Integral Reinforcement Learning for Linear Continuous-Time Zero-Sum Games With Completely Unknown Dynamics

In this paper, we develop an integral reinforcement learning algorithm based on policy iteration to learn online the Nash equilibrium solution for a two-player zero-sum differential game with completely unknown linear continuous-time dynamics. This algorithm is a fully model-free method solving the game algebraic Riccati equation forward in time. The developed algorithm updates value function, control and disturbance policies simultaneously. The convergence of the algorithm is demonstrated to be equivalent to Newton´s method. To implement this algorithm, one critic network and two action networks are used to approximate the game value function, control and disturbance policies, respectively, and the least squares method is used to estimate the unknown parameters. The effectiveness of the developed scheme is demonstrated in the simulation by designing an H_∞ state feedback controller for a power system.