Guaranteed Transient Performance with $\mathcal{L}_1$ Adaptive Controller for Systems with Unknown Time-varying Parameters: Part I

TL;DR

This paper introduces an $$ adaptive control method that guarantees bounded transient and asymptotic tracking for systems with unknown, time-varying parameters and disturbances, verified through robotic arm simulations.

Contribution

It proposes a novel adaptive control approach that ensures guaranteed transient performance for systems with unknown, time-varying parameters and disturbances.

Findings

Performance bounds improve with higher adaptation gain

The method ensures bounded transient and asymptotic tracking

Simulations confirm theoretical guarantees on a robotic arm

Abstract

This paper presents a novel adaptive control methodology for uncertain systems with time-varying unknown parameters and time-varying bounded disturbance. The adaptive controller ensures uniformly bounded transient and asymptotic tracking for system's both signals, input and output, simultaneously. The performance bounds can be systematically improved by increasing the adaptation gain. Simulations of a robotic arm with time-varying friction verify the theoretical findings.