Zonotopes

This title focuses on two significant problems in the field of automatic control, in particular state estimation and robust Model Predictive Control under input and state constraints, bounded disturbances and measurement noises. The authors build upon previous results concerning zonotopic set–membership state estimation and output feedback tube–based Model Predictive Control. Various existing zonotopic set–membership estimation methods are investigated and their advantages and drawbacks are discussed, making this book suitable both for researchers working in automatic control and industrial partners interested in applying the proposed techniques to real systems. The authors proceed to focus on a new method based on the minimization of the P–radius of a zonotope, in order to obtain a good trade–off between the complexity and the accuracy of the estimation. They propose a P–radius based set–membership estimation method to compute a zonotope containing the real states of a system, which are consistent with the disturbances and measurement noise. The problem of output feedback control using a zonotopic set–membership estimation is also explored. Among the approaches from existing literature on the subject, the implementation of robust predictive techniques based on tubes of trajectories is developed. Contents 1. Uncertainty Representation Based on Set Theory. 2. Several Approaches on Zonotopic Guaranteed Set–Membership Estimation. 3. Zonotopic Guaranteed State Estimation Based on P–Radius Minimization. 4. Tube Model Predictive Control Based on Zonotopic Set–Membership Estimation. About the Authors Vu Tuan Hieu Le is a Research Engineer at the IRSEEM/ESIGELEC Technopôle du Madrillet, Saint Etienne du Rouvray, France. Cristina Stoica is Assistant Professor in the Automatic Control Department at SUPELEC Systems Sciences (E3S), France. Teodoro Alamo is Professor in the Department of Systems Engineering and Automatic Control at the University of Seville, Spain. Eduardo F. Camacho is Professor in the Department of Systems Engineering and Automatic Control at the University of Seville, Spain. Didier Dumur is Professor in the Automatic Control Department, SUPELEC Systems Sciences (E3S), France. INDICE: Introduction  Chapter 1: Uncertainty representation based on set theory a. Basic set definitions : advantages and weaknesses i. Interval set ii. Ellipsoidal set iii. Polyhedral set iv. Zonotopic set b. Main properties of zonotopes c. Conclusion  Chapter 2: Existing approaches on zonotopic guaranteed set–membership estimation a. Context b. Problem formulation i. Singular Value Decomposition–based methods ii. Optimization–based methods 1. Minimizing the segments of the zonotope 2. Minimizing the volume of the zonotope 3. Minimizing the P–radius of the zonotope c. Conclusion  Chapter 3: Guaranteed state estimation based on P–radius minimization a. Single–Output systems approach b. Multi–Output systems approaches i. Extensions of the methodology for Single–Output systems ii. Dedicated approach for Multi–Output systems c. Conclusion Chapter 4: Tube Model Predictive Control based on zonotopic set–membership estimation a. Context b. Problem formulation c. Tube–based output feedback Model Predictive Control design d. Conclusion Conclusion, perspectives and open problems Appendix: Basic matrix operation definitions Notations and acronyms Bibliography Index

• ISBN: 978-1-84821-589-4
• Editorial: ISTE Ltd.
• Encuadernacion: Cartoné
• Páginas: 336
• Fecha Publicación: 25/10/2013
• Nº Volúmenes: 1
• Idioma: Inglés