Composite Learning Adaptive Control under Non-Persistent Partial Excitation

TL;DR

This paper introduces a composite learning adaptive control method that relaxes excitation requirements for uncertain nonlinear systems, ensuring convergence of excited parameter estimates even under non-persistent excitation conditions.

Contribution

It develops a novel spectral decomposition-based approach and Lyapunov function to achieve parameter convergence without persistent excitation, improving robustness.

Findings

Parameter estimation error converges under non-persistent excitation.

Control error and excited parameter error converge to zero.

Simulation verifies theoretical results.

Abstract

This paper focuses on relaxing the excitation conditions for the adaptive control of uncertain nonlinear systems. By adopting the spectral decomposition technique, a linear regression equation (LRE) is constructed to quantitatively collect historical excitation information, based on which the parameter estimation error is decomposed into the excited component and the unexcited component. By sufficiently utilizing the collected excitation information, the composite learning and {\mu}-modification terms are designed and incorporated into the "Lyapunov-based" parameter update law. By developing a novel Lyapunov function, it is demonstrated that under non-persistent partial excitation, the control error and the excited parameter estimation error component converge to zero, while the unexcited component remains bounded. Furthermore, the proposed adaptive control scheme can effectively eliminate the effects of parametric uncertainties and enhance the robustness of the closed-loop systems. Simulation results are provided to verify the theoretical findings.