Robust adaptive dynamic programming for a three-player zero-sum differential game with unmatched uncertainties

Abstract

This paper presents a novel model-free online algorithm to solve the linear continuous-time three-player zero-sum differential game problem in the presence of dynamic uncertainty. Based on robust adaptive dynamic programming (RADP) method, the saddle point control policy and disturbance policy are iteratively approximated for the game problem with unmatched uncertainties. The convergence of the proposed RADP method and the global asymptotic stability (GAS) of the closed-loop system are also analyzed. An application to a power system is adopted to illustrate the effectiveness of the derived algorithm.