Robust Internal Models for Nonlinear Output Regulation with Uncertain Exosystems

This paper presents a nonlinear internal model construction method by introducing certain coined Luenberger observer-like trial samples and further using Lyapunov's auxiliary theorem for confirmation. Specifically, it comes up with several novel types of parameterized nonlinear internal models with certain output in a constructive fashion, distinguishing themselves from existing ones proposed in the literature. In particular, they are most effective in tackling non-adaptive output regulation with uncertain exosystems, i.e., stabilizing control for the resulting augmented system can be treated independent of any adaptive control law. For an exemplary application, an output consensus control problem is proven solvable for multi-agent systems with uncertain leaders/exosystems under general directed communication topologies. As a major consequence, the hurdles can be circumvented arising in the same problem if the conventional canonical internal model were used.