Data-Driven Adaptive Dynamic Programming for H 2 /H∞ Control of Unknown Nonlinear System

In order to solve the practical problems that exact analytic solution of the coupled Hamilton-Jacobi-Isaacs (HJI) equations arising from the mixed $H_{2}/H_{\infty}$ control of nonlinear systems and the nonlinear system dynamics models is not generally known. According to the model-based iterative algorithm, a data-driven approximate dynamic programming algorithm for solving mixed $H_{2}/H_{\infty}$ control problems is derived by adding known noise into control strategy and disturbance strategy. The Nash equilibrium strategy of nonlinear system is obtained online by using input-output data of nonlinear system, which does not depend on the specific model information of the system. Two critic neural networks and two action neural networks are used to synchronously update two value functions, control strategy and disturbance strategy online. The unknown parameters of neural network are estimated by generalized least squares. The simulation results verify the feasibility of the algorithm.