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In this article, we consider the joint problems of state estimation and model identification for a class of continuous-time nonlinear systems in the 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 dataset 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. [ABSTRACT FROM AUTHOR]

This article concerns the problem of adaptive output regulation for multivariable nonlinear systems in normal form. We present a regulator employing an adaptive internal model of the exogenous signals based on the theory of nonlinear Luenberger observers. Adaptation is performed by means of discrete-time system identification schemes, in which every algorithm fulfilling some optimality and stability conditions can be used. Practical and approximate regulation results are given relating the prediction capabilities of the identified model to the asymptotic bound on the regulated variables, which become asymptotic whenever a “right” internal model exists in the identifier's model set. The proposed approach, moreover, does not require “high-gain” stabilization actions. [ABSTRACT FROM AUTHOR]

This article deals with the problem of output regulation in a “nonequilibrium” context for a special class of multivariable nonlinear systems stabilizable by high-gain feedback. A postprocessing internal model design suitable for the multivariable nature of the system, which might have more inputs than regulation errors, is proposed. Uncertainties in the system and exosystem are dealt with by assuming that the ideal steady-state input belongs to a certain “class of signals,” by which an appropriate model set for the internal model can be derived. The adaptation mechanism for the internal model is then cast as an identification problem, and a least-squares solution is specifically developed. In line with recent developments in the field, the vision that emerges from this article is that approximate, possibly asymptotic, regulation is the appropriate way of approaching the problem in a multivariable and uncertain context. New insights about the use of identification tools in the design of adaptive internal models are also presented. [ABSTRACT FROM AUTHOR]

We propose an adaptive observer scheme to estimate boundary parameters in first-order hyperbolic systems of Partial Differential Equations (PDE). The considered systems feature an arbitrary number of states traveling in one direction and one counter-convecting state. Uncertainties in the boundary reflection coefficients and boundary additive errors are estimated relying on a pre-existing observer design and a novel Lyapunov-based adaptation law. [ABSTRACT FROM AUTHOR]