Bridging Model Reference Adaptive Control and Data Informativity

TL;DR

This paper introduces a new framework based on data informativity for model reference adaptive control (MRAC), providing necessary and sufficient conditions for gain convergence, which broadens understanding beyond traditional persistent excitation requirements.

Contribution

It establishes necessary and sufficient conditions for MRAC gain convergence using data informativity, offering a new approach that relaxes traditional excitation conditions.

Findings

Necessary and sufficient conditions for convergence are identified.

Data informativity is shown to be less restrictive than persistent excitation.

A constructive method for designing adaptive laws is provided.

Abstract

The goal of model reference adaptive control (MRAC) is to ensure that the trajectories of an unknown dynamical system track those of a given reference model. This is done by means of a feedback controller that adaptively changes its gains using data collected online from the closed-loop system. One of the approaches to solve the MRAC problem is to impose conditions on the data that guarantee convergence of the gains to a solution of the so-called matching equations. In the literature, various extensions of the concept of persistent excitation have been proposed in an effort to weaken the conditions on the data required for this convergence. Despite these efforts, it is not well-understood what conditions are necessary and sufficient for ensuring convergence of MRAC to a solution of the matching equations. In this paper, we propose a new framework to study the MRAC problem, using the concept of data informativity. Our main contribution is to provide \emph{necessary and sufficient} conditions for the existence of an adaptive law that guarantees convergence of the gains to a solution of the matching equations, and to provide a recipe for its construction. While existing excitation conditions imply that the system can be uniquely identified from the collected data, our results show that this is not necessary for the convergence of the feedback gains.