Nonlinear Control Systems Design 1989 (eBook)

Selected Papers from the IFAC Symposium, Capri, Italy, 14-16 June 1989

A. Isidori (Herausgeber)

eBook Download: PDF

2014 | 1. Auflage
421 Seiten
Elsevier Science (Verlag)
978-1-4832-9892-4 (ISBN)

Infos

In the last two decades, the development of specific methodologies for the control of systems described by nonlinear mathematical models has attracted an ever increasing interest. New breakthroughs have occurred which have aided the design of nonlinear control systems. However there are still limitations which must be understood, some of which were addressed at the IFAC Symposium in Capri. The emphasis was on the methodological developments, although a number of the papers were concerned with the presentation of applications of nonlinear design philosophies to actual control problems in chemical, electrical and mechanical engineering.

Inhalt

Front Cover 1
Nonlinear Control Systems Design 4
Copyright Page 
5 
Table Of Contents 
10 
Ifac Symposium On Nonlinear Control Systems Design 
6 
Preface 
8 
CHAPTER 1. COMPUTER-AIDED DESIGN OF NONLINEAR OBSERVERS 16
INTRODUCTION 16
NONLINEAR OBSERVABILITY PROBLEM 16
EXTENDED LUENBERGER OBSERVER 17
PROGRAM FOR THE COMPUTER-AIDED OBSERVER DESIGN 18
EXAMPLE OF AN OBSERVER DESIGN 18
CONCLUSIONS 19
REFERENCES 19
CHAPTER 2. SHOULD THE THEORIES FOR CONTINUOUSTIME AND DISCRETE-TIME LINEAR AND NONLINEAR SYSTEMS REALLY LOOK ALIKE? 22
I. INTRODUCTION 22
II. DIFFERENCE ALGEBRA AND DISCRETE-TIME SYSTEMS 22
III. REALIZATON(5) 23
IV. SOME EXAMPLES OF THE RELATONSHIP BETWEEN DISCRETE-TIME AND CONTIUOUS-TIME SYSTEMS 24
V. FEEDBACK LINEARIZATON 25
VI. CONCLUSION 26
REFERENCES 26
CHAPTER 3. DIFFERENTIAL ALGEBRA AND CONTROLLABILITY 28
Introduction 28
Linear case 28
Definition 28
Nonlinear case 28
.. Haddak 29
DIFFERENTIAL ALGEBRAIC APPROACH OF CONTROLLABILITY 30
Conclusion 
31 
REFERENCES 
31 
CHAPTER 4. PRIME DIFFERENTIAL IDEALS IN NONLINEAR RATIONAL CONTROL SYSTEMS 32
INTRODUCTION 32
RATONAL CONTROL SYSTEMS 32
APPLICATION TO THE DIFFERENTIAL OUTPUT RANK OF A NONLINEAR SYSTEM 34
CONCLUSION 36
REFERENCES 36
CHAPTER 5. CONTROLLABILITY OF BILINEAR SYSTEMS—A SURVEY AND SOME NEW RESULTS 38
INTRODUCTION 38
BRIEF SURVEY ON CONTROLLABILITY OF BILINEAR SYSTEMS 38
CONTROLLABILITY OF NONLINEAR SYSTEMS 39
STRICTLY BILINEAR SYSTEMS 39
HOMOGENEOUS-IN-THE-STATE BILINEAR SYSTEMS 39
TWO-DIMENSIONAL HOMOGENEOUS-IN-THE-STATE BILINEAR SYSTEMS 40
THREE-DIMENSIONAL HOMOGENEOUS-IN-THE-STATE BILINEAR SYSTEMS 40
CONCLUSIONS 41
ACKNOWLEDGMENT 41
REFERENCES 41
APPENDIX 42
CHAPTER 6. CONTROLLABILITY OF BILINEAR SYSTEMS—A SURVEY AND SOME NEW RESULTS 38
INTRODUCTION 38
BRIEF SURVEY ON CONTROLLABILITY OF BILINEAR SYSTEMS 38
CONTROLLABILITY OF NONLINEAR SYSTEMS 39
STRICTLY BILINEAR SYSTEMS 39
HOMOGENEOUS-IN-THE-STATE BILINEAR SYSTEMS 39
TWO-DIMENSIONAL HOMOGENEOUS-IN-THE-STATE BILINEAR SYSTEMS 40
THREE-DIMENSIONAL HOMOGENEOUS-IN-THE-STATE BILINEAR SYSTEMS 40
CONCLUSIONS 41
ACKNOWLEDGMENT 41
REFERENCES 41
APPENDIX 42
CHAPTER 7. DIFFERENTIAL ALGEBRA AND PARTIAL DIFFERENTIAL CONTROL THEORY 44
INTRODUCTION 44
A) DIFFERENTIAL GEOMETRY 
45 
B) DIFFERENTIAL ALGEBRA: 45
CONCLUSION 47
REFERENCES 47
CHAPTER 8. CANONICAL FORMS FOR NONLINEAR SYSTEMS 48
1. INTRODUCTION 48
2. CONTROLLABILITY FORMS 49
3. CONTROLLER FORMS 50
4. OBSERVABILITY FORMS 50
5. OBSERVER FORMS 51
6. CONCLUSION 52
7. REFERENCES 53
CHAPTER 9. NEW SUFFICIENT CONDITIONS FOR DYNAMIC FEEDBACK LINEARIZATION 54
Abstract 54
1 INTRODUCTION 54
2 PRELIMINARIES 55
3 MAIN RESULT 55
4 EXAMPLES 57
5 CONCLUDING REMARKS 59
References 59
CHAPTER 10. ON THE STRUCTURE ALGORITHM, DEGENERATE CONTROLLED INVARIANT DISTRIBUTIONS AND THE BLOCK DECOUPLING PROBLEM 62
INTRODUCTION 62
THE STRUCTURE ALGORITHM OF HIRSCHORN(1979) 
62 
THE STATIC STATE FEEDBACK BLOCK DECOUPLING PROBLEM 63
THE DYNAMIC BLOCK DECOUPLING PROBLEM 64
REFERENCES 66
CHAPTER 11. NONLINEAR MODEL MATCHING WITH ANAPPLICATION TO HAMILTONIAN SYSTEMS 68
1. INTRODUCTION 68
2. THE MODEL MATCHING PROBLEM 68
3. MODEL MATCHING WITH PRESCRIBED TRACKING ERROR 70
4. APPLICATION TO HAMILTONIAN SYSTEMS 70

72 
ACKNOWLEDGMENTS 73
REFERENCES 73
CHAPTER 12. NONLINEAR MODEL MATCHING WITH AN APPLICATION TO HAMILTONIAN SYSTEMS 68
1. INTRODUCTION 68
2. THE MODEL MATCHING PROBLEM 68
3. MODEL MATCHING WITH PRESCRIBED TRACKING ERROR 70
4. APPLICATION TO HAMILTONIAN SYSTEMS 70
5. CONCLUSIONS 72
ACKNOWLEDGMENTS 73
REFERENCES 73
CHAPTER 13. NONLINEAR MODEL MATCHING WITH AN APPLICATION TO HAMILTONIAN SYSTEMS 68
1. INTRODUCTION 68
2. THE MODEL MATCHING PROBLEM 68
3. MODEL MATCHING WITH PRESCRIBED TRACKING ERROR 70
4. APPLICATION TO HAMILTONIAN SYSTEMS 70
5. CONCLUSIONS 72
ACKNOWLEDGMENTS 73
REFERENCES 73
CHAPTER 14. VIRTUAL DECOMPOSITION AND TIME SCALE DECOUPLING CONTROL OF NONLINEAR SYSTEMS 74
INTRODUCTION 74
VIRTUAL DECOMPOSITION TO FULL-CONTROLLED SUBSYSTEMS 74
FULL-CONTROLLED SYSTEMS 75
TIME SCALE DECOUPLING CONTROL 77

78 
ACKNOWLEDGMENT 78

78 
CHAPTER 15. TRAJECTORY EQUIVALENCE AND WEAKLY INVARIANT DISTRIBUTIONS OF NONLINEAR SYSTEMS 80
INTRODUCTION 80
TIME SCALE TRANSFORMATION 80
TRAJECTORY EQUIVALENCE 81
WEAKLY INVARIANT DISTRIBUTION 82
CONTROLLABILITY DECOMPOSITION 83
CONCLUSION 84
REFERENCES 85
CHAPTER 16. ON THE STRUCTURE OF SMALL-TIME REACHABLE SETS FOR MULTI-INPUT NONLINEAR SYSTEMS IN LOW DIMENSIONS 86
INTRODUCTION 86
THE STRUCTURE OF THE SMALL-TIMEREACHABLE SET FOR A 4-DIMENSIONALSYSTEM WITH 2 CONTROLS 87
CONCLUSIONS 91
REFERENCES 91
CHAPTER 17. STRUCTURAL PROPERTIES OF REALIZATIONS OF EXTERNAL DIFFERENTIAL SYSTEMS 92
1. INTRODUCTION 92
3. (STRONG) ACCESSIBILITY AND UNIQUENESS OF MINIMAL REALIZATIONS 95
2. REALIZATION OF EXTERNAL DIFFERENTIAL SYSTEMS 92
4. A CONTROLLER CANONICAL FORM 96
4. CONCLUSION 96
REFERENCES 96
CHAPTER 18. ON THE USE OF STABLE DISTRIBUTIONS IN DESIGN PROBLEMS 98
1. INTRODUCTION 98
2. THE CONSTRUCTION OF STABLE DISTRIBUTIONS 98
3. THE LOCAL DISTURBANCE DECOUPLING PROBLEM WITH STABILITY 101
4. THE LOCAL NONINTERACTING CONTROL PROBLEM WITH STABILITY 102
5. CONCLUSIONS 102
ACKNOWLEDGEMENT 103
LITERATURE 103
CHAPTER 18. TARGET-DIRECTED CONTROL OF NONLINEAR SYSTEMS 104
1. INTRODUCTION 104
2. MATHEMATICAL PROGRAMMING BACKGROUND 104
3. CONTROL OF A NOMINAL PLANT 106
4 . FEEDBACK CONTROL OF A NON-NOMINAL PLANT 107
5. ILLUSTRATIVE EXAMPLE 108
REFERENCES 109
CHAPTER 19. ON THE CONTROLLABILITY OF NONLINEAR DISCRETE-TIME SYSTEMS 110
1-INTRODUCTION 
110 
2-MAIN. RESULTS 
110 
3 . E 
111 
REFERENCES 111
CHAPTER 20. NONLINEAR DECOUPLING IN DISCRETE TIME 114
1. INTRODUCTION 114
2. PRELIMINARIES 114
3. STATE FREE INVERTIBILITY AND INVARIANT FOLIATIONS 115
4. INPUT-OUTPUT DECOUPLING VIA STATIC STATE FEEDBACK 117
5. INPUT-OUTPUT DECOUPLING VIA DYNAMIC STATE FEEDBACK 118
REFERENCES 120
APPENDIX THE INVERSE OF A SYSTEM OF FUNCTIONS 121
CHAPTER 21. RECURSIVE IDENTIFICATION ALGORITHMSAS NONLINEAR SYSTEMS: PARAMETER IDENTIFIABILITY AND CONTROLLABILITY 122
1. 
122 
2. Assumptions and Definitions 123
3.Controllability of the Nonlinear System 123
4.CONTROLLABILITY OF THE ALGOR 
124 
5. PARAMETER IDENTIFIABILITY 125
6.SOME 
126 
7. CONCLUDING REMARKS 126
R 
127 
CHAPTER 22. NICELY NONLINEAR MODELLING: A DF APPROACH WITH APPLICATION TO "LINEARIZED" PROCESS CONTROL 128
1. INTRODUCTION 128
2. A CLASS OF NICELY NONLINEAR MODELS 129
4. BINARY DISTILLATION COLUMN: A SIMULATION STUDY 132
5. CONCLUDING REMARKS 133
ACKNOWLEDGMENT 133
REFERENCES 133
CHAPTER 23. NONLINEAR PREDICTIVE CONTROL BY INVERSION 134
INTRODUCTION 134
IHE TECHNIQUE DESCRIPTIOI 134
SOME REMARKS ON INVERSION 135
EXAMPLES 135
CONCLUSION 138
ACKNOWLEDGEMENTS 139
REFERENCES 139
CHAPTER 24. A VOLTERRA METHOD FOR NONLINEAR CONTROL DESIGN 140
INTRODUCTION 140
PROBLEM FORMULATION 140
VOLTERRA KERNELS FOR LINEAR ANALYTIC SYSTEMS HAVING MULTIPLE INPUTS 141
REALIZATION : SECOND ORDER 142
REALIZATION : HIGHER ORDER 142
AN APPLICATION OF TENSOR REALIZATION 142

144 
REFERENCES 144
APPENDIX: BRIEF REVIEW OF REALIZATION 145
ACKNOWLEDGEMENT 145
CHAPTER 25. THE APPLICATION OF A COMPUTER ALGEBRA SYSTEM TO THE ANALYSIS OF ACLASS OF NONLINEAR SYSTEMS 146
INTRODUCTION 146
GRAPHICAL FRONT-END FOR NONLINEAR SYSTEM DESIGN 146
CONTINUOUS SYSTEMS 147
SAMPLED-DATA SYSTEMS 149
OTHER WORK 150
CONCLUSIONS 151
ACKNOWLEDGEMENT 151
REFERENCES 151
CHAPTER 26. INPUT-OUTPUT APPROXIMATIONS OF DYNAMICAL SYSTEMS 152
INTRODUCTION 152
NOTATION 152
MODELLING AS A MIN-MAX PROBLEM 153
THE EXISTENCE OF AN OPTIMALMODEL 153
GRADIENT COMPUTATION 155
CONCLUSIONS 157
ACKNOWLEDGEMENTS 157
REFERENCES 157
CHAPTER 27. HARMONIC BALANCING USING A VOLTERRA INPUT OUTPUT DESCRIPTION 158
INTRODUCTION 158
SYSTEM DESCRIPTION 158
CONDITIONS FOR AN OSCILLATION 158
PARTITION OF THE EQUATIONS 159
THE ALGORITHM 160
THE BALANCE EQUATIONS 160
A SPECIAL CASE 160
EXAMPLES 161
CONCLUSIONS 162
ACKNOWLEDGMENTS 162
REFERENCES 162
CHAPTER 28. SYMBOLIC CALCULUS AND VOLTERRA SERIES 164
1. WORDS , LANGUAGS AND FORMAL PWER SERIES ([1]) 164
2. CALCULUS OF THE FORMAL POWER SERIES EVALUATION 165
3. CHEN SERIES ([4], [15]) 167
4. REALIZATION 168
5. REFERENCES 169
CHAPTER 29. LOCAL AND MINIMAL REALIZATION OF NONLINEAR DYNAMICAL SYSTEMS AND LYNDON WORDS 170
INTRODUCTION 170
FORMAL POWER SERIES 170
LYNDON WORDS 171
VECTOR FIELDS ANDDYNAMICAL SYSTEMS 172
SYSTEM GEOMETRY ANDFORMAL POWDER SERIES 172
REALIZATION OFDYNAMICAL SYSTEMS 173
BIBLIOGRAPHIE 175
CHAPTER 30. AN INVESTIGATION OF LINEAR STABILIZABILITY OF PLANAR BILINEAR SYSTEMS 176
1.INTRODUCTION 176
2. STATEMENT OF THE PROBLEM 176
3. THE CASE (2.1) 177
4. THE CASE (2.2) 177
Proof 178
5. THE CASE (2.3) 178
REFERENCES 181
CHAPTER 31. VIBRATIONAL CONTROL OF NONLINEAR TIME LAG SYSTEMS: VIBRATIONAL STABILIZATION AND TRANSIENT BEHAVIOR* 182
I. INTRODUCTION 182
II. VIBRATIONAL STABILIZATION 183
III. TRANSIENT BEHAVIOR ANALYSIS OF VIBRATIONALLY CONTROLLED NONLINEAR TIME LAG SYSTEMS 185
IV. CONCLUSIONS 187
REFERENCES 187
APPENDIX 187
CHAPTER 32.STABILIZABILITY OF NONHOLONOMIC CONTROL SYSTEMS 188
1. INTRODUCTION 188
2. HAMILTONIAN CONTROL SYSTEMS ANDNONHOLONOMIC CONSTRAINTS 188
3. EQUILIBRIA OF NONHOLONOMIC CONTROL SYSTEMS 190
4. STABILIZABILITY 190
5. CONCLUDING REMARKS 192
REFERENCES 193
CHAPTER 33. A LYAPUNOV APPROACH TO STABILIZE FEEDBACK LINEARIZED NONLINEAR SYSTEMS WITH DISTURBANCES 194
INTRODUCTION 194
QUASI LINEAR SYSTEMS 194
STATEMENT OF THE PROBLEM 195
MAIN RESULT 195
DESIGN PROCEDURE 197
EXAMPLE 197
CONCLUSION 198
REFERENCES 198
CHAPTER 34. LOCAL ASYMPTOTIC STABILIZATION OF TWO DIMENSIONAL POLYNOMIAL SYSTEMS 200
1 Introduction 200
2 Preliminaries 200
3 Asymptotic stabilization 201
References 203
CHAPTER 35. NONLINEAR STABILIZATION OF A CLASS OF SINGULARLY PERTURBED UNCERTAIN SYSTEMS 204
INTRODUCTION 204
PROBLEM STATEMENT 204
STRUCTURE OF THE CONTROLLERA N D PROOF OF STABILITY 205
CONCLUSIONS 207
APPENDIX 207
REFERENCES 207
CHAPTER 36. STABILITY ANALYSIS OF QUADRATIC SYSTEMS 210
1. Introduction 210
2· Problem statement 210
3. Selection of the Lyapunov function 211
4. Domain of attraction 212
5. Some optimization problems 212
6. Numerical examples 213
7. Conclusions 213
Acknowledgements 214
References 214
CHAPTER 37. A GENERALISATION OF THE SMALL-GAIN THEOREM FOR NONLINEAR FEEDBACK SYSTEMS 216
NTRODUCTION 216
INPUT- OUTPUT STABILITY 216
FEEDBACK SYSTEM STABILITY 217
CONCLUSIONS 219
ACKNOWLEDGEMENT 219
REFERENCES 219
CHAPTER 38. ON A NONLINEAR MULTIVARIABLE SERVOMECHANISM PROBLEM 222
1. Introduction 222
2. Problem Description and Hypotheses 222
3. Feedback Control Law 223
4. Closed-Loop System Properties 225
5. Concluding Remarks 226
6. References 226
CHAPTER 39. GLOBAL DYNAMICS ACHIEVABLE BY FEEDBACK CONTROLS: SOME PRELIMINARY 228
1. INTRODUCTION 228
2. DEFINITIONS AND CLASSIFICATION RESULTS 229
3. EQUILIBRIUM POINTS 230
4. LIMIT CYCLES 231
5. SELECTION OF FEEDBACK CONTROLS 232
6. CONCLUSIONS 232
REFERENCES 232
CHAPTER 40. ON THE ABSOLUTE STABILITY CRITERIA IMPROVING AND ABSOLUTE STABILITY REGIONS CONSTRUCTION 234
INTRODUCTION 234
THE IMPROVED CRITERION 234
THE ABSOLUTE STABILITY CRITERION CONSTRUCTION 236
EXAMPLE 236
The polinomial 237
CONCLUSION 237
REFERENCES 237
CHAPTER 41. AN APPROACH TO NONLINEAR MULTIVARIABLE CONTROL SYSTEMS DESIGN 240
INTRODUCTION 240
PROBLEM STATEMENT AND SOME RELATED MINIMIZATION PROBLEMS 240
THE GENERAL FORM OF CONTROL 241
BILINEAR SYSTEMS 242
EXAMPLE 242
CONCLUSIONS 243
REFERENCES 243
CHAPTER 42. NONSINGULAR AND STABLE ADAPTIVE CONTROL OF DISCRETE-TIME BILINEAR SYSTEMS 244
INTRODUCTION 244
SYSTEM MODEL 244
PARAMETER ESTIMATION 245
ONE- STEP AHEAD CONTROLLER DESIGN 245
STABILITY ANALYSIS 247
EXAMPLE 248
CONCLUSIONS 248
REFERENCES 248
CHAPTER 43. DIRECT ADAPTIVE CONTROL OF NONLINEAR SYSTEMS 250
1. INTRODUCTION 250
2. SYSTEM DESCRIPTION 250
3. ASYMPTOTIC PROPERTIES 251
4. NONLINEAR PLANT 251
5. CONCLUDING DISCUSSION 252
REFERENCES 253
CHAPTER 44. DISCRETE TIME ADAPTIVE CONTROL FOR A CLASS OF NONLINEAR CONTINUOUS SYSTEMS 254
ABSTRACT 
254 
1. INTRODUCTION 
254 
2. SYSTEM DESCRIPTION IN CONTINUOUS TIME 
254 
3.EXACT SAMPLING OF NON LINEAR CONTINUOUS SYSTEMS 255
4.STATEMENT OF THE ADAPTIVE CONTROL PROBLEM 255
5. DISCRETE PARAMETER ESTIMATION 
256 
6. ADAPTIVE r-LINEARIZING CONTROL 
256 
7. CONCLUSIONS 
258 
APPENDIX 259
REFERENCES 
259 
CHAPTER 45. ROBUSTNESS OF ADAPTIVE NONLINEAR CONTROL UNDER AN EXTENDED MATCHING CONDITION1 260
1. INTRODUCTION AND PROBLEM STATEMENT 260
2. ADAPTIVE REGULATION 261
3. ROBUSTNESS OF ADAPTIVE REGULATION 264
4. CONCLUSIONS 265
REFERENCES 265
APPENDIX 265
CHAPTER 46. SWITCHING STABILIZATION CONTROL FOR A SET OF NONLINEAR TIME-VARYING SYSTEMS 266
1. Introduction 266
2. Set of the plants 266
3. Construction of the switching controIler 267
4. Quadratic stabilization and an example 268
5. C 
269 
ACKNOWLEDGEMENT 269
REFERENCE 269
CHAPTER 47. NONLINEAR DYNAMICS OF ADAPTIVE LINEAR SYSTEMS: AN ELEMENTARY EXAMPLE 272
1 Introduction 272
2 The frozen system 273
3 Equilibrium point and period-2 solutions 273
4 Locally invariant sets 274
5 Behavior of the solutions: technical results 275
6 Behavior of the solutions: interpretation 276
7 References 277
CHAPTER 48. ASYMPTOTIC LINEARIZATION OF UNCERTAIN SYSTEMS BY MEANS OF APPROXIMATE SLIDING MODES 278
INTRODUCTION 278
THE PROPOSED APPROACH FOR MINIMUM PHASE SYSTEMS 279
THE CASE OF UNAVAILABLE OUTPUT DERIVATIVES 280
CONCLUSIONS 281
REFERENCES 281
CHAPTER 49. ON THE BEHAVIOR OF VARIABLE STRUCTURE CONTROL SYSTEMS NEAR THE SLIDING MANIFOLD 284
INTRODUCTION 284
GENERALIZED APPROXIMABILITY 284
CONTROL SYSTEMS FULFILLING GENERALIZED APPROXIMABILITY 285
LINEAR TIME-INVARIANT SYSTEMS 285
REFERENCES 285
ON DISCRETE-TIME SLIDING MODES 288
INTRODUCTION 288
DISCRETE-TIME SLIDING MODE DEFINITION 288
SLIDING MODES SIMULATION 289
DSM CONTROL ALGORITHMS 290
REFERENCES 291
CHAPTER 50. A NEW METHOD FOR SUPPRESSING CHATTERING IN VARIABLE STRUCTURE FEEDBACK CONTROL SYSTEMS 294
INTRODUCTION 294
DESIGN METHOD FOR SLIDING CONTROLLER 294
Properties of a quasi-sliding mode 296
Example 298
Further modification of continuous control law using integral transformation 298
CONCLUSIONS 298
APPENDIX 299
REFERENCES 299
CHAPTER 51. SLIDING OBSERVER DESIGN FOR NONLINEAR STATE ESTIMATION 300
INTRODUCTION 300
DESIGN OF SLIDING OBSERVERS 300
The Main Result for Robust Sliding Observer Design 301
First Design Procedure 301
Second Design Procedure 302
NUMERICAL EXAMPLE 303
CONCLUDING REMARKS 304
REFERENCES 305
CHAPTER 52. TWO CHARACTERIZATIONS OF OPTIMAL TRAJECTORIES FOR MEYER PROBLEM 306
Introduction 306
1 Value function 307
2 Regularity of optimal feedback 308
3 Optimal trajectories and viability theory 308
4 End point constraints 309
References 310
CHAPTER 53. ON THE SOLUTION OF OPTIMIZATION PROBLEMS WITH INCLUSION CONSTRAINTS 312
1. INTRODUCTION AND NOTATIONS 312
2. EXACT PENALIZATION 313
3. APPLICATION TO DYNAMIC PROCESSES 314
CONCLUSION 317
REFERENCES 317
CHAPTER 54. OPTIMAL CONTROL BY POLYNOMIAL APPROXIMATION: THE DISCRETE TIME CASE 318
INTRODUCTION 318
TENSOR BACKGROUND 318
PROBLEM STATEMENT 320
PROBLEM SOLUTION 320
SOLUTION FOR HIGHER ORDER TERMS 322
SPECIAL CASES 323
ACKNOWLEDGEMENTS 323
REFERENCES 323
CHAPTER 55. RELAXATION AND OPTIMAL CONTROL OF NONLINEAR DISTRIBUTED PARAMETER SYSTEMS 324
INTRODUCTION 324
EXISTENCE OF OPTIMAL SOLUTIONS 324
RELAXED SYSTEM 325
NECESSARY CONDITIONS 326
REFERENCES 327
CHAPTER 56. THE DISCRETE MAXIMUM PRINCIPLE: TWO METHODS OF PROOF 328
INTRODUCTION 328
TKE DISCRETE MAXIMUM PRINCIPLE FOR PROBLEMS WITH LIPSCHITZIAN FUNCTIONS 328
VARIATIONAL APPROACH TO THE DISCRETE MAXIMUM PRINCIPLE 331
ALGORITHM BASED ON THE DISCRETE MAXIMUM PRINCIPLE 333
CONCLUSION 334
REFERENCES 334
CHAPTER 57. NECESSARY CONDITIONS FOR OPTIMALITY VIA VOLTERRA APPROXIMATIONS 336
§1 - Introduction 336
§2 - Notations and abstract results 336
§3. Applications 339
References 341
CHAPTER 58. A NOVEL COMPUTER APPROACH TO OPTIMAL FEEDBACK CONTROL OF BILINEAR SYSTEMS 342
INTRODUCTION 342
OPTIMAL CONTROL PROBLEM 342
COMPUTER APPROACH 343
EULERS METHOD OF CONVERGENCE ACCELERATION 344
EXAMPLE 345
DISCUSSIONS AND EXTENSIONS 346
REFERENCES 346
CHAPTER 59. ROBUST NONLINEAR CONTROL AND OBSERVER SCHEMES FOR A CHEMICAL REACTOR 348
INTRODUCTION 348
SLIDING MODES AND THEIR APPLICATION TO 
348 
ATPLI CATION TO A CONTINUOUS STIRRED TANK REACTOR 350
Sliding Observer Design 351
SIMULATION RESULTS 351
CONCLUSIONS 352
APPENDIX A 353
REFERENCES 353
CHAPTER 60. CONTROL OF A CONTINUOUS BIOPROCESS BY SIMPLE ALGORITHMS OF "P" AND"L/A" TYPE 354
NTRODUCTION 354
§1.- BRIEF PRESENTATION OF L/A CONTROL 354
§.2 - A CONTINUOUS BIOPROCESS 356
§.3 - REGULATION OF BIOMASS CONCENTRATION B YFIXED AND ADAPTIVE "P" CONTROLLERS 356
§.4 - REGULATION OF BIOMASS CONCENTRATION BY A MINIMAL L/A CONTROLLER 358
CONCLUSION 359
REFERENCES 359
CHAPTER 61. MODEL PREDICTIVE CONTROL OF NONLINEAR PROCESSES IN THE PRESENCE OF CONSTRAINTS 360
INTRODUCTION 360
THE ALGORITHM 360
SIMULATION RESULTS 361
COMPARISON AND DISCUSSION 362
CONCLUSIONS 362
ACKNOWLEDGEMENTS 362
LITERATURE CITED 362
CHAPTER 62. QUALITATIVE AND CONTROL BEHAVIOR OF A CLASS OF CHEMICAL AND BIOLOGICAL SYSTEMS 366
INTRODUCTION 366
PROBLEM FORMULATION 366
QUALITATIVE BEHAVIOR 367
CONTROLLABILITY AND STABILIZABILITY 368
REFERENCES 369
CHAPTER 63. NONLINEAR PROCESS CONTROL: AN ADAPTIVE APPROACH WHICH USES PHYSICAL MODELS 372
INTRODUCTION 372
CONTROLLING THE CSTR 373
THE EFFECT OF MISMATCH AND IMPLEMENTATION ISSUES 375
REFERENCES: 376

376 
NOMENCLATURE 
377 
CHAPTER 65. THE DESIGN OF LINEARIZING OUTPUTS FOR INDUCTION MOTORS 378
Introduction 378
Induction motor model 378
Full lineariza 
379 
Input - output linearization via dynamic feedback 380
Conclusions 382
References 382
CHAPTER 66. THE RADIO-FREQUENCY MAGNETIC FIELD DESIGN IN BIOMEDICINE:NUCLEAR MAGNETIC RESONANCE IMAGING 384
1 - INTRODUCTION 384
2 - THE BASIC EOUATIONS 384
3 - THE LIE ALGEBRAT STRUCTURE OF THE EQUATION 385
4 - THE DESIGN OF THE COMMAND 385
5- CONCLUSION 387
Appendix 387
References 387
CHAPTER 67. MODELLING AND CONTROL OF A TWO-AXIS ROBOT WITH FLEXIBLE LINKS 388
INTRODUCTION 388
THE MODEL 388
CONTINUOUS-TIME CONTROL 389
CONCLUSION 392
REFERENCES 392
APPENDIX I 393
APPENDIX II 393
CHAPTER 68. SLIDING OBSERVERS FOR ROBOT MANIPULATORS 394
1. INTRODUCTION 394
2. PROBLEM FORMULATION 394
3. OBSERVER DESIGN 396
4. DESIGN SIMPLIFICATIONS 398
5. CONCLUSIONS 399
6. REFERENCES 
399 
CHAPTER 69. NONLINEAR CONTROLLER DESIGN FOR FLIGHT CONTROL SYSTEMS 400
Introduction 400
I .Modeling of Aircraft Dynamics 400
II . Linearization by State Feedback 401
III. A Formal Approach to the Controlof Slightly Non-minimum PhaseSystems 404
Conclusion 405
References 405
CHAPTER 70. LYAPUNOV DESIGN FOR ADAPTIVE CONTROL OF ROBOTS 406
INTRODUCTION 406
PROBLEM STATEMENT 406
CONCLUSIONS 410
APPENDIX — PROOF OF LEMMA 1 410
REFERENCES 411
CHAPTER 71. NONLINEAR IDENTIFICATION ANDOBSERVER BASED COMPENSATION OF FRICTION IN MECHANICAL SYSTEMS 412
1. INTRODUCTION 412
2. MODELING AND IDENTIFICATION OF THE PROCESS DYNAMICS 412
3. DESIGN OF A LINEAR AND NONLINEAR FRICTION OBSERVER 414
4. Compensation of the estimated friction 415
5. EXAMPLE 416
6. CONCLUSIONS 417
7. REFERENCES 417
CHAPTER 72. DESIGN OF NONLINEAR OBSERVERS FOR ELASTIC JOINT ROBOTS 418
INTRODUCTION 418
MANIPULATOR MODEL 418
OBSERVER DESIGN 420
APPLICATION TO A THREE LINK ROBOT 422
CONCLUSIONS 423
REFERENCES 423
AUTHOR INDEX 424
KEYWORD INDEX 426
SYMPOSIA VOLUMES 428

Produkt-Details

• Erscheint lt. Verlag: 23.5.2014
• Sprache: englisch
• Themenwelt: Technik ► Bauwesen
• Themenwelt: Technik ► Elektrotechnik / Energietechnik
• Themenwelt: Technik ► Maschinenbau
• ISBN-10: 1-4832-9892-2 / 1483298922
• ISBN-13: 978-1-4832-9892-4 / 9781483298924