ADP-based nonlinear optimal output regulation with nonlinear exosystem

This paper discusses the optimal output regulation problem for nonlinear systems with a nonlinear exosystem. Adaptive dynamic programming and internal model principle are integrated to deal with this problem. The control scheme process is designed in the following two steps. In the first step, a nonlinear internal model is constructed to obtain the feedforward controller, which allows for the conversion of the output regulation problem into a stabilization problem. Compared with feedforward design approach, the common assumption that the exosystem is linear and neutral stable has been eliminated successfully. In the second step, the control cost is taken into account and the optimal feedback controller is learned through adaptive dynamic programming. After that, we demonstrate that the closed-loop system is uniformly ultimately bounded by the Lyapunov stability theory. As a distinctive feature, the proposed control framework can tolerate the nonlinear exosystem. Finally, the effectiveness of the control scheme is shown by a simulation example.