An online integral reinforcement learning algorithm to solve N-player Nash games

In this paper we introduce an online algorithm that uses integral reinforcement knowledge for learning the continuous-time Nash game (zero-sum and non-zero-sum) solution for nonlinear systems with infinite horizon costs and partial knowledge of the system dynamics. This algorithm is a data based approach to the solution of the coupled Hamilton-Jacobi equations and it does not require explicit knowledge on the system´s drift dynamics. A novel adaptive control algorithm is given that is based on policy iteration and implemented using an actor/critic structure for every player in the game having 2N adaptive approximator structures. All 2N approximation networks are adapted simultaneously. Novel adaptive control tuning algorithms are given for the critic and actor networks. The convergence to the Nash solution of the game is proven, and stability of the system is also guaranteed. Simulation examples support the theoretical result.