A Unified Approach to High-Gain Adaptive Controllers

TL;DR

This paper unifies and generalizes high-gain adaptive controllers for linear systems using dynamic equations on time scales, proving their stability across various sampling and system conditions.

Contribution

It introduces a unified framework for high-gain adaptive controllers on arbitrary time scales, extending stability results to discrete, continuous, and hybrid systems.

Findings

Unified stability proof for high-gain adaptive controllers on various time scales

Generalization of discrete and continuous controller implementations

Enhanced understanding of adaptive control stability in hybrid systems

Abstract

It has been known for some time that proportional output feedback will stabilize MIMO, minimum-phase, linear time-invariant systems if the feedback gain is sufficiently large. High-gain adaptive controllers achieve stability by automatically driving up the feedback gain monotonically. More recently, it was demonstrated that sample-and-hold implementations of the high-gain adaptive controller also require adaptation of the sampling rate. In this paper, we use recent advances in the mathematical field of dynamic equations on time scales to unify and generalize the discrete and continuous versions of the high-gain adaptive controller. We prove the stability of high-gain adaptive controllers on a wide class of time scales.