Discrete-time optimal zero-sum games for nonlinear systems via adaptive dynamic programming

In this paper, a novel discrete-time iterative zero-sum adaptive dynamic programming (ADP) algorithm is developed for solving the optimal control problems of nonlinear systems. Two iteration processes, which are lower and upper iterations, are employed to solve the lower and upper value functions, respectively. Arbitrary positive semi-definite functions are acceptable to initialize the upper and lower iterations of the iterative zero-sum ADP algorithm. It is proven that the upper and lower value functions converge to the optimal performance index function if the optimal performance index function exists, where the existence criterion of the optimal performance index function is unnecessary. Simulation examples are given to illustrate the effective performance of the present method.