Zoho For Dummies

Steve Holzner, PhD, is the award-winning author of 112 books, including Joomla! For Dummies and Physics For Dummies. He also teaches programming classes and has consulted for Fortune 100 companies in the area of content management. Steve has been a faculty member at Cornell University and MIT.

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