Zonotopes E-Book

Vu Tuan Hieu Le

• Herausgeber: John Wiley & Sons
• Kategorie: Fachliteratur
• Sprache: Englisch

Seitenzahl: 141

Veröffentlichungsjahr: 2013

Beschreibung

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.

Leseprobe

Table of Contents

Notations

Acronyms

Introduction

Chapter 1: Uncertainty Representation Based on Set Theory

1.1. Basic set definitions: advantages and weaknesses

1.2. Main properties of zonotopes

Chapter 2: Several Approaches on Zonotopic Guaranteed Set-Membership Estimation

2.1. Context

2.2. Problem formulation

Chapter 3: Zonotopic Guaranteed State Estimation Based on P-Radius Minimization

3.1. Single-Output systems approach

3.2. Multi-Output systems approaches

Chapter 4: Tube Model Predictive Control Based on Zonotopic Set-Membership Estimation

4.1. Context

4.2. Problem formulation

4.3. Tube-based output feedback Model Predictive Control design

4.4. Application on the magnetic levitation system

Conclusion and Perspectives

Appendix: Basic Matrix Operation Definitions

Bibliography

Index

First published 2013 in Great Britain and the United States by ISTE Ltd and John Wiley & Sons, Inc.

Apart from any fair dealing for the purposes of research or private study, or criticism or review, as permitted under the Copyright, Designs and Patents Act 1988, this publication may only be reproduced, stored or transmitted, in any form or by any means, with the prior permission in writing of the publishers, or in the case of reprographic reproduction in accordance with the terms and licenses issued by the CLA. Enquiries concerning reproduction outside these terms should be sent to the publishers at the undermentioned address:

ISTE Ltd27-37 St George’s RoadLondon SW19 4EUUKwww.iste.co.uk

John Wiley & Sons, Inc.111 River StreetHoboken, NJ 07030USAwww.wiley.com

© ISTE Ltd 2013 The rights of Vu Tuan Hieu Le, Cristina Stoica, Teodoro Alamo, Eduardo F. Camacho and Didier Dumur to be identified as the author of this work have been asserted by them in accordance with the Copyright, Designs and Patents Act 1988.

Library of Congress Control Number: 2013945045

British Library Cataloguing-in-Publication Data

A CIP record for this book is available from the British Library

ISBN: 978-1-84821-589-4

Notations

Set of real numbers

Set of strictly positive real numbers

Set of

n

-dimensional real vector

B

n

Unitary box in

α

General notation for a scalar

a

General notation for a vector

A

General notation for a matrix

A

T

Transpose of matrix

A

A

−1

Inverse of matrix

A

det

(

A

)

Determinant of matrix

A

tr

(

A

)

Trace of matrix

A

Im

(

A

)

Image of matrix

A

General notation for strictly positive definite matrix

A

General notation for positive definite matrix

A

General notation for strictly negative definite matrix

A

General notation for negative definite matrix

A

I

n

Identity matrix in

O

n

Zeros matrix in

diag

(

a

1

,...,

a

n

)

Diagonal matrix of dimension

n

General notation of a

m

-zonotope

rs

(

H

)

Round-sum of matrix

H

Approximation of zonotope by a box

Approximation of zonotope by a parallelotope

Zonotope inclusion

Absolute value

Infinity norm

P

-norm

Frobenius norm

∈

It belongs to

⊂

Subset

Intersection

Minkowski sum

Pontryagin difference

M

(

S

)

Image of a set

S

Distance between the sets and (also called “normal” distance)

Hausdorff distance between the sets and

n

combination of

m

elements

n

!

Factorial of

n

The ith row of vector

y

k

conv

(·)

Convex hull

ω

~

N

(0,

Q

)

Random variable

ω

having zero means, normal distribution and covariance matrix

Q

Acronyms

BMI

Bilinear Matrix Inequality

CARIMA

Controlled Auto-Regressive Integrated Moving Average

CRHPC

Constrained Receding Horizon Predictive Control

DMC

Dynamic Matrix Control

EHAC

Extended Horizon Adaptive Control

EPSAC

Extended Prediction Self-Adaptive Control

ESO

Equivalent Single-Output

ESOCE

Equivalent Single-Output with Coupling Effect

EVP

Eigenvalue Problem

GPC

Generalized Predictive Control

LMI

Linear Matrix Inequality

LQ

Linear Quadratic control

LQR

Linear Quadratic Regulator

LTI

Linear Time Invariant

MAC

Model Algorithmic Control

MIMO

Multi-Input Multi-Output

MPC

Model Predictive Control

MPHC

Model Predictive Heuristic Control

MPT

Multi-Parametric Toolbox

MURHAC

Multi-predictor Receding Horizon Adaptive Control

MUSMAR

Multi-step Multivariable Adaptive Control

PAZI

Polytope and Zonotope Intersection

PFC

Predictive Functional Control

PMI

Polynomial Matrix Inequality

QP

Quadratic Programming

SISO

Single-Input Single-Output

SOS

Sum of Squares

SVD

Singular Value Decomposition

TMPC

Tube-based Model Predictive Control

UPC

Unified Predictive Control

Introduction

This book stands at a crossroad between two major axes in automatic control: state estimation and robust control, applied to uncertain discrete-time linear time invariant systems. The goal is to take into account disturbances, measurement noises and constraints in order to build a zonotopic guaranteed state estimation and an output feedback control which can guarantee the feasibility and the stability of the closed-loop system in this specific context. Part of the results proposed in this book were developed and published in the PhD thesis of Hieu Le [LE 12c], under the supervision of the co-authors of this book.