Unknown Piecewise Constant Parameters Identification with Exponential Rate of Convergence

TL;DR

This paper introduces a new online algorithm for identifying unknown piecewise constant parameters in linear regression models, achieving exponential convergence and robustness under finite excitation conditions.

Contribution

It presents a novel DREM-based estimation method that detects switching times and ensures global exponential convergence despite unknown switching signals.

Findings

Algorithm achieves exponential convergence of parameters.

Method is robust to external disturbances.

Effective in numerical experiments with regressions and plant models.

Abstract

The scope of this research is the identification of unknown piecewise constant parameters of linear regression equation under the finite excitation condition. Compared to the known methods, to make the computational burden lower, only one model to identify all switching states of the regression is used in the developed procedure with the following two-fold contribution. First of all, we propose a new truly online estimation algorithm based on a well-known DREM approach to detect switching time and preserve time alertness with adjustable detection delay. Secondly, despite the fact that a switching signal function is unknown, the adaptive law is derived that provides global exponential convergence of the regression parameters to their true values in case the regressor is finitely exciting somewhere inside the time interval between two consecutive parameters switches. The robustness of the proposed identification procedure to the influence of external disturbances is analytically proved. Its effectiveness is demonstrated via numerical experiments, in which both abstract regressions and a second-order plant model are used.