# Nonadaptive Output Regulation of Second-Order Nonlinear Uncertain Systems

arXiv: https://arxiv.org/abs/2505.21838 · HTML: https://mlsanity.com/paper/2505.21838/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 3 of its 35 references that are in the map.
- First posted on arXiv 28 May 2025.

## Builds on (most cited first, 3 of 3)

- [A nonparametric learning framework for nonlinear robust output regulation](https://mlsanity.com/paper/2309.14645/) (2023)
- [Approximate Nonlinear Regulation via Identification-Based Adaptive Internal Models](https://mlsanity.com/paper/1907.05050/) (2019)
- [Nonparametric Steady-State Learning for Nonlinear Output Feedback Regulation](https://mlsanity.com/paper/2402.16170/) (2024)

## Abstract (arXiv)

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.