基于ADP方法求解未知非线性零和微分对策问题

ADP Approach to Solve Unknown Nonlinear Zero-Sum Game

针对一类未知非线性系统的二人零和微分对策问题,提出了一种基于近似动态规划(ADP)方法的控制方案.该方案首先通过设计一个基于递归神经网络(RNN)模型的辨识方案来近似未知非线性系统动态.通过在RNN模型中增加一个新型的调整项,保证了所建立的RNN模型的动态与原未知系统动态的误差渐近收敛到零.然后在此RNN模型基础上,应用ADP方法求解鞍点存在或者不存在情况下的最优性能指标以及最优控制策略.最后通过一个仿真例子验证了所提方案的有效性.

An approximate dynamic programming（ADP） approach was proposed for a class of unknown nonlinear zero-sum game.A model based on a recurrent neural network（RNN） was used to approximate the unknown system dynamics.A novel adjustable term related to the modeling error was added to the RNN model,which guaranteed the modeling error convergent to zero.Then,an ADP approach was given to solve the optimal performance index and the optimal control pair under the saddle point of the zero-sum game existence or not.Simulation results demonstrated the effectiveness of the proposed control scheme.