Le / Stoica / Alamo Zonotopes

From Guaranteed State-estimation to Control
1. Auflage 2013
ISBN: 978-1-118-76159-5
Verlag: John Wiley & Sons
Format: EPUB
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 176 Seiten, E-Book

This title focuses on two significant problems in the field ofautomatic control, in particular state estimation and robust ModelPredictive Control under input and state constraints, boundeddisturbances and measurement noises. The authors build uponprevious results concerning zonotopic set-membership stateestimation and output feedback tube-based Model Predictive Control.Various existing zonotopic set-membership estimation methods areinvestigated and their advantages and drawbacks are discussed,making this book suitable both for researchers working in automaticcontrol and industrial partners interested in applying the proposedtechniques to real systems.
The authors proceed to focus on a new method based on theminimization of the P-radius of a zonotope, in order to obtain agood trade-off between the complexity and the accuracy of theestimation. They propose a P-radius based set-membership estimationmethod to compute a zonotope containing the real states of asystem, which are consistent with the disturbances and measurementnoise. The problem of output feedback control using a zonotopicset-membership estimation is also explored. Among the approachesfrom existing literature on the subject, the implementation ofrobust predictive techniques based on tubes of trajectories isdeveloped.
Contents
1. Uncertainty Representation Based on Set Theory.
2. Several Approaches on Zonotopic Guaranteed Set-MembershipEstimation.
3. Zonotopic Guaranteed State Estimation Based on P-RadiusMinimization.
4. Tube Model Predictive Control Based on Zonotopic Set-MembershipEstimation.
About the Authors
Vu Tuan Hieu Le is a Research Engineer at the IRSEEM/ESIGELECTechnopôle du Madrillet, Saint Etienne du Rouvray,France.
Cristina Stoica is Assistant Professor in the Automatic ControlDepartment at SUPELEC Systems Sciences (E3S), France.
Teodoro Alamo is Professor in the Department of Systems Engineeringand Automatic Control at the University of Seville, Spain.
Eduardo F. Camacho is Professor in the Department of SystemsEngineering and Automatic Control at the University of Seville,Spain.
Didier Dumur is Professor in the Automatic Control Department,SUPELEC Systems Sciences (E3S), France.

Autoren/Hrsg.

Le, Vu Tuan Hieu

Stoica, Cristina

Alamo, Teodoro

Camacho, Eduardo F.

Dumur, Didier

Inhaltsverzeichnis

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 95
4.2. 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