Zero-Sum Game for a Class of Second-Order Systems

This paper studies the zero-sum game problem for second-order strict-feedback nonlinear systems. By using the simplified reinforcement learning algorithm, the solution of Hamilton-Jacobi-Isaacs equation can be achieved. Based on the Lyapunov functional method, the proposed control scheme ensure that the system output signal can follow the given desired signal, and it is proved that the tracking error can converge to a small area near zero, and all signals of the closed-loop system are semi-globally uniformly ultimately bounded. Finally, a simulation example is provided to testify the validity of the control strategy.