Robust zero-sum differential game for uncertain nonlinear systems via adaptive dynamic programming

In this paper, the robust control problem for uncertain differential game dynamics is transformed into a nominal zero-sum differential game control problem by introducing an appropriate cost function. Then the robust Nash equilibrium solution is derived by modifying the Nash solution of the nominal system. By using the adaptive dynamic programming (ADP) approach, the corresponding Hamilton-Jacobi-Isaacs equation is solved and an additional stabilizing term is introduced to guarantee the boundedness of the system states during the online learning process. Finally, the estimated weight error of the critic network and the closed-loop system are proved to be stable based on Lyapunov approach. An example is provided to verify the effectiveness of the proposed robust control law.