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

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 consists of an extended high-gain observer interconnected with 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 observer according to the new estimated model. The design of the identifier is approached as a system identification problem, and a set of sufficient conditions are presented that, if satisfied, allow different identification algorithms to be used for the adaptation phase. The case of recursive least-squares and of wavelet-based identifiers performing a multiresolution black-box identification are specifically addressed. Stability results are provided relating the asymptotic estimation error to the prediction capabilities of the identifier. Robustness to additive disturbances affecting the system equations and measurements is also given in terms of an input-to-state stability property relative to the ideal estimates.