Research On Nonlinear Data-driven Control And Game Based On Differential Dynamic Programming

Optimal control is a comprehensive strategy to optimize the performance index of the controlled system.Tracking control theory and two-person game have always been the research focus in the control field.For complex nonlinear systems,the existing optimal control methods are difficult to obtain analytical solutions and the dynamic characteristics of the system are difficult to be described by accurate mathematical models,which brings greater challenges to the control of nonlinear systems.This paper presents a data-driven approach based on unknown model nonlinear system,which solves the optimal tracking problem and two-person game problem.The research contents and results are as follows:(1)The optimal tracking control is studied for uncertain nonlinear systems.Firstly,a dynamic model of tracking error is established based on affine nonlinear continuous system model and expected trajectory;Then,we construct a data-driven model of differential expression of second-order Hamilton-Jacobi-Bellman(HJB)equation based on differential dynamic programming(DDP)algorithm and test data;The approximate system equation and value function are constructed by using the basis function;Then,a data-driven ifferential dynamic programming algorithm is developed based on the established model;Finally,simulation experiments show the effectiveness of this method.(2)A data-driven optimization method based on differential dynamic programming is proposed to solve the two-person zero sum game problem of nonlinear affine systems.Firstly,the system index function is given based on the nonlinear continuous game system model.Then,we introduce the concept of test data into DDP algorithm,so the data-driven model of differential expression of second-order Hamilton-Jacobi-Isaacs(HJI)equation can be established;Next,the unknown system equation and value function are approximated by the basis function respectively;Based on the constructed model,we propose a data-driven optimization method to obtain the unknown coefficients of the basis function;Finally,a numerical example is given to verify the effectiveness of the method.The research results of this paper are of great significance and can solve the optimal control and game control problems of complex nonlinear systems with unknown model.