem is transformed into an equivalent unconstrained optimal control problem. Second, leveraging an off-policy data iteration mechanism, combined with polynomial fitting techniques and the Integral Reinforcement Learning (IRL) method, a model-free iterative control strategy is derived within a purely data-driven control law framework, addressing the challenges posed by unknown system dynamics. Furthermore, an event-triggering mechanism based on game theory is designed, effectively reducing the number of samples and computational burden by modeling event-triggering sampling errors and control strategies as a zero-sum game. Then, a single critic neural network is employed to approximate the optimal control solution, with the proposed strategy used to update the network weights. Finally, theoretical analysis and simulation results demonstrate the convergence and effectiveness of the proposed method.

关键词

零和博弈 / 自适应动态规划 / 事件触发 / 预定性能控制 / 积分强化学习

Key words

zero-sum game / adaptive dynamic programming / event-triggering control / prescribed performance control / integral reinforcement learning

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基金资助

上海市科技创新行动计划项目(24511104302)