Exponentially stable adaptive control. Part I. Time-invariant plants

TL;DR

This paper introduces a new adaptive control law for linear time-invariant plants that guarantees exponential stability without requiring prior knowledge of certain plant parameters, relaxing classical assumptions.

Contribution

A novel adaptive control law is proposed that ensures exponential stability under less restrictive conditions than traditional methods.

Findings

The proposed law guarantees exponential stability for LTI plants.

It relaxes the need to know the sign of the plant's high-frequency gain.

The method is applicable to adaptive state and output feedback control.

Abstract

In this research we consider linear time-invariant plants and assume that the regressor finite excitation requirement is met. In such case, a new law to adjust the controller parameters, which ensures the exponential stability of the classical dynamic model of the tracking error under the condition that its states are not included in such a law, is proposed in this study. In addition, it also relaxes a number of classical assumptions and requirements of the adaptive control theory, i.e. the necessity to know the sign/value of the plant high-frequency gain, the need of experimentally based choice of the proposed law adaptive gain value, the requirement to the tracking error transfer function to be strictly positive real considering the output feedback control. The applicability of the proposed law to the problems of adaptive state and output feedback control is shown. The advantages of the proposed method over the well-known ones are demonstrated.