Lecture Notes in Control and Information Sciences 244

Editor: M. Thoma

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H. Nijmeijer and T.I. Fossen (Eds)

New Directions in Nonlinear Observer Design

~ Springer

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British Library Cataloguing in Publication Data New directions in nonlinear observer design. - (Lecture

notes in control and information sciences ; 224) 1.Observers (Control theory) 2.Nonlinear control theory 3.Feedback control systems l.Nijmeijer, Henk, 1955- II.Fossen, Thor I. 629.8'36 ISBN 1852331348

Library of Congress Cataloging-in-Publication Data New directions in nonlinear observer design / H. Nijmeijer and

T.I. Fossen (eds.). p. cm. - (Lecture notes in control and information sciences

; 244) Includes bibliographical references and index. ISBN 1-85233-134-8 (alk. Paper) 1.Observers (Control theory)--Congresses. 2. Nonlinear control

Theory--Congresses. I. Nijmeijer, H. (Henk), 1955- . II. Fossen, Thor I. III. Series. QA402.3.N487 1999 99-12174 629.8'312--dc21 CIP

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vi

Acknowledgments The editors are grateful to:

Stra tegic Univers i ty P r o g r a m (SUP) in Mar ine C y b e r n e t i c s at the Norwegian University of Science and Technology (NTNU), De- partments of Engineering Cybernetics, Marine Hydrodynamics and Marine Strutures (Professor Dr.-Ing. Olav Egeland, Program Man- ager).

• ABB (Professor Dr.-Ing. Asgeir J. SCrensen, Technology Manager - Business Area Marine and Turbochargers)

for their financial support. The authors want to thank all the workshop contributors for contributing

to this book project. Finally, Mrs. Alison Jackson at Springer-Verlag London should be thanked

for editorial suggestions and for helping us with general publishing ques- tions.

Trondheim, February 1999 Enschede, February 1999

Thor I. Fossen Henk Nijmeijer

Contr ibutors Alcorta Garcia, E., Department of Measurement and Control, University

of Duisburg, Duisburg, Germany.

Ashton, S. A., School of MIS, Coventry University, U.K.

Astolfi, A., Centre for Process Systems Engineering, Imperial College of Science, London, U.K.

Bastin, G., Centre for Systems Engineering and Applied Mechanics, Uni- versite Catholique de Louvain, Louvain-La Neuve, Belgium.

Battilotti, S., Dipartimento di Informatica e Sistemistica, Universit~ di Roma "La Sapienza", Italy.

Besan~on, G., Laboratoire d'Automatique de Grenoble, ENSIEG, Saint- Martin d'H~res, France.

Blanke, M., Department of Automatic Control, Aalborg University, Den- mark.

Canudas de Wit, C. Laboratoire d'Automatique de Grenoble, ENSIEG- INPG, ST. Martin d'H~res, France.

Cruz, C., Department of Electronics ~ Telecom., Scientific Research and Advanced Studies Center of Ensenada (CICESE), M~xico.

Deng, H., Department of Applied Mechanics and Engineering Sciences University of California at San Diego, La Jolla, USA.

Egeland, O., Department of Engineering Cybernetics, Norwegian Univer- sity of Science and Technology, Trondheim, Norway.

El Bahir, L., Department of Control Engineering, Universit~ Libre de Bruxelles, Brussels, Belgium.

El Yaagoubi, E. H., LCPI ENSEM Cassablanca, Morocco.

Fossen, T. I., IDepartment of Engineering Cybernetics, Norwegian Uni- versity of Science and Technology, Trondheim, Norway and 2ABB Industri AS, Marine Division, Oslo, Norway.

V l l l

Frank, P. M., Department of Measurement and Control, University of Duisburg, Duisburg, Germany.

Glumineau, A. Institut de Recherche en Cybern~tique de Nantes, France.

Hammouri, H., LAGEPT University of Lyon, France.

Huijberts, H. J. C., Department of Mathematics and Computing Science, Eindhoven University of Technology, The Netherlands.

Horowitz, R. Department of Mechanical Engineering, University of Cali- fornia, Berkeley, CA, U.S.A.

Isidori, A., IDepartment of Systems Science and Mathematics, Washing- ton University, St. Louis, USA and 2Dipartimento di Informatica e Sistemistica, Universit~t di Roma "La Sapienza", Italy.

Izadi-Zamanabadi, R., Department of Automatic Control, Aalborg Uni- versity, Denmark.

Jiang, Z.-P., Department of Electrical Engineering, Polytechnic University, Brooklyn, U.S.A.

Junge, L., Drittes Physikalisches Institut, Universitttt G6ttingen, Ger- many.

Khalil, H. K., Department of Electrical and Computer Engineering, Michi- gan State University, USA.

Kinnaert, M., Department of Control Engineering, Universit~ Libre de Bruxelles, Brussels, Belgium.

Kocarev, L., Department of Electrical Engineering, St Cyril and Method- ius University, Skopje, Macedonia.

Kristiansen, D., Department of Engineering Cybernetics, Norwegian Uni- versity of Science and Technology, Trondheim, Norway.

Krstid, M., Department of Applied Mechanics and Engineering Sciences University of California at San Diego, La Jolla, USA.

Lilge, T., Institut flit Regelungstechnik, University of Hannover, Hannover, Germany.

Lohmiller, W., Nonlinear Systems Laboratory, Massachusetts Institute of Technology, Cambridge, Massachusetts, USA.

Ldpez-Morales, V., Institut de Recherche en Cybern~tique de Nantes, France.

ix

Loria, A., Laboratoire d'Automatique de Grenoble, ENSIEG, St. Martin d'H~res, France.

Nijmeijer, H., 1Faculty of Mathematical Sciences, Dept. of Systems, Sig- nals and Control, University of Twente and 2Faculty of Mechanical Engineering, Eindhoven University of Technology, The Netherlands.

Ortega, R., Laboratoire des Signaux et Syst~mes, Ecole Sup6rieure d'Electricit6, Paris, Prance.

Panteley, E., I.N.R.I.A., Rh6ne Alpes, St. Martin d'Hfires, France.

Parlitz, U., Drittes Physikalisches Institut, Universitat GSttingen, Ger- many.

Pettersen, K. Y., Department of Engineering Cybernetics, Norwegian Uni- versity of Science and Technology, Trondheim, Norway.

Praly, L., Centre Automatique et Syst~mes, t~cole des Mines de Paris, Fontainebleau, prance.

Rodrigues-Cortes, H., Laboratoire des Signaux et Syst~mes, Ecole Sup~rieure d'Electricit~, Paris, prance.

Schaffner, J., Institute for Systems, Informatics and Safety, European Commission Joint Research Centre, Ispra, Italy

Schreier, G., Department of Measurement and Control, University of Duis- burg, Duisburg, Germany.

Shields, D. N., School of MIS, Coventry University, U.K.

Shiriaev, A., Department of Engineering Cybernetics, Norwegian Univer- sity of Science and Technology, Trondheim, Norway.

Slotine, J. J. E., Nonlinear Systems Laboratory, Massachusetts Institute of Technology, Cambridge, Massachusetts, USA.

Strand, J. P., ABB Industri AS, Marine Division, Oslo, Norway.

Teel, A., Department of Electrical and Computer Engineering, University of California, Santa Barbara, USA.

Tsiotras, P., Georgia Institute of Techology, School of Aerospace Eng., Atlanta, Georgia, USA.

Vik, B. Department of Engineering Cybernetics, Norwegian University of Science and Technology, Trondheim, Norway.

Zeitz, M., Institut ftir Systemdynamik und Regelungstechnik, University of Stuttgart, Germany.

C o n t e n t s

Nonlinear Observer Design

A V i e w p o i n t o n O b s e r v a b i l i t y a n d O b s e r v e r D e s i g n for

N o n l i n e a r S y s t e m s 3

G. Besanf~on 1 I n t r o d u c t i o n . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2 Basic Definit ions and Proposed "Classif ication" . . . . . . . 4

3 Examples of Non Uni form and Uni form Observa t ion . . . . 7

3.1 Non Uniform Observat ion: the Case of State-Affine

Systems . . . . . . . . . . . . . . . . . . . . . . . . . 7 3.2 Uniform Observat ion: the Case of Uni formly Observ-

able Systems . . . . . . . . . . . . . . . . . . . . . . 8

3.3 An Example of Uni form Observa t ion of Non-un i fo rmly

observable Systems . . . . . . . . . . . . . . . . . . . 9

Observer In te rconnec t ion . . . . . . . . . . . . . . . . . . . 11

State Trans format ions and Observer Design . . . . . . . . . 15

Conclus ions . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

M o d e l - B a s e d O b s e r v e r s for T i r e / R o a d C o n t a c t F r i c t i o n P r e d i c t i o n C. Canudas de Wit, R. Horowitz and P. Tsiotras

1

2

3 4

5

23

In t roduc t i on . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

T i re - road Frict ion Models . . . . . . . . . . . . . . . . . . . 25

2.1 Pseudo-Steady Sta te Models . . . . . . . . . . . . . 26

2.2 L u m p e d Dynamic Models . . . . . . . . . . . . . . . 28

2.3 Dis t r ibu ted Dynamic Models . . . . . . . . . . . . . 29

2.4 Rela t ion Between Dis t r ibu ted D yna mi c a l Model a n d the Magic Formula . . . . . . . . . . . . . . . . . . . 30

P rob l em Formula t ion . . . . . . . . . . . . . . . . . . . . . . 32

Genera l Observer Design . . . . . . . . . . . . . . . . . . . . 33

Appl ica t ion to the One-Whee l Model . . . . . . . . . . . . . 36

5.1 S imula t ion Resul ts . . . . . . . . . . . . . . . . . . . 39

Conclus ions . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

xii

Observer Des ign for Nonl inear Osci l latory Sys tems D. Kristiansen and O. Egeland 1 2 3

4 5

6 7

43

In t roduc t ion . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

Con t r ac t i on T h e o r y . . . . . . . . . . . . . . . . . . . . . . 44

Sys tem Equa t ions . . . . . . . . . . . . . . . . . . . . . . . . 46

3.1 Analys is . . . . . . . . . . . . . . . . . . . . . . . . . 47

Observer Design . . . . . . . . . . . . . . . . . . . . . . . . 49

S imula t ions . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

5.1 E x a m p l e 1: 2 - D O F Osci l la tory Sys t em wi th Cub ic

Nonl inear i t ies . . . . . . . . . . . . . . . . . . . . . . 51

5.2 E x a m p l e 2: Cyl inder Gyroscope . . . . . . . . . . . . 52

Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

Transformation to State Affine Des ign A. Glumineau and V. Ldpez-M. 1 2 3

4

5

6

Sys tem and Observer 59

In t roduc t ion . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

Defini t ions and No ta t i on . . . . . . . . . . . . . . . . . . . . 60

P r o b l e m S t a t e m e n t . . . . . . . . . . . . . . . . . . . . . . . 61 3.1 T h e I n p u t - O u t p u t Different ial E q u a t i o n for S ta t e At t ine

Sys tems ~ a - . . . . . . . . . . . . . . . . . . . . . . 61

3.2 S ta te Affine Trans fo rma t ion A l g o r i t h m . . . . . . . . 62

Synthesis Observer for S ta te Affine Sys tems . . . . . . . . 65

4.1 Phys ica l E x a m p l e . . . . . . . . . . . . . . . . . . . 66

4.2 S imula t ion Resul ts . . . . . . . . . . . . . . . . . . . 67

Conclus ions . . . . . . . . . . . . . . . . . . . . . . . . . . . 68

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

On Exis tence o f E x t e n d e d O b s e r v e r s fo r Nonl inear Discrete- T ime Systems 73

H. J. C. Huijberts In t roduc t ion . . . . . . . . . . . . . . . . . . . . . . . . . . . 73

Differential Forms . . . . . . . . . . . . . . . . . . . . . . . 75

Observer Design using Observer Forms . . . . . . . . . . . . 79

Observer Design using E x t e n d e d Observer Forms . . . . . . 84

Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . 90

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91

Stabil ity Analysis and Observer Des ign for Nonl inear Diffusion Processes 93

W. Lohmiller and J.-J. E. Slotine 1 In t roduc t ion . . . . . . . . . . . . . . . . . . . . . . . . . . . 93

2 Con t r ac t ion Analysis . . . . . . . . . . . . . . . . . . . . . . 94

2.1 Basic Tools . . . . . . . . . . . . . . . . . . . . . . . 94

xiii

4

5 6 A

2.2 Nonl inear Observer Design using Con t r a c t i on Theo ry 96 2.3 Weakly Con t rac t ing Systems . . . . . . . . . . . . . 97

Nonl inear Diffusion Equa t ions . . . . . . . . . . . . . . . . . 99 3.1 Con t rac t ion Proper t ies of React ion-Diffus ion Pro-

cesses . . . . . . . . . . . . . . . . . . . . . . . . . . 100 3.2 Observer Design for Nonl inear Diffusion Processes 103 Spat ia l Discre t iza t ion and Numer ica l I m p l e m e n t a t i o n . . . . 104

Fur ther Extens ions . . . . . . . . . . . . . . . . . . . . . . . 105 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109 C o m p u t a t i o n of Con t r ac t i on Rates . . . . . . . . . . . . . . 109

N o n l i n e a r P a s s i v e O b s e r v e r D e s i g n for S h i p s w i t h A d a p t i v e

W a v e Fi l ter ing 113 J. P. Strand and T. L Fossen 1 In t roduc t i on . . . . . . . . . . . . . . . . . . . . . . . . . . . 113 2 Model ing . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115

2.1 Kinemat ics . . . . . . . . . . . . . . . . . . . . . . . 115

2.2 Vessel Dynamics . . . . . . . . . . . . . . . . . . . . 115 2.3 Total Ship Model . . . . . . . . . . . . . . . . . . . . 118

3 Non-Adap t ive Observers . . . . . . . . . . . . . . . . . . . . 118

3.1 Observer in the E F frame . . . . . . . . . . . . . . . 119 3.2 A u g m e n t e d Observer . . . . . . . . . . . . . . . . . . 123

4 Adapt ive Observer . . . . . . . . . . . . . . . . . . . . . . . 125 4.1 Adapt ive Observer Equa t ions . . . . . . . . . . . . . 126 4.2 Adapt ive Observer Error Dynamics . . . . . . . . . . 126

4.3 Stabi l i ty and Pass ivi ty . . . . . . . . . . . . . . . . . 126

5 Expe r imen ta l Resul ts . . . . . . . . . . . . . . . . . . . . . . 128 6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . 130

7 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133

N o n l i n e a r O b s e r v e r D e s i g n for I n t e g r a t i o n o f D G P S a n d I N S 135 B. Vik, A. Shiriaev and T. L Fossen 1 In t roduc t i on . . . . . . . . . . . . . . . . . . . . . . . . . . . 135

1.1 Nomenc la tu re . . . . . . . . . . . . . . . . . . . . . . 135 1.2 Mot iva t ion . . . . . . . . . . . . . . . . . . . . . . . 136

2 Review of GPS F u n d a m e n t a l s . . . . . . . . . . . . . . . . . 138 3 S t rapdown Equa t ions . . . . . . . . . . . . . . . . . . . . . 140

3.1 Local Frame Represen ta t ion . . . . . . . . . . . . . . 140

3.2 Ea r th Frame Represen ta t ion . . . . . . . . . . . . . 141 3.3 Angula r Velocity Equa t ions . . . . . . . . . . . . . . 142

4 Nonl inear Observer Design . . . . . . . . . . . . . . . . . . . 142 4.1 Angula r Velocity Observer . . . . . . . . . . . . . . . 143 4.2 Velocity and Posi t ion Observers . . . . . . . . . . . . 145

5 Case S tudy . . . . . . . . . . . . . . . . . . . . . . . . . . . 157

xiv

6 7

C o n c l u s i o n s a n d F u t u r e W o r k . . . . . . . . . . . . . . . . . 158

R e f e r e n c e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158

V a r i a n t s o f N o n l i n e a r N o r m a l F o r m O b s e r v e r Design J. Schaffner and M. Zeitz 1 2 3 4 5 6 7

161

I n t r o d u c t i o n . . . . . . . . . . . . . . . . . . . . . . . . . . . 161

N o r m a l F o r m O b s e r v e r . . . . . . . . . . . . . . . . . . . . . 162

C o n t i n u o u s O b s e r v e r . . . . . . . . . . . . . . . . . . . . . . 163

E x t e n d e d L u e n b e r g e r O b s e r v e r . . . . . . . . . . . . . . . . 167

B l o c k - T r i a n g u l a r O b s e r v e r . . . . . . . . . . . . . . . . . . . 171

C o n c l u s i o n s . . . . . . . . . . . . . . . . . . . . . . . . . . . 179

R e f e r e n c e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179

I I

1

3

Output Feedback Control Design 181

Separation Results for Semiglobal Stabil ization Nonlinear Systems via Measurement Feedback S. Battilotti 1 2 3

o f

1 8 3

I n t r o d u c t i o n . . . . . . . . . . . . . . . . . . . . . . . . . . . 183

N o t a t i o n s . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185

R e g i o n a l S t a b i l i z a t i o n v i a M e a s u r e m e n t F e e d b a c k . . . . . . 186

3.1 T o o l s . . . . . . . . . . . . . . . . . . . . . . . . . . 186

3 .2 A p p l i c a t i o n s . . . . . . . . . . . . . . . . . . . . . . 191

3 .3 S e m i g l o b a l S t a b i l i z a t i o n of U n c e r t a i n N o n l i n e a r Sys -

t e m s . . . . . . . . . . . . . . . . . . . . . . . . . . . 196

R e f e r e n c e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205

O b s e r v e r - C o n t r o l l e r D e s i g n f o r G l o b a l T r a c k i n g o f

Nonholonomic Systems Z.-P. 1 2 3 4

207 Jiang and H. Ni jmei jer

I n t r o d u c t i o n . . . . . . . . . . . . . . . . . . . . . . . . . . . 207

P r o b l e m S t a t e m e n t . . . . . . . . . . . . . . . . . . . . . . . 208

R e d u c e d - O r d e r O b s e r v e r . . . . . . . . . . . . . . . . . . . . 210

O u t p u t - F e e d b a c k D e s i g n . . . . . . . . . . . . . . . . . . . . 212

4.1 B a c k s t e p p i n g - B a s e d T r a c k e r s . . . . . . . . . . . . . 213

4 .2 A M o d i f i c a t i o n . . . . . . . . . . . . . . . . . . . . . 217

E x a m p l e : A K n i f e - E d g e . . . . . . . . . . . . . . . . . . . . 219

C o n c l u s i o n s a n d F u t u r e W o r k . . . . . . . . . . . . . . . . . 225

R e f e r e n c e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . 226

A Separation Principle f o r a C l a s s o f Euler-Lagrange Systems 229 A. Loria and E. Panteley 1 I n t r o d u c t i o n . . . . . . . . . . . . . . . . . . . . . . . . . . . 229

xix

I V S y n c h r o n i z a t i o n a n d O b s e r v e r s

1 Synchronization Through Extended Kalman Filtering C. Cruz and H. Nijmeijer 1 2 3

4 6 7

469

I n t r o d u c t i o n . . . . . . . . . . . . . . . . . . . . . . . . . . . 469 A n Ex tended K a l m a n Fi l te r as Receiver . . . . . . . . . . . 472

Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . 479

3.1 Synchroniza t ion . . . . . . . . . . . . . . . . . . . . 479 3.2 Secure C o m m u n i c a t i o n . . . . . . . . . . . . . . . . . 483

Conc lud ing Remarks . . . . . . . . . . . . . . . . . . . . . . 487 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . 488

2 Nonlinear Discrete-Time Observers for Synchronizat ion P r o b l e m s 491

T. Lilge 1 I n t r o d u c t i o n . . . . . . . . . . . . . . . . . . . . . . . . . . . 491 2 State Equivalence to a Sys tem in Ex tended Observer Form 494

3 Observer Design via Ex t ended Observer Form . . . . . . . . 497 4 Al t e rna t ive Observer S t ruc tures via E O F . . . . . . . . . . 499

4.1 Observer Equa t ions . . . . . . . . . . . . . . . . . . 499 4.2 Main Character is t ics of the Observers . . . . . . . . 500 A n Example in the Field of C o m m u n i c a t i o n . . . . . . . . . 501

Observer Design for the R6ssler Sys tem . . . . . . . . . . . 503 6.1 Observer Design in C o n t i n u o u s - T i m e . . . . . . . . . 505 6.2 Observer Design in Disc re te -Time . . . . . . . . . . 506 6.3 Observer Errors for Slow Error Dynamics . . . . . . . 506 6.4 Observer Errors for Fast Error Dynamics . . . . . . 507

6.5 Concluding Remarks . . . . . . . . . . . . . . . . . . 508 Discussion and Conclus ions . . . . . . . . . . . . . . . . . . 509

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . 509 7 8

Chaos Synchronization U. Parlitz, L. Junge and L. Kocarev 1 2 3 4 5 6

511

I n t r o d u c t i o n . . . . . . . . . . . . . . . . . . . . . . . . . . . 511 Synchron iza t ion of Spat ia l ly Ex t ended Systems . . . . . . . 512

Genera l ized Synchroniza t ion . . . . . . . . . . . . . . . . . . 515 Phase Synchron iza t ion . . . . . . . . . . . . . . . . . . . . . 518 Conclus ions . . . . . . . . . . . . . . . . . . . . . . . . . . . 522

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . 522

4

5

X V

4

5

6 A

Model and P rob lem Formula t ion . . . . . . . . . . . . . . . 232 A Cascades Approach to a Separa t ion Pr inc ip le . . . . . . . 234 3.1 Observer Design . . . . . . . . . . . . . . . . . . . . 235 3.2 Sta te Feedback Control ler . . . . . . . . . . . . . . . 236

3.3 A Separa t ion Pr inciple . . . . . . . . . . . . . . . . . 237 Appl i ca t ion to Robot Man ipu la to r s . . . . . . . . . . . . . . 240

Conclus ions . . . . . . . . . . . . . . . . . . . . . . . . . . . 243

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . 244 A Theo rem on UGAS for Str ic t ly Passive Systems . . . . . 246

H i g h - G a i n O b s e r v e r s i n N o n l i n e a r F e e d b a c k C o n t r o l

H. K. Khalil

249

1 I n t r o d u c t i o n . . . . . . . . . . . . . . . . . . . . . . . . . . . 249 2 Mot iva t ing Example . . . . . . . . . . . . . . . . . . . . . . 250

3 Separa t ion Pr inciple . . . . . . . . . . . . . . . . . . . . . . 255 4 S tab i l iza t ion and Semiglobal S tab i l iza t ion . . . . . . . . . . 258

5 Nonl inear Servomechanisms . . . . . . . . . . . . . . . . . . 259 6 Adap t ive Control . . . . . . . . . . . . . . . . . . . . . . . . 261 7 Sliding Mode Contro l . . . . . . . . . . . . . . . . . . . . . . 262 8 Unmode led Fast Dynamics . . . . . . . . . . . . . . . . . . 262 9 Disc re te -Time I m p l e m e n t a t i o n . . . . . . . . . . . . . . . . 263 10 Appl ica t ion to I nduc t i on Motors . . . . . . . . . . . . . . . 263

11 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . 264

O u t p u t - F e e d b a c k C o n t r o l

t e m s M. Krstid and H. Deng 1 2 3 4 5 6 A B C

of S t o c h a s t i c N o n l i n e a r S y s - 269

I n t r o d u c t i o n . . . . . . . . . . . . . . . . . . . . . . . . . . . 269 Pre l iminar ies on Stochast ic Stabi l i ty . . . . . . . . . . . . . 270 Ou tpu t -Feedback Stabi l iza t ion in P robab i l i ty . . . . . . . . 271 Ou tpu t -Feedback Noise- to-State S tab i l iza t ion . . . . . . . . 276 Ou tpu t -Feedback Adap t ive S tab i l iza t ion . . . . . . . . . . . 280

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . 284 Proof . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 287 Proof . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 288 Proof . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 289

O u t p u t F e e d b a c k C o n t r o l o f F o o d - C h a i n S y s t e m s R. Ortega, A. Astolfi, G. Bastin and H. Rodrigues Cortes

1 2 3 4 5 6

291

I n t r o d u c t i o n . . . . . . . . . . . . . . . . . . . . . . . . . . . 291 Control ler Design Procedure . . . . . . . . . . . . . . . . . . 292 S ta t e -Feedback Contro l of a Simple P r e y - P r e d a t o r Sys tem 295

O u t p u t - F e e d b a c k Stabi l iza t ion . . . . . . . . . . . . . . . . 299 Ma in Resul t . . . . . . . . . . . . . . . . . . . . . . . . . . . 301

S imula t ions . . . . . . . . . . . . . . . . . . . . . . . . . . . 305

xvi

7

8

7 Conc lud ing Remarks . . . . . . . . . . . . . . . . . . . . . . 306

8 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . 307

A Maple Code . . . . . . . . . . . . . . . . . . . . . . . . . . . 308

Output Feedback Tracking Control for Ships K. Y. Pettersen and H. Ni jmei jer 1 2 3 4 5 6 7 8

311

In t roduc t ion . . . . . . . . . . . . . . . . . . . . . . . . . . . 311

T h e Ship Model . . . . . . . . . . . . . . . . . . . . . . . . . 313

Design of an O u t p u t Feedback Tracking Con t ro l Law . . . . 314

Simula t ions . . . . . . . . . . . . . . . . . . . . . . . . . . . 319

Bias E s t i m a t i o n . . . . . . . . . . . . . . . . . . . . . . . . . 324

Simula t ions wi th an E n v i r o n m e n t a l D i s tu rbance . . . . . . 327

Conclusions and ~ t u r e Work . . . . . . . . . . . . . . . . . 329

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . 331

Dynamic U C O Controllers and Semiglobal Stabi l izat ion of Uncerta in N o n m i n i m u m Phase Systems by Output Feed- back 335 A. Isidori, A. R. Teel and L. Praly 1 In t roduc t i on . . . . . . . . . . . . . . . . . . . . . . . . . . . 335

2 Pre l iminar ies . . . . . . . . . . . . . . . . . . . . . . . . . . 336

3 S tab i l i za t ion of N o n m i n i m u m Phase Sys tems by O u t p u t Feed-

back . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 338

3.1 T h e Re la t ive Degree One Case . . . . . . . . . . . . 338

3.2 T h e Re la t ive Degree Grea te r t han One Case . . . . 341

4 On D y n a m i c U C O Feedback . . . . . . . . . . . . . . . . . . 344

4.1 Genera l Resul ts . . . . . . . . . . . . . . . . . . . . . 344 4.2 App l i ca t ion to N o n m i n i m u m Phase Sys tems . . . . . 347

5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . 349

6 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . 349

III Fau l t D e t e c t i o n a n d I s o l a t i o n 351

Fault Detec t ion O b s e r v e r fo r a C l a s s o f Nonl inear Sys tems 353 S. A. Ashton and D. N. Shields 1 In t roduc t i on . . . . . . . . . . . . . . . . . . . . . . . . . . . 353

2 Sys tem Descr ip t ion . . . . . . . . . . . . . . . . . . . . . . . 354

3 Observer Design . . . . . . . . . . . . . . . . . . . . . . . . 354

4 Genera l De tec tab i l i ty Condi t ions . . . . . . . . . . . . . . . 363

5 Tes table De tec t ab i l i t y Condi t ions . . . . . . . . . . . . . . . 365

5.1 A Special Class (Step-Faul ts ) . . . . . . . . . . . . . 368

5.2 Numer ica l Ca lcu la t ion P rocedure . . . . . . . . . . . 371

6 Conc lud ing Remarks . . . . . . . . . . . . . . . . . . . . . . 372

7 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . 373

xvii

Nonl inear Observer for Signal and Parameter Fault Detec- t ion in Ship Propuls ion Control 375

M. Blanke and R. Izadi-Zamanabadi 1 In t roduc t i on . . . . . . . . . . . . . . . . . . . . . . . . . . . 375

2 Ship Propuls ion Sys tem . . . . . . . . . . . . . . . . . . . . 376

2.1 Prope l le r T h r u s t and Torque . . . . . . . . . . . . . 377

2.2 Diesel Eng ine P r ime Mover . . . . . . . . . . . . . . 377

2.3 Hull Res is tance . . . . . . . . . . . . . . . . . . . . . 378

2.4 A c t u a t o r s for Fuel In jec t ion and Prope l le r P i t ch . . 378

2.5 Sensors . . . . . . . . . . . . . . . . . . . . . . . . . 378

3 Cont ro l Hierarchy . . . . . . . . . . . . . . . . . . . . . . . 379

4 S t ruc tu ra l Analys is . . . . . . . . . . . . . . . . . . . . . . . 380

4.1 Descr ip t ion of the Model . . . . . . . . . . . . . . . 380

4.2 Formal Represen ta t ion . . . . . . . . . . . . . . . . . 380

4.3 Sensor Fusion for Re-conf igura t ion . . . . . . . . . . 381

5 Isola t ion of Shaft Speed and Engine Faul t s . . . . . . . . . 384

5.1 A d a p t i v e Observer . . . . . . . . . . . . . . . . . . . 384

5.2 Ident i f ica t ion of Prope l le r P a r a m e t e r s . . . . . . . . 386

5.3 Ident i f iabi l i ty f rom Usual M a n e u v e r i n g D a t a . . . . 388

6 Faul t I so la t ion . . . . . . . . . . . . . . . . . . . . . . . . . 389

6.1 Re-conf igura t ion . . . . . . . . . . . . . . . . . . . . 392

7 S imula t ion Resul t s . . . . . . . . . . . . . . . . . . . . . . . 394

8 Conclus ions . . . . . . . . . . . . . . . . . . . . . . . . . . . 395

9 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . 395

Nonlinear Observers for Fault Detec t ion and Isolation P. M. Frank, G. Schreier and E. Alcorta Garcia

1 2 3

4

3 9 9

In t roduc t i on . . . . . . . . . . . . . . . . . . . . . . . . . . . 399

Pre l iminar ies . . . . . . . . . . . . . . . . . . . . . . . . . . 400

Observer -Based Res idua l Gene ra t i on . . . . . . . . . . . . . 401

3.1 Nonl inear Iden t i ty Observer A p p r o a c h . . . . . . . . 401

3.2 Nonl inear U n k n o w n Inpu t Observer A p p r o a c h . . . 403

3.3 T h e Dis tu rbance Decoupl ing Nonl inear Observer Ap-

proach . . . . . . . . . . . . . . . . . . . . . . . . . . 404

3.4 A d a p t i v e Nonl inear Observer A p p r o a c h . . . . . . . 406

3.5 T h e Nonl inear Faul t De tec t i on F i l t e r A p p r o a c h . . . 408

3.6 Observer for Faul t Diagnosis in Bi l inear Sys tems . . 410

Nonl inear Observer Design v ia Lipschi tz Cond i t i on . . . . . 412

4.1 Observer P re sen t a t i on . . . . . . . . . . . . . . . . . 412

4.2 Con t r ibu t ion of this Observer . . . . . . . . . . . . . 415

4.3 Res idua l Gene ra t i on . . . . . . . . . . . . . . . . . . 417

Conclus ions . . . . . . . . . . . . . . . . . . . . . . . . . . . 418

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . 418

X V l l l

4 Ap p l i c a t ion of Non l inear Observers to Fault D e t e c t i o n a n d

Iso lat ion 423 H. Hammouri, M. Kinnaert and E.H. El Yaagoubi

1 In t roduc t i on . . . . . . . . . . . . . . . . . . . . . . . . . . . 423

2 Res idua l Gene ra t i on for Linear Sys tems . . . . . . . . . . . 424

2.1 P r o b l e m S t a t e m e n t . . . . . . . . . . . . . . . . . . . 424

2.2 Second P r o b l e m F o r m u l a t i o n . . . . . . . . . . . . . 425

2.3 Pr inc ip le of the Solu t ion . . . . . . . . . . . . . . . . 426

3 Res idua l Gene ra t i on for Nonl inear Sys tems . . . . . . . . . 428

3.1 In t roduc t ion . . . . . . . . . . . . . . . . . . . . . . 428

3.2 Basic Not ions . . . . . . . . . . . . . . . . . . . . . . 428

3.3 High Gain Observers for Uni fo rmly Observab le Sys-

tems . . . . . . . . . . . . . . . . . . . . . . . . . . 429

3.4 T h e F h n d a m e n t a l P r o b l e m of Res idua l G e n e r a t i o n

for Nonl inear Sys tems . . . . . . . . . . . . . . . . . 431

3.5 App l i ca t ion of Nonl inear Observers to the F P R G . . 434

Hydrau l ic Sys tem . . . . . . . . . . . . . . . . . . . . . . . . 437

4.1 Model l ing of the Sys tem . . . . . . . . . . . . . . . . 437

4.2 Design of a Res idual G e n e r a t o r . . . . . . . . . . . . 438

Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . 441

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . 441

Numer ica l Values used for the S imula t ion of the Hydrau l i c

Sys tem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 443

5

6

A

Innovat ion G e n e r a t i o n for Bi l inear S y s t e m s w i t h U n k n o w n I n p u t s 445 M. Kinnaert and L. El Bahir

1 In t roduc t ion . . . . . . . . . . . . . . . . . . . . . . . . . . . 445

2 P r o b l e m S t a t e m e n t . . . . . . . . . . . . . . . . . . . . . . . 447

3 Design P r o c e d u r e . . . . . . . . . . . . . . . . . . . . . . . . 448

4 Innova t ion Moni to r ing . . . . . . . . . . . . . . . . . . . . . 456

4.1 I n t r o d u c t o r y R e m a r k . . . . . . . . . . . . . . . . . . 456

4.2 Innova t ion in the Presence of Add i t i ve Faul t s . . . . 456

4.3 Genera l ized Likel ihood R a t i o Test . . . . . . . . . . 457

5 Design and Val ida t ion of a F D I Sys t em for a th ree Tank

Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 459

5.1 Process Descr ip t ion . . . . . . . . . . . . . . . . . . 459

5.2 Design and Val ida t ion of the Innova t ion G e n e r a t o r . 460

5.3 Eva lua t ion of the Innova t ion Sequence . . . . . . . . 462

6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . 463

7 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . 463