Model Identification and Adaptive State Observation for a Class of Nonlinear Systems

TL;DR

This paper introduces an adaptive observer for nonlinear systems that combines model identification and state estimation, using high-gain observers and various identification algorithms, with proven stability and robustness.

Contribution

It presents a novel adaptive observer framework integrating high-gain observers with system identification methods for nonlinear systems.

Findings

Stable asymptotic estimation error linked to identifier prediction capabilities

Robustness established against additive disturbances in system and measurements

Flexible identification algorithms, including recursive least-squares and wavelet-based methods

Abstract

In this paper we consider the joint problems of state estimation and model identification for a class of continuous-time nonlinear systems in output-feedback canonical form. An adaptive observer is proposed that combines an extended high-gain observer and a discrete-time identifier. The extended observer provides the identifier with a data set permitting the identification of the system model and the identifier adapts the extended observer according to the new estimated model. The design of the identifier is approached as a system identification problem and sufficient conditions are presented that, if satisfied, allow different identification algorithms to be used for the adaptation phase. The cases of recursive least-squares and multiresolution black-box identification via wavelet-based identifiers are specifically addressed. Stability results are provided relating the asymptotic estimation error to the prediction capabilities of the identifier. Robustness with respect to additive disturbances affecting the system equations and measurements is also established in terms of an input-to-state stability property relative to the noiseless estimates.