Approximate dynamic programming for two-player zero-sum game related to H ∞ control of unknown nonlinear continuous-time systems

This paper develops a concurrent learning-based approximate dynamic 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 is formulated as a 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 the corresponding Nash solution of the game. All NNs are tuned at the same time. By using the idea of concurrent learning the need to check for the persistency of excitation 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 shown. Simulation results show the effectiveness of the algorithm.