Neural-network-based zero-sum game for discrete-time nonlinear systems via iterative adaptive dynamic programming algorithm

In this paper, we solve the zero-sum game problems for discrete-time affine nonlinear systems with known dynamics via iterative adaptive dynamic programming algorithm. First, a greedy heuristic dynamic programming iteration algorithm is developed to solve the zero-sum game problems, which can be used to solve the Hamilton–Jacobi–Isaacs equation associated with H∞H∞ optimal regulation control problems. The convergence analysis in terms of value function and control policy is provided. To facilitate the implementation of the algorithm, three neural networks are used to approximate the control policy, the disturbance policy, and the value function, respectively. Then, we extend the algorithm to H∞H∞ optimal tracking control problems through system transformation. Finally, two simulation examples are presented to demonstrate the effectiveness of the proposed scheme.