Adaptive Control of Time-Varying Parameter Systems with Asymptotic Tracking

TL;DR

This paper presents an adaptive control method for nonlinear systems with time-varying uncertainties, ensuring asymptotic tracking and stability through a Lyapunov-based approach and a RISE-like adaptation law.

Contribution

It introduces a novel adaptive control design incorporating a RISE-like term to handle time-varying uncertainties in nonlinear systems.

Findings

Ensures asymptotic tracking in systems with time-varying parameters.

Guarantees boundedness of all closed-loop signals.

Provides a Lyapunov-based stability proof.

Abstract

A continuous adaptive control design is developed for nonlinear dynamical systems with linearly parameterizable uncertainty involving time-varying uncertain parameters. The key feature of this design is a robust integral of the sign of the error (RISE)-like term in the adaptation law which compensates for potentially destabilizing terms in the closed-loop error system arising from the time-varying nature of uncertain parameters. A Lyapunov-based stability analysis ensures asymptotic tracking, and boundedness of the closed-loop signals.