When is a Parameterized Controller Suitable for Adaptive Control?

TL;DR

This paper analyzes when parameterized controllers for plants with unknown parameters can be realized independently of those parameters, showing that certain standard controllers inherently admit such realizations, thus questioning the necessity of adaptation.

Contribution

It proves that standard model reference controllers with input filters for linear systems can be realized independently of unknown parameters, challenging the need for adaptation in these cases.

Findings

Standard model reference controllers admit parameter-independent realizations.

Adding input filters does not require adaptation, contrary to some beliefs.

The result questions the effectiveness of L1-adaptive control modifications.

Abstract

In this paper we investigate when a parameterized controller, designed for a plant depending on unknown parameters, admits a realization which is independent of the parameters. It is argued that adaptation is unnecessary for this class of parameterized controllers. We prove that standard model reference controllers (state and output--feedback) for linear time invariant systems with a filter at the plant input admit a parameter independent realization. Although the addition of such a filter is of questionable interest, our result formally, and unquestionably, establishes the deleterious effect of such a modification, which has been widely publicized in the control literature under the name L1-adaptive control.