Zonotopes (PDF)

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.