具有未知动态的线性系统二人零和博弈问题在线学习方案

针对具有未知动态线性系统的二人零和博弈问题,本文提出了一种新的基于单环迭代方法的在线学习方案.为保证单环迭代方法的收敛性,给出了一种新的分析方法.在系统内部矩阵A,控制输入矩阵B以及干扰输入矩阵D均未知的情况下,通过在线迭代策略,同步得到了博弈代数黎卡提方程的近似解,以及控制和干扰策略.仿真结果表明了所提方法的有效性.

Online solution of two-player zero-sum games for linear systems with unknown dynamics

For two-player zero-sum games of continuous-time linear systems with unknown dynamics, we present an online adaptive learning algorithm based on the policy iteration (PI) scheme with only one loop. A new analytical method to prove the convergence of the PI scheme is presented. An approximate solution to the generalized game algebraic Riccati equation without using a priori knowledge of the system matrices is developed. Simulation results illustrate the effectiveness of the proposed method.