离散非线性零和博弈的事件驱动最优控制方案

Event-triggered optimal control scheme for discrete-time nonlinear zero-sum games

在求解离散非线性零和博弈问题时,为了在有效降低网络通讯和控制器执行次数的同时保证良好的控制效果,本文提出了一种基于事件驱动机制的最优控制方案.首先,设计了一个采用新型事件驱动阈值的事件驱动条件,并根据贝尔曼最优性原理获得了最优控制对的表达式.为了求解该表达式中的最优值函数,提出了一种单网络值迭代算法.利用一个神经网络构建评价网.设计了新的评价网权值更新规则.通过在评价网、控制策略及扰动策略之间不断迭代,最终获得零和博弈问题的最优值函数和最优控制对.然后,利用Lyapunov稳定性理论证明了闭环系统的稳定性.最后,将该事件驱动最优控制方案应用到了两个仿真例子中,验证了所提方法的有效性.

In order to reduce the network communication and controller execution frequency while guarantee a desired control performance, an event-triggered optimal control scheme is proposed for solving the optimal control pair of discretetime nonlinear zero-sum games in this paper. Firstly, an event-triggered condition with new event-triggered threshold is designed. The expression of the optimal control pair is obtained based on the Bellman optimality principle. Then, a single network value iteration algorithm is proposed to solve the optimal value function in this expression. A neural network is used to construct the critic network. Novel weight update rule of the critic network is derived. Through the iteration between the critic network, the control policy and the disturbance policy, the optimal value function and the optimal control pair can be solved. Further, the Lyapunov theory is used to prove the stability of the event-triggered closed-loop system.Finally, the event-triggered optimal control mechanism is applied to two examples to verify its effectiveness.