基于零和博弈方法的多智能体系统H∞一致性

H∞ Consensus for Multiagent System Using Zero-Sum Game Approach

针对存在外部扰动情形下离散多智能体系统的H∞一致性问题,利用二人零和博弈方法,一致性协议和外部扰动分别被看作博弈双方参与者,通过寻找二人零和博弈的纳什均衡点,可以设计出针对最坏情形干扰时的最优一致性协议.而获得博弈问题的纳什均衡需要求解耦合Hamilton-Jacobi-Isaacs(HJI)方程,因此给出了解耦方法,并且使用强化学习中的双环策略迭代算法对解耦后的HJI方程进一步求解.最后给出的算例仿真结果验证了提出方法的有效性.

For solving H∞ consensus problem in discrete-time multiagent system with external disturbance,the zero-sum game theoretic method is adopted in this paper.The consensus protocol and external disturbance are regarded as two players respectively.Optimal consensus protocol under worst-case disturbance can be designed by acquiring Nash equilibrium point of zero-sum game.It is shown that obtaining of Nash equilibrium requires the solution of coupled HJI equations.Therefore,a decouple approach is given and,as the reinforcement learning algorithm,a double loop policy iteration is used for solving decoupled HJI equations.Finally,a numerical simulation is studied to verify the effectiveness of proposed method.