Model-free adaptive optimal control of continuous-time nonlinear non-zero-sum games based on reinforcement learning

In this paper, two novel algorithms to find the Nash equilibrium solution of the non-zero-sum games for continuous-time input-affine nonlinear systems are presented. Based on integral reinforcement learning method, the integral-exploration-coupled Hamilton-Jacobi (HJ) equations are derived, which does not contain any information of the system dynamics. Then, based on neural networks approximation, two different adaptive tuning law of weights are given to estimate the approximate solution of the coupled HJ equations. Both two algorithms can estimate the value function and the policy without knowing or identifying the system dynamics. The closed-loop system stability and the convergence of weights are guaranteed based on Lyapunov analysis. Finally, the simulation results of a two-player non-zero-sum game demonstrate the effectiveness of our algorithms.