Krener / Mayne Nonlinear Control Systems Design 1995

1. Auflage 2016
ISBN: 978-1-4832-9687-6
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 434 Seiten, Web PDF

Reihe: IFAC Postprint Volume

The series of IFAC Symposia on Nonlinear Control Systems provides the ideal forum for leading researchers and practitioners who work in the field to discuss and evaluate the latest research and developments. This publication contains the papers presented at the 3rd IFAC Symposium in the series which was held in Tahoe City, California, USA.

Autoren/Hrsg.

Krener, A. J.

Mayne, D. Q.

Inhaltsverzeichnis

1;Front Cover;1
2;Nonlinear Control Systems Design 1995;2
3;Copyright Page;3
4;Table of Contents;6
5;Dediction;3
6;PART I: NONLINEAR CONTROL OF CHEMICAL PROCESSES;16
6.1;CHAPTER 1. ON-LINE UPDATING OF RADIAL BASIS FUNCTION NETWORK MODELS;16
6.1.1;1. INTRODUCTION;16
6.1.2;2. RBFN ADAPTATION;17
6.1.3;3. SIMULATION RESULTS;19
6.1.4;4. CONCLUSIONS;20
6.1.5;REFERENCES;21
6.2;CHAPTER 2. Nonlinear Control of Distributed Parameter Processes with Disturbances;22
6.2.1;Abstract.;22
6.2.2;1 Introduction;22
6.2.3;2 Quasi-linear first-order PDEs;22
6.2.4;3 Characteristic index;24
6.2.5;4 Control of hyperbolic PDE systems with disturbances;25
6.2.6;Acknowledgement;27
6.2.7;References;27
6.3;CHAPTER 3. CONTROL OF NONLINEAR SYSTEMS SUBJECT TOINPUT CONSTRAINTS;28
6.3.1;Abstract.;28
6.3.2;1. Introduction;28
6.3.3;2. Description of the System;29
6.3.4;3. General nonlinear MPC formulation;29
6.3.5;4. Description of the Controllers;29
6.3.6;5. Examples;31
6.3.7;6. REFERENCES;33
6.4;CHAPTER 4. Stability of model predictive control under perturbations;34
6.4.1;1. Introduction;34
6.4.2;2. Outline of the paper;34
6.4.3;3. Stability results;35
6.4.4;4. Nonlinear model predictive control;37
6.4.5;5. Nonlinear state estimation;38
6.4.6;6. Conclusions;39
6.4.7;7. REFERENCES;39
6.5;CHAPTER 5. DYNAMIC STATE FEEDBACK IN A CONTINUOUS STIRREDTANK REACTOR;40
6.5.1;1. INTRODUCTION;40
6.5.2;2. CONTROL OF A CSTR MODEL;41
6.5.3;3. SIMULATIONS;43
6.5.4;4. CONCLUSIONS;44
6.5.5;5. REFERENCES;44
7;PART II: STABILITY;46
7.1;CHAPTER 6. A NEW CRITERION FOR ASYMPTOTIC STABILITY OFNONAUTONOMOUS DIFFERENTIAL EQUATIONS:AN ILLUSTRATIVE EXAMPLE;46
7.1.1;1. INTRODUCTION;46
7.1.2;2. AN ASYMPTOTIC STABILITYCRITERION;47
7.1.3;3. HARMONIC OSCILLATOR WITHTIME-DEPENDENT DAMPING;48
7.1.4;4. CONCLUSIONS;49
7.1.5;5. REFERENCES;50
7.2;CHAPTER 7. TOWARD A GEOMETRIC APPROACH FOR THE STABILITYANALYSIS OF MULTIVARIABLE SYSTEMS AFFECTED BYPHASE PERTURBATIONS;52
7.2.1;1. INTRODUCTION;52
7.2.2;2. ANALYSIS;53
7.2.3;3. EXAMPLES;54
7.2.4;4. DISCUSSION;56
7.2.5;REFERENCES;56
7.3;CHAPTER 8. A STABILITY RADIUS FOR NONLINEAR DIFFERENTIAL EQUATIONS SUBJECT TO TIME VARYING PERTURBATIONS;58
7.3.1;ABSTRACT;58
7.3.2;1. Introduction;58
7.3.3;2. Stability and Instability for Perturbed Differential Equations.;59
7.3.4;3. A Stability Radius for Nonlinear Differential Equations;60
7.3.5;References;60
7.4;CHAPTER 9. RESONANCE AND FEEDBACK STABILIZATION;62
7.4.1;Abstract;62
7.4.2;1. INTRODUCTION;62
7.4.3;2. RESONANCE;63
7.4.4;3. CONCLUSIONS;66
7.4.5;REFERENCES;66
7.5;CHAPTER 10. NONLINEAR CONTROL DESIGN IN THE FREQUENCY DOMAIN;68
7.5.1;Abstract;68
7.5.2;1. INTRODUCTION;68
7.5.3;2. NONLINEAR SYSTEMS IN THE FREQUENCY DOMAIN;69
7.5.4;3. INVERSION OF THE LAPLACE TRANSFORM;69
7.5.5;4. APPLICATION TO CONTROL THEORY;72
7.5.6;5. Conclusions;73
7.5.7;6. REFERENCES;73
7.6;CHAPTER 11. FEEDBACK STABILIZATION OF BIFURCATION PHENOMENA AND ITSAPPLICATION TO THE CONTROL OF VOLTAGE INSTABILITIES AND COLLAPSE;74
7.6.1;ABSTRACT;74
7.6.2;1.Introduction;74
7.6.3;2. A Model of Voltage Collapse;74
7.6.4;3. Normal Forms Analysis of the Power Plant Model;75
7.6.5;4.Resonance Control of Voltage Instabilities;76
7.6.6;5. Discussion and Conclusion;77
7.6.7;References;78
8;PART III: IDENTIFICATION AND CONTROL PROBLEMS INCOMPUTER VISION;80
8.1;CHAPTER 12. Multistage Nonlinear Observer with Application to Vision Based Estimation;80
8.1.1;1. INTRODUCTION;80
8.1.2;2. MULTISTAGE NONLINEAR OBSERVER;80
8.1.3;3. HIGH-GAIN OBSERVERS FOR NONLINEAR
SYSTEMS;82
8.1.4;4. MOTION AND RANGE ESTIMATION FOR APOINT MASS FALLING FREELY UNDER GRAVITY;83
8.1.5;5. CONCLUSION;84
8.1.6;6. REFERENCES;84
8.2;CHAPTER 13. A MODEL FOR BINOCULAR VISION;86
8.2.1;1 Introduction;86
8.2.2;2 A Model for the Motion ofa Single Eye;86
8.2.3;3 The Tracking Problem for Monocular Vision;87
8.2.4;4 Binocular Eye Motion and Tracking;87
8.2.5;5 Monocular and Binocular Observability;88
8.2.6;6 Conclusion;89
8.2.7;References;89
8.3;CHAPTER 14. A Realization Theory for Perspective Systems;90
8.3.1;1. Introduction and Motivation;90
8.3.2;2. The Perspective Realization Problem;90
8.3.3;3. State Space Realization;91
8.3.4;4. A Sketch of the Proof;92
8.3.5;5. A Rescaling Algorithm;94
8.3.6;6. Conclusion;95
8.3.7;7. REFERENCES;95
8.4;CHAPTER 15. STRUCTURE FROM VISUAL MOTION AS A NONLINEAR OBSERVATION PROBLEM;96
8.4.1;1. INTRODUCTION;96
8.4.2;2. UNFEASIBILITY OF THE THE OBSERVER LINEARIZATION;97
8.4.3;3. ALTERNATIVE OBSERVERS;98
8.4.4;4. LOCAL LINEARIZATION-BASEDSTRUCTURE FROM MOTION;99
8.4.5;5. MOTION-INDEPENDENT STRUCTURE ESTIMATION;99
8.4.6;6. EXPERIMENTS;99
8.4.7;7. CONCLUSIONS;100
8.4.8;8. REFERENCES;100
9;PART IV: DECOUPLING;102
9.1;CHAPTER 16. A new result on almost disturbance decoupling for nonlinear minimum phase systems;102
9.1.1;1 Introduction;102
9.1.2;2 Main result;102
9.1.3;References;104
9.2;CHAPTER 17. COMPLETE INVARIANTS OF NONLINEAR CONTROL SYSTEMS;106
9.2.1;1. INTRODUCTION;106
9.2.2;2. CASCADE STRUCTURE;107
9.2.3;3. FINER STRUCTURE;108
9.2.4;4. CONCLUSION;111
9.2.5;REFERENCES;111
10;PART V: ADAPTIVE NONLINEAR CONTROL;112
10.1;CHAPTER 18. BLOCK BACKSTEPPING FOR ADAPTIVE NONLINEARCONTROL*;112
10.1.1;1. INTRODUCTION;112
10.1.2;2. BLOCK BACKSTEPPING;113
10.1.3;3. ADAPTIVE BLOCK BACKSTEPPING;114
10.1.4;4. BLOCK-STRICT-FEEDBACK SYSTEMS;116
10.1.5;REFERENCES;116
10.2;CHAPTER 19. LYAPUNOV AND ISS FRAMEWORKS FORADAPTIVE NONLINEAR STABILIZATION;118
10.2.1;1. INTRODUCTION;118
10.2.2;2. LYAPUNOV FRAMEWORK;118
10.2.3;3. ISS FRAMEWORK;120
10.2.4;4. CONCLUSIONS;123
10.2.5;REFERENCES;123
10.3;CHAPTER 20. ADAPTIVE TRACKING WITHDISTURBANCE ATTENUATION FOR ACLASS OF NONLINEAR SYSTEMS;124
10.3.1;Abstract.;124
10.3.2;INTRODUCTION;124
10.3.3;MAIN RESULT;125
10.3.4;References;129
10.4;CHAPTER 21. ROBUSTNESS OF KRSTIC'S NEW ADAPTIVE CONTROL SCHEME;130
10.4.1;Abstract.;130
10.4.2;1 INTRODUCTION;130
10.4.3;2 TWO WORK EXAMPLES ;131
10.4.4;3 SIMULATION RESULTS AND DISCUSSIONS;132
10.4.5;4 CONCLUSIONS;135
10.4.6;REFERENCES;135
11;PART VI: OPTIMAL CONTROL;136
11.1;CHAPTER 22. AGAIN ON TANGENT CONES AND HIGH ORDER MAXIMUMPRINCIPLES;136
11.1.1;Abstract;136
11.1.2;1. INTRODUCTION;136
11.1.3;2. NOTATIONS AND DEFINITIONS;136
11.1.4;3. VARIATIONAL CONE;137
11.1.5;4. REFERENCES;140
11.2;CHAPTER 23. FLOW DIFFERENTIABILITY WITH CONTROLS IN Lp;142
11.2.1;Abstract.;142
11.2.2;1. INTRODUCTION;142
11.2.3;2. MAIN RESULTS;143
11.2.4;3. Bounded controls;144
11.2.5;4. REFERENCES;144
11.3;CHAPTER 24. THE RICCATI EQUATION FOR REGULAR LQ-CONTROLPROBLEMS WITH CONSTRAINTS;146
11.3.1;Abstract;146
11.3.2;1. INTRODUCTION;146
11.3.3;2. STATEMENT OF THE PROBLEM ANDMAIN RESULTS;147
11.3.4;3. REFERENCES;150
12;PART VII: HOMOGENEOUS SYSTEMS;152
12.1;CHAPTER 25. FEEDBACK STABILIZATION OF HOMOGENEOUS POLYNOMIAL SYSTEMS;152
12.1.1;Abstract;152
12.1.2;1. INTRODUCTION;152
12.1.3;2. NOTATIONS AND PRELIMINARIES;153
12.1.4;3. STABILIZATION OF ODD HOMOGENEOUS VECTOR FIELDS;153
12.1.5;4. STABILIZATION OF EVEN HOMOGENEOUS VECTOR FIELDS;154
12.1.6;5. REFERENCES;155
12.2;CHAPTER 26. Zubov Theorem and Domain of Attraction for Controlled Dynamic Systems;158
12.2.1;Abstract.;158
12.2.2;1. Introduction;158
12.2.3;2. Domain of attraction;158
12.2.4;3. Homogeneous systems;161
12.2.5;4. REFERENCES;161
12.3;CHAPTER 27. GEOMETRIC HOMOGENEITY AND STABILIZATION MATTHIAS KAWSKI;162
12.3.1;Abstract;162
12.3.2;1. WHY HOMOGENEITY;162
12.3.3;2. TRADITIONAL DILATIONS;163
12.3.4;3. GEOMETRIC HOMOGENEITY;163
12.3.5;4. APPLICATIONS TO STABILITY AND STABILIZATION;166
12.3.6;5. REFERENCES;167
12.4;CHAPTER 28. Adding an integrator to a non stabilizable homogeneous planarsystem;168
12.4.1;Abstract.;168
12.4.2;1. INTRODUCTION;168
12.4.3;2. PRELIMINARIES;169
12.4.4;3. "NON-ATTRACTIVE MODE" AND HOMOGENEOUS STABILIZATION;170
12.4.5;4. "NON-ATTRACTIVE CENTER" AND HOMOGENEOUS SATBILIZATION;171
12.4.6;5. CONCLUSIONS;173
12.4.7;6. REFERENCES;173
12.5;CHAPTER 29. Stabilizing time-varying feedback;174
12.5.1;Abstract;174
12.5.2;1 Introduction;174
12.5.3;2 Time-varying feedback;175
12.5.4;3 Time-varying output feedback;179
12.5.5;References;180
13;PART VIII: CHEMICAL PROCESSES;182
13.1;CHAPTER 30. FEEDBACK LINEARIZING CONTROLLER DESIGN FORCHEMICAL PROCESSES: CHALLENGES AND RECENT ADVANCES;182
13.1.1;Abstract.;182
13.1.2;1. INTRODUCTION;182
13.1.3;2. NONLINEAR CHEMICAL PROCESSES;182
13.1.4;3. INPUT-OUTPUT LINEARIZATION;184
13.1.5;4. CONCLUSIONS;187
13.1.6;5. ACKNOWLEDGEMENTS;187
13.1.7;6. REFERENCES;187
13.2;CHAPTER 31. NONLINEAR PROCESS CONTROL BY A COMBINATION OF EXACT LINEARIZATION AND GAIN SCHEDULING TRAJECTORY CONTROL;188
13.2.1;Abstract.;188
13.2.2;1. INTRODUCTION;188
13.2.3;2. BASIC CONCEPTS;189
13.2.4;3. GAIN SCHEDULING TRAJECTORY CONTROL;190
13.2.5;4. EXAMPLE;191
13.2.6;5. CONCLUSIONS;192
13.2.7;6. REFERENCES;193
13.3;CHAPTER 32. Feedback Stabilization of Non Linear End Milling Process;194
13.3.1;Abstract;194
13.3.2;1. Introduction;194
13.3.3;2.CNC Milling System Modelling;194
13.3.4;3.Preliminaries and Definitions;194
13.3.5;4.Derivation of Output Feedback Stabilization Control Law(Relative Degree p -1;195
13.3.6;5. Lyapunov Stability Analysis;196
13.3.7;6.Application Example to Milling Process;196
13.3.8;7. Simulation;196
13.3.9;8.Control Lav Derivation ViaLyapunov Stability Criteria;197
13.3.10;9. Simulation;198
13.3.11;10. Conclusi ons;198
13.3.12;References;199
13.4;CHAPTER 33. Positiveness and Asymptotic Stability of a Double Effect Evaporator;200
13.4.1;Abstract;200
13.4.2;1 Introduction*;200
13.4.3;2 The double effect evaporator;200
13.4.4;3 Quasimonotone positive nonlinear systems;202
13.4.5;4 Sign-stability of equilibria;202
13.4.6;5 Application to the double effect evaporator;203
13.4.7;6 Conclusions;205
13.4.8;References;205
13.4.9;Appendix A;205
13.5;CHAPTER 34. Nonlinear Dynamic Control of a Non-Minimum-Phase CSTR;206
13.5.1;Abstract.;206
13.5.2;1. INTRODUCTION;206
13.5.3;2. NOTATION AND PRELIMINARIES;206
13.5.4;3. BRIEF DESCRIPTION OF PROCESS ANDCONTROL PROBLEM;207
13.5.5;4. ALGEBRAIC ANALYSIS;207
13.5.6;5. STATIC FEEDBACK DESIGN;208
13.5.7;6. CONTROLLER DESIGN VIA APPROXIMATE INPUT-OUTPUT DECOUPLING;209
13.5.8;7. CONCLUSION;211
13.5.9;8. REFERENCES;211
14;PART IX: EXTERNAL STABILITY OF NONLINEAR CONTROL SYSTEMS;212
14.1;CHAPTER 35. EXTERNAL STABILITY OF NONLINEAR SYSTEMS;212
14.1.1;Abstract.;212
14.1.2;1. INTRODUCTION;212
14.1.3;2. DEFINITIONS AND PRELIMINARIES;212
14.1.4;3. LINEAR SYSTEMS;213
14.1.5;4. A NONLINEAR FINITE GAIN PROPERTY;214
14.1.6;5. INTERCONNECTED SYSTEMS;215
14.1.7;6. GENERAL SYSTEMS;215
14.1.8;7. AFFINE SYSTEMS;216
14.1.9;8. REFERENCES;217
14.2;CHAPTER 36. On Characterizations of Input-to-State Stability with Respect to Compact Sets;218
14.2.1;1. Introduction;218
14.2.2;2. Set Input to State Stability;218
14.2.3;3. ISS-Control Lyapunov Functions;221
14.2.4;4. Appendix;223
14.2.5;5. REFERENCES;223
14.3;CHAPTER 37. EXAMPLES OF STABILIZATION USING SATURATION: AN INPUT-OUTPUT APPROACH;224
14.3.1;Abstract.;224
14.3.2;1. NOTATION;224
14.3.3;2. INTRODUCTION;224
14.3.4;3. BALL AND BEAM WITH FRICTION;224
14.3.5;4. A GENERAL FORMALISM;225
14.3.6;5. PVTOL;226
14.3.7;6. INVERTED PENDULUM ON A CART;228
14.3.8;7. REFERENCES;229
14.4;CHAPTER 38. OUTPUT FEEDBACK GLOBAL STABILIZATION FOR TRIANGULAR SYSTEMS;230
14.4.1;Abstract;230
14.4.2;1. INTRODUCTION;230
14.4.3;2. DYNAMIC STABILIZATION;231
14.4.4;3. THE GENERAL CASE-USE OFARTSTEIN'S THEOREM;233
14.4.5;4. APPENDIX;234
14.4.6;5. REFERENCES;235
15;PART X: H-INFINITY CONTROL;236
15.1;CHAPTER 39. NONLINEAR L2-GAIN SUBOPTIMAL CONTROL;236
15.1.1;Abstract;236
15.1.2;1. INTRODUCTION;236
15.1.3;2. PRELIMINARIES;236
15.1.4;3. MAIN RESULTS;238
15.1.5;4. CONCLUSION;241
15.1.6;5. ACKNOWLEDGEMENT;241
15.1.7;6. REFERENCES;241
15.2;CHAPTER 40. ADAPTIVE Hoc CONTROL USING COPRIME FACTORS AND SET-MEMBERSHIP IDENTIFICATION : THE NONLINEAR CASE;242
15.2.1;Abstract;242
15.2.2;I. INTRODUCTION;242
15.2.3;II. AN INCREMENTAL APPROACH FOR NONLINEARCONTROL;243
15.2.4;III. ROBUSTNESS ANALYSIS;244
15.2.5;IV. SET MEMBERSHIP IDENTIFICATION;246
15.2.6;V. STABILITY AND ROBUSTNESS OF THE ADAPTIVESCHEME;246
15.2.7;VI. APPLICATION;245
15.2.8;REFERENCES;247
15.3;CHAPTER 41. Nonlinear H8 Method for Volterra Systems;248
15.3.1;Abstract.;248
15.3.2;1. Introduction;248
15.3.3;2. Volterra System and the Laplace Transform;248
15.3.4;3. Hoo Norm of Nonlinear Systems;250
15.3.5;4. Hoo Norm of Bilinear Systems;251
15.3.6;5. Conclusions;251
15.3.7;6. REFERENCES;251
15.4;CHAPTER 42. GLOBAL NONLINEAR H8-CONTROL VIA OUTPUTFEEDBACK;254
15.4.1;Abstract;254
15.4.2;1 INTRODUCTION;254
15.4.3;2 PRELIMINARIES;254
15.4.4;3 H8-CONTROL PROBLEMS;255
15.4.5;4 STATE-FEEDBACK H8-CONTROL;256
15.4.6;5 OUTPUT-FEEDBACK H8-CONTROL;257
15.4.7;Acknowledgements;259
15.4.8;References;259
15.5;CHAPTER 43. ON ROBUST STABILIZATION AND H8 CONTROL FORLINEAR AND BILINEAR SYSTEMS WITH NONLINEARUNCERTAINTY;260
15.5.1;1. INTRODUCTION;260
15.5.2;2. LINEAR SYSTEMS WITH NONLINEAR UNCERTAINTY;260
15.5.3;3. BILINEAR SYSTEMS WITH NONLINEAR UNCERTAINTY;263
15.5.4;4. REFERENCES;265
15.6;CHAPTER 44. H°° CONTROL FOR SYSTEMS WITH SECTOR BOUND NONLINEARITIES;266
15.6.1;Abstract.;266
15.6.2;1. INTRODUCTION;266
15.6.3;2. PRELIMINARIES;267
15.6.4;3. MAIN RESULTS;267
15.6.5;4. CONCLUSIONS;270
15.6.6;5. REFERENCES;270
16;PART XI: FEEDBACK LINEARIZATION;272
16.1;CHAPTER 45. Definition and Computation of a Nonlinearity Measure;272
16.1.1;Abstract.;272
16.1.2;1. Introduction;272
16.1.3;2. Definition of a nonlinearity measure;272
16.1.4;3. Computation of the nonlinearity measure;273
16.1.5;4. Example;275
16.1.6;5. Conclusions;277
16.1.7;6. REFERENCES;277
16.2;CHAPTER 46. Approximate Feedback Linearization:Higher Order Approximate Integrating Factors*;278
16.2.1;Abstract;278
16.2.2;Introduction;278
16.2.3;1. Notation and Auxiliary Results;279
16.2.4;2. 5-Metric;280
16.2.5;3. Higher Order Approximate Integrating Factors;281
16.2.6;4. Higher Order Approximate Integrating Factors for Systems Close to Being Linearizable;281
16.2.7;5. Application of Higher Order Approximate Integrating Factors to Approximate Feedback Linearization;282
16.2.8;6. REFERENCES;283
16.3;CHAPTER 47. Feedback Linearization of Transverse Dynamicsfor Periodic Orbits in R3with Points of Transverse Controllability Loss;284
16.3.1;Abstract.;284
16.3.2;Introduction;284
16.3.3;1. Results;285
16.3.4;2. Example;288
16.3.5;3. REFERENCES;289
16.3.6;Conclusion;289
16.4;CHAPTER 48. LINEARIZING THE BALL AND BEAM SYSTEM WITH A PD CONTROL LAW;290
16.4.1;Abstract.;290
16.4.2;1. INTRODUCTION;290
16.4.3;2. COORDINATE CHANGES;290
16.4.4;3. IDEAL CONTROL LAW;292
16.4.5;4. PRACTICAL CONTROL LAW;292
16.4.6;5. STABILITY;293
16.4.7;6. CONCLUSION;294
16.4.8;7. References;294
16.5;CHAPTER 49. A Procedure towards Linearizing Dynamic Feedback;296
16.5.1;Abstract.;296
16.5.2;1. Introduction;296
16.5.3;2. Notations;297
16.5.4;3. Generalized Controller Form;297
16.5.5;4. Transformation Procedure;298
16.5.6;5. Example;300
16.5.7;6. REFERENCES;301
16.6;CHAPTER 50. THE RELATIVE DEGREE ENHANCEMENT PROBLEM FOR MIMO NONLINEAR SYSTEMS;302
16.6.1;Abstract.;302
16.6.2;1. PROBLEM STATEMENT;302
16.6.3;2. DESIGN STEPS;303
16.6.4;3. EXAMPLES;304
16.6.5;4. CONCLUDING REMARKS;305
16.6.6;5. ACKNOWLEDGEMENTS;306
16.6.7;6. REFERENCES;306
17;PART XI: ADAPTIVE NONLINEAR CONTROL;308
17.1;CHAPTER 51. DECENTRALIZED ADAPTIVE CONTROL OF MISMATCHEDLARGE SCALE INTERCONNECTED NONLINEAR SYSTEMS;308
17.1.1;Abstract.;308
17.1.2;1. INTRODUCTION;308
17.1.3;2. THE CLASS OF LARGE-SCALENONLINEAR SYSTEMS;308
17.1.4;3. DECENTRALIZED ADAPTIVE DESIGN;309
17.1.5;4. CONCLUSION;313
17.1.6;5. REFERENCES;313
17.2;CHAPTER 52. ON ADAPTIVE FEEDBACK STABILISATION FOR NONLINEAR SYSTEMS MODELED BY DISCRETE TIME EQUIVALENTS;314
17.2.1;Abstract;314
17.2.2;1 INTRODUCTION;314
17.2.3;2 ADAPTIVE FEEDBACK STABILIZATION;314
17.2.4;3 A PARAMETER UPDATE SCHEME;315
17.2.5;4 APPLICATION TO SOME SPECIFIC EXAMPLES;317
17.2.6;5 SIMULATIONS;317
17.2.7;REFERENCES;318
17.3;CHAPTER 53. roENTIFICATION AND ADAPTIVE NONLINEAR CONTROLOF DRIVES WITH FRICTION;320
17.3.1;1. INTRODUCTION;320
17.3.2;2. MODELLING AND IDENTIFICATION OF DRIVES;320
17.3.3;3. MODEL BASED NONLINEAR CONTROL SCHEMES;322
17.3.4;4. APPLICATION;323
17.3.5;5. CONCLUSION;325
17.3.6;REFERENCES;325
18;PART XII: OPTIMAL CONTROL II;326
18.1;CHAPTER 54. COMPACT FORMS OF THE GENERALIZED LEGENDRECLEBSCHCONDITIONS AND THE DERIVATION OF SINGULAR CONTROL TRAJECTORIES;326
18.1.1;Abstract.;326
18.1.2;1. INTRODUCTION;326
18.1.3;2. OPTIMAL CONTROL PROBLEM;327
18.1.4;3. LEGENDRE-CLEBSCH CONDITIONS;327
18.1.5;4. CONCLUSIONS;329
18.1.6;5. REFERENCES;329
18.2;CHAPTER 55. DIDO'S PROBLEM WITH A FIXED CENTER OF MASS;332
18.2.1;Abstract;332
18.2.2;1. INTRODUCTION;332
18.2.3;2. PROBLEM STATEMENT;333
18.2.4;3. EXTREMALS;333
18.2.5;4. ACKNOWLEDGEMENT;335
18.2.6;5. REFERENCES;335
18.3;CHAPTER 56. On the Structure of Optimal Oscillatory Trajectories for Two-Input Driftless Smooth Systems in Dimension Three;338
18.3.1;Abstract.;338
18.3.2;1. Introduction;338
18.3.3;2. The value function;339
18.3.4;3. Basic properties of optimal trajectories;340
18.3.5;4. Optimal oscillatory trajectories;341
18.3.6;5. REFERENCES;343
19;PART XIII: DIFFERENTIAL ALGEBRAIC SYSTEMS;344
19.1;CHAPTER 57. ON SYSTEM STRUCTURE THEORY AND NONLINEARINTERACTOR;344
19.1.1;Abstract;344
19.1.2;1. PRELIMINARIES;345
19.1.3;2. THE NEW DEFINITION OF SYSTEM INTERACTOR;346
19.1.4;3. EXAMPLES;348
19.1.5;4. REFERENCES;348
19.2;CHAPTER 58. Calculation of Zero Dynamics for Affine MIMO-Systems using the Ritt Algorithm;350
19.2.1;Abstract.;350
19.2.2;1. INTRODUCTION;350
19.2.3;2. THE ZERO DYNAMICS OF ANONLINEAR SYSTEM;350
19.2.4;3. BASIC ALGEBRAIC CONCEPTS;351
19.2.5;4. USING THE RITT ALGORITHM TOCALCULATE THE ZERO DYNAMICS;352
19.2.6;5. EXAMPLES;354
19.2.7;6. CONCLUSIONS;355
19.2.8;7. REFERENCES;355
19.3;CHAPTER 59. ON DIFFERENTIAL ALGEBRAIC SYSTEMS;356
19.3.1;Abstract;356
19.3.2;1. INTRODUCTION;356
19.3.3;2. GENERAL MATHEMATICAL MODELS;356
19.3.4;3. SOLUTIONS of ADE's;358
19.3.5;4. DIFFERENTIAL ALGEBRA;359
19.3.6;5. PA- AND GPA-SOLUTIONS;359
19.3.7;6. DIFFERENTIAL ALGEBRAIC SYSTEMS;360
19.3.8;7. CONCLUSIONS;363
19.3.9;8. REFERENCES;363
20;PART XIV: PLENARY PAPER II;364
20.1;CHAPTER 60. Nonlinear Control of Mechanical Systems:A Lagrangian Perspective;364
20.1.1;1. INTRODUCTION;364
20.1.2;2. LAGRANGIAN CONTROL SYSTEMS;366
20.1.3;3. CONTROLLABILITY;369
20.1.4;4. TRAJECTORY GENERATION;372
20.1.5;5. DISCUSSION AND OPEN PROBLEMS;374
20.1.6;6. REFERENCES;375
21;PART XV: CONTROL OF MOBILE ROBOTS;376
21.1;CHAPTER 61. Regulation of the Acrobot;376
21.1.1;1. Introduction;376
21.1.2;2. Stabilizing the Acrobot;377
21.1.3;3. Generalization;380
21.1.4;4. REFERENCES;381
21.2;CHAPTER 62. MODELING AND CONTROL DESIGN FOR A MOBILE ROBOT;382
21.2.1;Abstract.;382
21.2.2;1. Introduction;382
21.2.3;2. Kinematic Analysis and Approximation;382
21.2.4;3. Dynamic Model - Formulation of Lagrangian;383
21.2.5;4. A Simple Gait Algorithm;385
21.2.6;5. Simulation Results;385
21.2.7;6. Conclusion;385
21.2.8;7. REFERENCES;386
21.3;CHAPTER 63. AN APPLICATION OF NONLINEAR ROBUST CONTROL;388
21.3.1;Abstract;388
21.3.2;1. INTRODUCTION;388
21.3.3;2. FUEL-INJECTION MODEL;388
21.3.4;3. SLIDING MODE CONTROL;389
21.3.5;4. DYNAMIC SLIDING MODE CONTROL;389
21.3.6;5. TRANSIENT FUEL CORRECTION;389
21.3.7;6. EXPERIMENTAL RESULTS;390
21.3.8;7. CONCLUSIONS;392
21.3.9;REFERENCES;392
21.4;CHAPTER 64. ON THE QUADRATIC MODELING OF NONLINEAR PLANTSWITH APPLICATION TO AN ELECTRO-HYDRAULIC DRIVE;394
21.4.1;Abstract;394
21.4.2;1. INTRODUCTION;394
21.4.3;2. QUADRATIC MODELING METHODS;395
21.4.4;3. DERIVATION OF THE IDENTIFICATIONALGORITHM;396
21.4.5;4. APPLICATION TO ANELECTRO-HYDRAULIC DRIVE;398
21.4.6;5. CONCLUSION;398
21.4.7;6. REFERENCES;399
21.5;CHAPTER 65. STOCHASTIC AND REGULAR MOTIONSIN SYSTEM WITH 'YAWN';400
21.5.1;Abstract;400
21.5.2;1. Introduction and Problem Statement;400
21.5.3;2. Simplified Model of System with 'Yawn1.;401
21.5.4;3. Conclusion;404
21.5.5;References;404
22;PART XVI: NONLINEAR STABILIZATION;406
22.1;CHAPTER 66. Static Stabilizing Feedback Controls for a Class of Singularly Perturbed Nonlinear Uncertain Systems;406
22.1.1;Abstract;406
22.1.2;1. INTRODUCTION;406
22.1.3;2. Full-order singularly perturbed uncertainsystem;406
22.1.4;3. The reduced-order uncertain system;407
22.1.5;4. Design objectives;407
22.1.6;5. Class of static state feedback controls;408
22.1.7;6. Boundary-layer system;408
22.1.8;7. The feedback controlled reduced-order system;408
22.1.9;8. Lyapunov analysis for the full-order system;409
22.1.10;9. REFERENCES;410
22.2;CHAPTER 67. STABILITY ANALYSIS OF NONLINEAR MODEL MATCHINGFOR A CLASS OF PERTURBED DISCRETE-TIME SYSTEMS;412
22.2.1;Abstract.;412
22.2.2;1. INTRODUCTION;412
22.2.3;2. AN ASSOCIATED DISTURBANCEDECOUPLING PROBLEM;413
22.2.4;3. THE NONLINEAR MODEL MATCHINGPROBLEM;413
22.2.5;4. NONLINEAR MODEL MATCHING UNDERPERTURBATIONS;415
22.2.6;5. CONCLUSIONS;417
22.2.7;6. REFERENCES;417
22.3;CHAPTER 68. Feedback Stabilization of General Nonlinear Control Systems *Wei Lin;418
22.3.1;Abstract.;418
22.3.2;1. Introduction;418
22.3.3;2. Notations and Main Results;419
22.3.4;3. Examples;420
22.3.5;4. The Proofs of Main Theorems;421
22.3.6;5. Conclusions;423
22.3.7;6. REFERENCES;423
23;PART XVII: H-INFINITY RISK-SENSITIVE FILTERING AND CONTROL;424
23.1;CHAPTER 69. NONLINEAR FILTERING: The SET-MEMBERSHIP(BOUNDING) and the H8 TECHNIQUES;424
23.1.1;Abstract;424
23.1.2;INTRODUCTION;424
23.1.3;1. THE NONLINEAR FILTERING PROBLEM;424
23.1.4;2. THE SET-MEMBERSHIP (BOUNDING) AND THE H8 APPROACHES;425
23.1.5;3. THE INFORMATION DOMAIN AND THE INFORMATION STATE;425
23.1.6;4. HAMILTON-JACOBI TECHNIQUES (INTEGRAL QUADRATIC INDEX;426
23.1.7;5. HAMILTON-JACOBI TECHNIQUES (INSTANTANEOUS QUADRATIC BOUNDS;427
23.1.8;6. ESTIMATES AND ERROR BOUNDS;428
23.1.9;7. Conclusions;429
23.1.10;8. Bibliography;429
23.2;CHAPTER 70. A CLASS OF ADAPTIVE NONLINEAR H8-FILTERS WITHGUARANTEED L2-STABILITY;432
23.2.1;Abstract.;432
23.2.2;INTRODUCTION;432
23.2.3;PROBLEM STATEMENT;433
23.2.4;AN APPROXIMATE LINEAR MODEL;433
23.2.5;CONVERGENCE AND L2– STABILITY OFTHE APPROXIMATE FILTER;434
23.2.6;AN EXAMPLE: THE CASE OF SYSTEMS WITH SHIFT STRUCTUR;435
23.2.7;INSTANTANEOUS-GRADIENT-BASEDIIR ADAPTIVE FILTERS;436
23.2.8;1. REFERENCES;437
23.3;CHAPTER 71. RISK SENSITIVE GENERALIZATION OF MINIMUM VARIANCE ESTIMATION AND CONTROL;438
23.3.1;Abstract;438
23.3.2;1. INTRODUCTION;438
23.3.3;2. RISK-SENSITIVE ESTIMATION;439
23.3.4;3. RISK-SENSITIVE GENERALIZATION OF MINIMUM VARIANCE CONTROL;442
23.3.5;4. CONCLUSION;443
23.3.6;5. REFERENCES;443
23.4;CHAPTER 72. FINITE DIMENSIONAL RISK SENSITIVE INFORMATIONSTATES;444
23.4.1;Abstract.;444
23.4.2;1. INTRODUCTION;444
23.4.3;2. DYNAMICS AND A MODIFIED ZAKAI EQUATION;444
23.4.4;3. BENES' FILTER;446
23.4.5;4. FINITE DIMENSIONAL INFORMATION STATES;447
23.4.6;5. REFERENCES;449