Nonadaptive Output Regulation of Second-Order Nonlinear Uncertain Systems
Maobin Lu, Martin Guay, Telema Harry, Shimin Wang, Jordan Cooper
TL;DR
The paper addresses robust output regulation for a class of second-order nonlinear uncertain systems with an unknown exosystem. It proposes a nonadaptive control framework built around a generic internal-model design that converts the regulation problem into stabilization of an augmented system, and proves global asymptotic stability via a Lyapunov function. Key contributions include the construction of steady-state internal models for both state and input, the transformation to an error dynamics system, and a nonadaptive stabilizing law that achieves regulation under unknown exosystem parameters, demonstrated on a Duffing system. The approach offers improved robustness to unmodeled disturbances and avoids the complexity of adaptive parameter estimation typical in adaptive internal-model strategies, with explicit Lyapunov-based guarantees.
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.