An Algorithm for Solving Zero-Sum Differential Game Related to the Nonlinear H∞ Control Problem

This paper presents an approach for the solution of a zero-sum differential game associated with nonlinear state-feedback H∞ control problem. Instead using approximation methods solving corresponding Hamilton–Jacobi–Isaacs (HJI) partial equation, we propose algorithm that calculates explicit inputs to dynamic system by directly performing minimization simultaneous maximization same objective function. In order achieve numerical robustness and stability, proposed uses: quasi-Newton method, conjugate gradient line search method Wolfe conditions, Adams time discretization complex-step calculation derivatives. The is evaluated in computer simulations on examples first- second-order systems analytical solutions