This paper develops a novel concurrent learning-based approximate dynamics programming (ADP) algorithm for solving the two-player zero-sum (ZS) game arising in H∞ control of continuous-time (CT) systems with unknown nonlinear dynamics. First, the H∞ control problem is formulated as a zero-sum (ZS) game and then, an online algorithm is developed that learns the solution to the Hamilton-Jacobi-Isaacs (HJI) equation without using any knowledge on the system dynamics. This is achieved by using a neural network (NN) identifier to approximate the uncertain system dynamics. The algorithm is implemented on actor-critic-disturbance NN structure along with the NN identifier to approximate the optimal value function and corresponding Nash solution of the game. All NNs are tuned at the same time. By using the idea of concurrent learning for adaptation of the identifier and critic NN weights the need to check for the persistence of excitation (PE) condition is relaxed to simplified condition. The stability of the overall system is guaranteed and the convergence to the Nash solution of the game is obtained. Simulation results show the effectiveness of the proposed method.

Keywords