Optimal identification experiment design

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Table of contents

1 Introduction 
1.1 System Identification
1.2 Optimal identification experiment design
1.3 Resonance frequency tracking of a MEMS gyroscope
1.4 Content of the thesis
2 Prediction Error Identification and Optimal Experiment Design 
2.1 Introduction and description of the to-be-identified system
2.2 Prediction-error identification in open loop
2.3 Prediction-error identification in closed loop
2.4 Optimal experiment design: least costly experiment design
3 Robust Optimal Identification Experiment Design for Multisine Excitation
3.1 Introduction
3.2 Open-loop identification in a BJ model structure
3.3 Robust optimal experiment design
3.4 Tackling the robustified cost constraint using robustness analysis tools
3.5 Tackling the robustified accuracy constraint
3.6 Convex formulation of the optimal experiment design problem
3.7 Possible extensions of the framework
3.8 Dealing with the numerical complexity
3.9 Numerical illustrations
3.10 Summary
4 Least Costly Identification Experiment for the Identification of One Module in a Dynamic Network 
4.1 Introduction
4.2 Description of the network configuration
4.3 Identification of one module in the network and cost of the experiment
4.4 Optimal experiment design problem
4.5 Tackling the robust cost constraint in a convex way
4.6 Computation of (!) using the hierarchical approach
4.7 Numerical illustrations
4.8 Summary
5 Resonance Frequency Tracking of a MEMS Gyroscope 
5.1 Introduction
5.2 The drive mass closed-loop system
5.3 Recursive Identification
5.4 Extremum Seeking
5.5 Comparison of the RLS and the ES algorithms: Tracking of !r,x(t)
5.6 Summary
6 Conclusion 
6.1 Summary
6.2 Suggestions for future works
Bibliography 
A Appendix for Chapter 2
B Appendices for Chapter 3
B.1 Example for Observation 3.1
B.2 Proof of Proposition 3.1
B.3 LFT representation of Fu,(z, )
B.4 Useful lemma for the proof of Proposition 3.3
C Appendices for Chapter 4
C.1 Derivation of the expression for Ru(z, 0) and Ry(z, 0)
C.2 Proof of Proposition 4.1
C.3 Consistency and accuracy of (4.23)
C.4 Proof of Proposition 4.3
C.5 Computation of the quantities ˜ci(!) and i(!)
C.6 Proof of Proposition 4.5
D Appendix for Chapter 5
E Résumée de la Thèse
E.1 Introduction
E.2 Conception Optimale Robuste de l’Expérience d’Identification avec une Excitation Multisinusoïdal
E.3 Expérience least costly pour l’identification d’un module dans un réseau dynamique
E.4 Suivi de la fréquence de résonance d’un gyroscope MEMS
E.5 Conclusion