Robust Actor–Critic Learning for Continuous-Time Nonlinear Systems With Unmodeled Dynamics

This article considers the robust optimal control problem for a class of nonlinear systems in the presence of unmodeled dynamics. An adaptive optimal controller is designed using the online actor–critic learning and is robustified against unmodeled dynamics. To deal with unmodeled dynamics, an auxiliary signal with the system state as its input signal is designed to capture the input-to-state stability. In addition to the critic network for value function approximation, a novel robustifying term is developed and introduced into the actor network to ensure robustness during the learning process. It is shown that both the actor and the critic weights learning converge to their optimal values while guaranteeing the boundedness of all the signals in the closed loop. Simulation examples are conducted to verify the efficacy of the presented scheme.