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.
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.
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