Table of Contents
Notations vii
Acronyms ix
Introduction xi
Chapter 1. Uncertainty Representation Based on Set Theory 1
1.1. Basic set definitions: advantages and weaknesses 3
1.1.1. Interval set 5
1.1.2. Ellipsoidal set 7
1.1.3. Polyhedral set 9
1.1.4. Zonotopic set 12
1.2. Main properties of zonotopes 17
Chapter 2. Several Approaches on Zonotopic Guaranteed Set-Membership Estimation 27
2.1. Context 27
2.2. Problem formulation 32
2.2.1. Singular Value Decomposition-based method 35
2.2.2. Optimization-based methods 40
Chapter 3. Zonotopic Guaranteed State Estimation Based on P-Radius Minimization 49
3.1. Single-Output systems approach 49
3.2. Multi-Output systems approaches 63
3.2.1. General formulation 64
3.2.2. Extensions of the Single-Output systems methodology 67
3.2.3. Dedicated approach for Multi-Output systems 85
Chapter 4. Tube Model Predictive Control Based on Zonotopic Set-Membership Estimation 95
4.1. Context 954.2. Problem formulation 100
4.3. Tube-based output feedback Model Predictive Control design 100
4.4. Application on the magnetic levitation system 112
4.4.1. System description 113
4.4.2. Control problem 116
Conclusion and Perspectives 125
Appendix. Basic Matrix Operation Definitions 129
Bibliography 133
Index 149
