Input-Delay Compensation in a Robust Adaptive Control Framework

TL;DR

This paper extends the ${ m extstyle L}_1$ adaptive control framework to include input-delay compensation, ensuring stability and performance for uncertain systems with actuator delays through a delay-dependent analysis.

Contribution

It introduces a delay compensation method within the ${ m extstyle L}_1$ control framework, providing stability conditions and demonstrating effectiveness through analysis and examples.

Findings

Delay compensation improves stability in uncertain systems with actuator delays.

A delay-dependent stability condition guarantees close tracking of a reference system.

Numerical analysis explores the stability region for delay and compensation delay pairs.

Abstract

A modification to the ${\cal L}_1$ control framework for uncertain systems with actuator delay is presented. Specifically, a time delay is introduced in the control input of the state predictor to compensate for the destabilizing effect of input delay in the plant. For this modified framework, the analysis shows that the output of the adaptive system closely follows the behavior of a suitably defined, nonadaptive, stable reference system provided that a delay-dependent stability condition is satisfied and the adaptive gain is chosen sufficiently large. The set of combinations of input delay and compensation delay for which the stability condition is satisfied contains an open set of pairs of positive values provided that a filter bandwidth, characteristic of ${\cal L}_1$ adaptive control is chosen sufficiently large. The efficacy of the delay compensation is illustrated by a simple example. A numerical continuation is also performed to explore the stability region for a case where this can be approximated a priori.