Optimal identification experiment design : contributions to its robustification and to its use for dynamic network identification : resonance frequency tracking.

Summary At the foundation of every field of engineering are mathematical models. They allow us to make predictions about the evolution of a process, to monitor the health of a system and to design a control law. Systems Identification provides us with techniques to obtain a model directly from experimental data collected on the system we want to model and which allows us to obtain a model that is sufficiently accurate. To obtain a good model, using the tools of Systems Identification, the user must choose: a model structure, the experimental data and an identification criterion.The choice of the experimental data is based on the design of the experiment and has important consequences on the final quality of the model. Indeed, if we consider the identification of a model among a set of transfer functions (model structure) in the framework of the Prediction Error, the "larger" the spectrum of the excitation signal, the more accurate the model is. On the other hand, a "large" spectrum of the excitation signal represents a high cost for the experiment. In this context, the framework of least costly design of experiment has been proposed, where the cost is minimized by requiring a sufficiently accurate model.In any optimal design of experiment problem, the underlying optimization problem depends on the unknown real system one wants to identify. This problem is usually circumvented by replacing the real system with an initial estimate. An important drawback of this approach is that it may underestimate the actual cost of the experiment. In addition, the accuracy of the identified model may be lower than desired. Many efforts have been made in the literature to make this optimization problem robust, which has led to the research area of robust optimal experiment design. However, with the exception of simple cases, all the approaches proposed so far do not completely robustify the optimization problem. In this thesis, we propose a convex optimization approach, which minimizes the worst-case cost associated with a given a-priori set of parametric uncertainties and which guarantees that the accuracy of the model is at least the desired one. We do this by considering that the excitation signal is a multisine signal.In the last few years, we have observed in the field of Automatic Control a growing interest in networks. Although several problems for identification in the context of a network have been recently tackled, this is not the case for the optimal design of experiments. In this thesis, we consider the optimal experiment design for the identification of a module in a network of locally controlled systems. The identification experiment will be designed to obtain a sufficiently accurate model of the module to be identified with the lowest identification cost, i.e., with the lowest network perturbation.Finally, in the second part of this thesis, we consider the mass drive system of a MEMS gyroscope. This mass drive system is supposed to oscillate at its resonant frequency in order to obtain the desired performance. However, during its operation, the gyroscope experiences environmental changes, such as temperature changes, which affect the resonant frequency of the resonator. Therefore, it is important to track these changes during the operation of the gyroscope. To this end, in this thesis, we study two solutions: one from adaptive control, the so-called Extremum Seeking scheme, and the other from System Identification, the Recursive Least Squares algorithm.