Adaptive Observer for a Class of Systems with Switched Unknown Parameters Using DREM

TL;DR

This paper introduces an adaptive observer for nonlinear systems with switched unknown parameters, using DREM to ensure asymptotic convergence of states and parameters despite switching disturbances.

Contribution

The paper proposes a novel adaptive observer that treats zero-input responses as excitations and employs DREM for decoupled, robust parameter estimation in switched systems.

Findings

Estimation errors converge to zero asymptotically.

The method is robust against disturbances and noise.

Numerical example confirms effectiveness.

Abstract

In this note, we develop an adaptive observer for a class of nonlinear systems with switched unknown parameters to estimate the states and parameters simultaneously. The main challenge lies in how to eliminate the disturbance effect of zero-input responses caused by the switching on the parameter estimation. These responses depend on the unknown states at switching instants (SASI) and constitute an additive disturbance to the parameter estimation, which obstructs parameter convergence to zero. Our solution is to treat the zero-input responses as excitations instead of disturbances. This is realized by first augmenting the system parameter with the SASI and then developing an estimator for the augmented parameter using the \textit{dynamic regression extension and mixing} (DREM) technique. Thanks to its property of element-wise parameter adaptation, the system parameter estimation is decoupled from the SASI. As a result, the estimation errors of system states and parameters converge to zero asymptotically. Furthermore, the robustness of the proposed adaptive observer is guaranteed in the presence of disturbances and noise. A numerical example validates the effectiveness of the proposed approach.