模型未知非零和博弈问题的策略迭代算法

提出了一种在线积分策略迭代算法,用来求解内部非线性动力模型未知的双人非零和博弈问题.通过在控制策略和干扰策略中引入探测信号,从而避开了系统的模型信息,得到了一个求解非零和博弈的无模型的近似动态规划算法.该算法同步更新值函数、控制策略、扰动策略,并且最终得到收敛的策略权值.在算法实现过程中,使用4个神经网络分别近似两个值函数、控制策略和扰动策略,使用最小二乘法估计神经网络的未知参数.最后仿真结果验证了算法的有效性.

Policy Iteration Algorithm for Nonzero-Sum Games with Unknown Models

An online integral policy iteration algorithm was proposed to find the solution of two-player nonzero-sum differential games with completely unknown nonlinear continuous-time dynamics. Exploration signals can be added into the control and disturbance policies， rather than having to find the model information. An approximate dynamic programming (ADP) of model-free approach can be constructed， and the nonzero-sum games can be solved. The value function， control and disturbance policies simultaneously can be updated by the proposed algorithm， and converged policy weight parameters are obtained. To implement the algorithm， four neural networks are used respectively to approximate the two game value functions， the control policy and the disturbance policy. The least squares method is used to estimate the unknown parameters of the neural networks. The effectiveness of the developed scheme is demonstrated by a simulation example.