State and Parameter Estimation Based on Filtered Transformation for a Class of Second-Order Systems

TL;DR

This paper introduces a novel filtered transformation method for state and parameter estimation in second-order systems, requiring weaker conditions than classical methods, demonstrated through simulations with non-PE regressors.

Contribution

A new filtered transformation approach for second-order systems that relaxes the persistency of excitation requirement using a dynamic matrix and invariance techniques.

Findings

Requires weaker non-square-integrability condition

Effective with regressors not satisfying PE condition

Simulation confirms robustness of the proposed method

Abstract

This paper addresses the problem of state and parameter estimation for a class of second-order systems with single output. A new filtered transformation is proposed for the system via dynamic vector and matrix. In this method, the dynamics of the vector and matrix are derived by immersion and invariance technique such that the state estimation condition is guaranteed. Compared to the classical approaches that persistency of excitation (PE) condition is required for parameter convergence, the proposed method needs a weaker one, so called non-square-integrability condition, in the transformation via dynamic matrix. Simulation results are concluded for a class of regressors which are not PE but satisfy the new condition.