Nonadaptive Learning in Robust Nonlinear Output Regulation

2026-08-17

AI Summary

本文提出了一种非自适应方法，结合输入驱动滤波器、通用内部模型和递归反步法，解决高相对度非线性系统的鲁棒输出调节问题。

Abstract

This paper considers robust nonadaptive regulation for general nonlinear systems in an output-feedback setting with arbitrarily high relative degree. We develop a nonadaptive design that combines an input-driven filter and a generic internal model with a recursive backstepping law, thereby recasting the regulation problem as the robust input-to-state stabilization of an augmented error system. Unlike adaptive schemes, the proposed method does not rely on linearly parameterized regressors and does not require the construction of Lyapunov functions having merely nonpositive derivatives. Under standard assumptions on the exosystem, including purely imaginary and simple eigenvalues, together with a minimum-phase input-to-state stability condition on the internal dynamics, we establish global asymptotic regulation and derive explicit, verifiable inequalities for selecting the design gains. The resulting nonadaptive framework guarantees convergence of the estimation and tracking errors even when the controlled-system dynamics are complex or only partially known. The effectiveness of the theoretical results is demonstrated using a benchmark controlled Duffing system.

Problem

• nonadaptive regulation
• nonlinear systems
• output feedback
• robust control
• error convergence

Innovation

• nonadaptive design
• input-driven filter
• generic internal model
• recursive backstepping law
• robust input-to-state stabilization