I-DREM MRAC with Time-Varying Adaptation Rate & No A Priori Knowledge of Control Input Matrix Sign to Relax PE Condition

TL;DR

This paper introduces an advanced MRAC system that adapts online without prior knowledge of control input matrix sign, ensuring exponential convergence even without persistent excitation, and demonstrates its effectiveness through numerical experiments.

Contribution

It develops a new I-DREM MRAC method with time-varying adaptation rate that relaxes PE conditions and does not require prior control input matrix sign knowledge.

Findings

Achieves exponential convergence of controller parameters

Ensures monotonic convergence of parameter error

Adapts the rate online based on current regressor values

Abstract

The known dynamic regressor extension and mixing method (DREM) is combined with the proposed filter of a new type, which uses the integration operation with forgetting, and the recursive least-squares method to develop the new I-DREM model reference adaptive control (MRAC) system. It does not require a priori knowledge of the sign or the elements values of the control input matrix of the plant. It also provides the exponential convergence of the adaptation process (with the automatically adjustable adaptation rate) without the regressor persistent excitation. Such control system allows to solve three actual problems of the adaptive control: 1) to provide the exponential convergence of the controller parameter error under the condition of the regressor initial excitation, 2) to make such convergence monotonic, 3) to calculate the adaptation rate online according to the current regressor value. Some numerical experiments are conducted to demonstrate the effectiveness of the proposed method.