Multiple Models Approach in Automation E-Book

Mohammed Chadli

• Herausgeber: John Wiley & Sons
• Kategorie: Wissenschaft und neue Technologien
• Sprache: Englisch

Seitenzahl: 119

Veröffentlichungsjahr: 2012

Beschreibung

Much work on analysis and synthesis problems relating to the multiple model approach has already been undertaken. This has been motivated by the desire to establish the problems of control law synthesis and full state estimation in numerical terms. In recent years, a general approach based on multiple LTI models (linear or affine) around various function points has been proposed. This so-called multiple model approach is a convex polytopic representation, which can be obtained either directly from a nonlinear mathematical model, through mathematical transformation or through linearization around various function points. This book concentrates on the analysis of the stability and synthesis of control laws and observations for multiple models. The authors' approach is essentially based on Lyapunov's second method and LMI formulation. Uncertain multiple models with unknown inputs are studied and quadratic and non-quadratic Lyapunov functions are also considered.

Leseprobe

Contents

Notations

Introduction

Chapter 1 Multiple Model Representation

1.1. Introduction

1.2. Techniques for obtaining multiple models

1.3. Analysis and synthesis tools

Chapter 2 Stability of Continuous Multiple Models

2.1. Introduction

2.2. Stability analysis

2.3. Relaxed stability

2.4. Example

2.5. Robust stability

2.6. Conclusion

Chapter 3 Multiple Model State Estimation

3.1. Introduction

3.2. Synthesis of multiple observers

3.3. Multiple observer for an uncertain multiple model

3.4. Synthesis of unknown input observers

3.5. Synthesis of unknown input observers: another approach

3.6. Conclusion

Chapter 4 Stabilization of Multiple Models

4.1. Introduction

4.2. Full state feedback control

4.3. Observer-based controller

4.4. Static output feedback control

4.5. Conclusion

Chapter 5 Robust Stabilization of Multiple Models

5.1. Introduction

5.2. State feedback control

5.3. Output feedback control

5.4. Observer-based control

5.5. Conclusion

Conclusion

APPENDICES

Appendix 1: LMI Regions

A1.1. Definition of an LMI region

A1.2. Interesting LMI region examples

Appendix 2: Properties of M-Matrices

Appendix 3: Stability and Comparison Systems

A3.1. Vector norms and overvaluing systems

A3.2. Vector norms and the principle of comparison

A3.3. Application to stability analysis

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:

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©ISTE Ltd 2013

The rights of Mohammed Chadli and Pierre Borne 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: 2012950089

British Library Cataloguing-in-Publication Data

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

ISBN: 978-1-84821-412-5

Notations

Notations relating to multiple modeling

PDC

Parallel distributed compensation

(control law based on state feedback)

OPDC

Output PDC

(control law based on output feedback)

(

x

(·),

u

(·),

y

(·))

State, input and output of the system, respectively, (

x

(·),

u

(·),

y

(·))∈

n

×

m

×

l

(

A

i

,

B

i

,

C

i

)

State, input and output matrices of the

i

th local LTI model, such that (

A

i

,

B

i

,

C

i

)∈

n.n

×

n.m

×

l

.

n

μ

i

(·)

i

th activation function corresponding to the

i

th local LTI model, such that

N

Number of local LTI models

This expression represents

This expression represents

Sets and domains

Matrices and operators

Acronyms

LMI

Linear matrix inequality

BMI

Bilinear matrix inequality

LTI

Linear time invariant

GEVP

Generalized eigenvalues problem

PLDI

Polytopic linear differential inclusion

MIMO

Multiple input, multiple output

SIMO

Single input, multiple output

Introduction

In recent decades, many studies on analysis and synthesis problems relating to the multiple model (also called multimodels) approach have been undertaken. This has been motivated by the desire to establish the design problems in numerical terms. These have become possible as a result of the convex polytopic representation of the multiple model approach and the development of effective numerical resolution tools based on convex optimization software.