  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.
