Nonadaptive Output Regulation of Second-Order Nonlinear Uncertain Systems

TL;DR

This paper presents a robust, nonadaptive control method for second-order nonlinear uncertain systems with unknown exosystems, ensuring output regulation without adaptive control's drawbacks.

Contribution

It introduces a nonadaptive internal model approach and a coordinate transformation to solve the robust output regulation problem for uncertain nonlinear systems.

Findings

Guarantees robustness against unmodeled disturbances

Ensures the output zeroing manifold is attractive

Demonstrates effectiveness on the Duffing system

Abstract

This paper investigates the robust output regulation problem of second-order nonlinear uncertain systems with an unknown exosystem. Instead of the adaptive control approach, this paper resorts to a robust control methodology to solve the problem and thus avoid the bursting phenomenon. In particular, this paper constructs generic internal models for the steady-state state and input variables of the system. By introducing a coordinate transformation, this paper converts the robust output regulation problem into a nonadaptive stabilization problem of an augmented system composed of the second-order nonlinear uncertain system and the generic internal models. Then, we design the stabilization control law and construct a strict Lyapunov function that guarantees the robustness with respect to unmodeled disturbances. The analysis shows that the output zeroing manifold of the augmented system can be made attractive by the proposed nonadaptive control law, which solves the robust output regulation problem. Finally, we demonstrate the effectiveness of the proposed nonadaptive internal model approach by its application to the control of the Duffing system.