Adaptive Dynamic Programming algorithm for finding online the equilibrium solution of the two-player zero-sum differential game

This paper will present an Approximate/Adaptive Dynamic Programming (ADP) algorithm for determining online the Nash equilibrium solution for the two-player zero-sum differential game with linear dynamics and infinite horizon quadratic cost. The algorithm is built around an iterative method that has been developed in the control engineering community for solving the continuous-time game algebraic Riccati equation (CT-GARE) that is underlying the game problem. We here show how the ADP techniques will enhance the capabilities of the offline method allowing an online solution without the requirement of complete knowledge of the system dynamics.