# MODEL IDENTIFICATION AND ADAPTIVE STATE OBSERVATION FOR A CLASS OF NONLINEAR SYSTEMS

Topic: Observers

Séance du jeudi 9 janvier 2020, Salle V334, 14h00-15h00.

Michelangelo BIN, Imperial College London, UK

State estimation is a problem of primary interest in control engineering, and its applications are ubiquitous in all the related areas.

Having available good models, on the other hand, is of crucial importance in many control-related problems, in which they

can be used to cast predictions, extract information on the environment, or to detect events.

In this talk 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 presented combining an extended high-gain observer and a discrete-time identification logic. The extended observer provides the identifier with the (necessarily noisy) data set permitting the identification of the system's model. The identifier, on the other hand, provides new estimates of the system's model, on the basis of which the observer is adapted. Under certain conditions, this "loop" is proved to be convergent and, in presence of disturbances and noise acting on the system, an input-to-state property is guaranteed.

Contrary to common approaches, the design of the identifier is approached as a system identification problem, without relying on the

existence of a "true parameter" and ad hoc adaptation procedures, but rather looking at model estimation as an optimization problem cast on the available measurements.

Instead of developing a single identification algorithm, that would inexorably make sense only for a restricted class of models, sufficient conditions are given under which arbitrary identifiers can be used. Moreover, some algorithms covering relevant cases, such as linear parametrizations and Wavelet decomposition, are shown to fit in the framework. As a main result, we formally relate the prediction capabilities of the "optimal model" in the inferred model set to the asymptotic estimation error.

Finally, applications of the proposed theory to the problem of output regulation for nonlinear systems are discussed.

Michelangelo BIN, Imperial College London, UK

State estimation is a problem of primary interest in control engineering, and its applications are ubiquitous in all the related areas.

Having available good models, on the other hand, is of crucial importance in many control-related problems, in which they

can be used to cast predictions, extract information on the environment, or to detect events.

In this talk 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 presented combining an extended high-gain observer and a discrete-time identification logic. The extended observer provides the identifier with the (necessarily noisy) data set permitting the identification of the system's model. The identifier, on the other hand, provides new estimates of the system's model, on the basis of which the observer is adapted. Under certain conditions, this "loop" is proved to be convergent and, in presence of disturbances and noise acting on the system, an input-to-state property is guaranteed.

Contrary to common approaches, the design of the identifier is approached as a system identification problem, without relying on the

existence of a "true parameter" and ad hoc adaptation procedures, but rather looking at model estimation as an optimization problem cast on the available measurements.

Instead of developing a single identification algorithm, that would inexorably make sense only for a restricted class of models, sufficient conditions are given under which arbitrary identifiers can be used. Moreover, some algorithms covering relevant cases, such as linear parametrizations and Wavelet decomposition, are shown to fit in the framework. As a main result, we formally relate the prediction capabilities of the "optimal model" in the inferred model set to the asymptotic estimation error.

Finally, applications of the proposed theory to the problem of output regulation for nonlinear systems are discussed.