Federico MORELLI defends his PhD on Jan. 27, 2021 at 9:00 AM.

**Place : ** Ecole Centrale de Lyon, visio conference only.

**Jury** :

Rapporteurs :

M. Cristian Rojas, Professeur Associé, KTH Royal Institute of Technology

M. Guillaume Mercère, Maître de Conférence (HdR), Université de Poitiers (LIAS)

Autres membres :

Mme Marion Gilson, Professeure, Université de Lorraine (CRAN)

M Thierry Poinot, Professeur, Université de Poitiers (LIAS)

Encadrement :

M. Xavier Bombois, Directeur de Recherche CNRS, Ecole Centrale de Lyon (Ampère)

M. Laurent Bako, Maître de Conférence (HdR), Ecole Centrale de Lyon (Ampère)

**Abstract** :

At the roots of every engineering field there are mathematical models. They allow us to make predictions on the evolution of a process, monitor the health of a plant and design a control scheme. System Identification provides us with techniques for obtaining such a model directly from experimental data collected from the system we want to model. In order to identify a good model, a user has to choose: a model structure, experimental data and an estimation method.

The design of the experimental data (i.e. the design of the identification experiment) has important consequences on the final quality of the model. Indeed, in the Prediction Error framework, the “larger” the power spectrum of the excitation signal, the more accurate the model and the higher the experiment cost. In this context, the least-costly experiment design framework has been proposed, where the cost of the identification experiment is minimized while guaranteeing that the accuracy of the identified model is larger than a given threshold.

In all optimal experiment design problems, the underlying optimisation problem depends on the unknown true system that we want to identify. To tackle this issue, the area of robust experiment design has been developed. However, except for simple cases, all the approaches present the risk of underestimating the actual cost of the experiment and the risk of an accuracy of the identified model that is lower than the desired one. In this thesis, using the tools of robustness analysis, we propose a convex optimization approach that tackles these issues. We do this considering that the excitation signal is a multisine signal.

In recent years, a rising interest for the identification of the modules in a dynamic network is observed. However, the problem of the optimal design of such identification experiments remains largely unexplored. In this thesis, we consider a network made up of locally controlled systems and we develop an approach to design an identification experiment leading to a sufficiently accurate model of a given module of such a network while minimizing the perturbation induced by the excitation signal on the network (i.e., the cost of the experiment).

Finally, in the second part of this thesis we consider the resonator of a MEMS gyroscope. This resonator is meant to oscillate at its resonance frequency in order to have the desired performance. However, this resonance frequency changes with the temperature and it is therefore necessary to track this resonance frequency over the time. For this purpose, we investigate two solutions in this thesis: one coming from adaptive control, the Extremum Seeking scheme, and one coming from recursive identification, the RLS algorithm.

**Keywords : **

System Identification, Optimal Experiment Design, Robust Experiment Design, Dynamic Networks, Resonant Frequency, Recursive Identification, Extremum Seeking

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