Zonotopes: From Guaranteed State-estimation to Control [Hardcover]

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.

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