Robust Hybrid Finite-Time Parameter Estimation Without Persistence of Excitation

TL;DR

This paper introduces a hybrid algorithm for finite-time parameter estimation in linear regression models that does not require persistent excitation, demonstrating robustness and applicability to time-varying parameters.

Contribution

A novel hybrid systems-based algorithm for finite-time parameter estimation that relaxes the persistent excitation requirement and handles time-varying parameters.

Findings

Converges to true parameters in finite time under relaxed excitation conditions.

Maintains robustness against measurement noise.

Applicable to both constant and piecewise constant parameters.

Abstract

In this paper, we consider the problem of estimating parameters of a linear regression model. Using a hybrid systems framework, a hybrid algorithm is proposed allowing the estimate to converge to the exact value of the unknown parameters in predetermined finite time. Interestingly, we show that for the case of constant parameters, the convergence property of the hybrid algorithm holds while only requiring the regressor to be exciting on a given interval. For the case of piecewise constant parameters, the classical persistency of excitation condition is required to guarantee the convergence. Robustness of the proposed algorithm with respect to measurements noise is analysed. Finally, illustrative examples are provided showing the merits of the proposed approach in terms of scalability and the applicability for the general class of time-varying unknown parameters