Nonadaptive Output Regulation of Second-Order Nonlinear Uncertain Systems

2025-05-28

AI Summary

This paper addresses the robust output regulation problem for second-order nonlinear uncertain systems subject to unknown exosystem disturbances. We propose a non-adaptive internal model control (IMC) approach. Our key contributions are: (1) a novel universal internal model structure that uniformly characterizes the steady-state input–state mapping; (2) a coordinate transformation that recasts the output regulation problem as non-adaptive stabilization of an augmented system; and (3) a rigorously constructed Lyapunov function that explicitly accounts for unmodeled dynamics and external disturbances, ensuring global robustness. Crucially, the method avoids the parameter explosion issue inherent in adaptive laws. Theoretically, it guarantees global asymptotic attraction to the output-zeroing manifold. Simulation results on a Duffing oscillator validate both the effectiveness and engineering applicability of the proposed scheme.

Technology Category

• Intelligent Robots: State Estimation
• Machine Learning: Calibration & Uncertainty Quantification
• Cognitive Modeling & Cognitive Systems: Adaptive Behavior

Application Category

• User Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systems
• Responsible Web: Machine-in-the-loop, human agency and autonomy
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

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.

Problem

• Robust output regulation for second-order nonlinear uncertain systems
• Nonadaptive control to avoid bursting phenomenon in uncertain systems
• Internal models for steady-state state and input variables

Innovation

• Robust control for nonlinear uncertain systems
• Generic internal models for steady-state variables
• Nonadaptive stabilization via coordinate transformation