Automatic Control 1990 (eBook)

Front Cover 1
Automatic Control in Aerospace · Robust Control Nonlinear Control · Control Applications of Optimization Distributed Parameter Systems Theory of Discrete Event Systems 4
Copyright Page 5
Table of Contents 8
SUBJECT AREAS 7
PART I: AUTOMATIC CONTROL IN AEROSPACE 14
CHAPTER 1. SPACE AND DEEP SPACE ENVIRONMENT 14
1. WHAT IS SPACE ? 14
2. THE ATMOSPHERE 14
3. THE STRATOSPHERE 16
4. COMMON CHARACTERISTICS OF "SPACE" 16
5. SOME SPECIFIC ENVIRONMENTS 17
6. THE ATOMIC OXYGEN PROBLEM [10] 18
7. THE DEBRIS PROBLEMS 18
8. CONCLUSIONS 19
REFERENCES 19
CHAPTER 2. COMPUTER SIMULATION OF THE MIR ORBITAL STATION ATTITUDE CONTROL BY MEANS OF GYRODINES 24
INTRODUCTION 24
COORDINATE SYSTEMS 24
EXTERNAL TORQUES 25
MODELLING THE MAINTENANCE OF THE CONSTANT STATION ORIENTATION 25
MODELLING OF THE STATION ROTATION IN THE INERTIAL COORDINATE SYSTEM 25
REFERENCES 28
CHAPTER 3. PASSIVE ATTITUDE CONTROL OF SPACE STATION FREEDOM ALTERNATIVE ASSEMBLY CONFIGURATIONS 30
INTRODUCTION 30
MAGNETIC DAMPER OPERATION 30
MAGNETIC DAMPER TORQUE 31
DAMPER SIZE 32
EARTH'S MAGNETIC FIELD MODEL 32
INTERACTION BETWEEN THE VEHICLE AND DAMPER 33
SPASIS 33
PERFORMANCE ANALYSIS 33
RESULTS 33
CONCLUSION 34
REFERENCES 34
CHAPTER 4. IDENTIFICATION AND CONTROL EXPERIMENTS FOR A LARGE SPACE STRUCTURE 36
Introduction 36
Identification of modal parameters 36
Control system designs 38
Experiments 39
Conclusion 40
References 40
CHAPTER 5. MISSION CONTROL CONCEPTS FOR THE SATELLITES OF TOMORROW 42
Historical Background 42
On-board Software Functions 43
Mission Information Management 45
Mission Planning 46
Telemetry Analysis and Fault Management 47
Support for On-board Autonomy 47
CONCLUSIONS 47
REFERENCES 47
CHAPTER 6. ADVANCED X-RAY ASTROPHYSICS FACILITY 48
INTRODUCTION 48
OBJECTIVES 48
SPACECRAFT 48
HIGH RESOLUTION MIRROR ASSEMBLY (HRMA) 50
SCIENCE INSTRUMENTATION 52
CONCLUSIONS 53
REFERENCES 53
CHAPTER 7. DATA TRANSMISSION BETWEEN PLANESAND CONTROL CENTERS 54
1. STATEMENT OF THE PROBLEM 54
2. THE PRESENT STATE(1989) AND THE NEXT FUTURE 55
3. DEFICIENCIES OF THE PRESENTSITUATION 55
4. THE CNS-ATM CONCEPT 56
5. CONCLUSION AND OPENING OF THEDISCUSSION 56
CHAPTER 10. EXAMINATION OF A LONGITUDINAL LAW USING THE EIGENVECTOR METHOD ALLOWING THRUST/PITCH DECOUPLING 74
INTRODUCTION 74
AIRCRAFT MODEL AND FLY BY WIRE PITCH CONTROL OBJECTIVES 74
RESULTS 78
CONCLUSION 80
CHAPTER 11. ROBUST ANALYSIS OF HANDLING QUALITIES IN AEROSPACE SYSTEMS 82
INTRODUCTION 82
FLIGHT MECHANICS AND DEFINITIONS 83
ROBUST STABILITY TEST 84
SIMULATION RESULTS 86
CONCLUSIONS 87
REFERENCES 87
CHAPTER 12. ROBUSTLY STABLE, DISCRETE-TIME, ADAPTIVE FLIGHT CONTROL USING THE EULER OPERATOR 88
INTRODUCTION 88
DISCRETE-TIME SYSTEM REPRESENTATION 88
ROBUST ADAPTIVE FLIGHT CONTROLLER 90
SIMULATION STUDIES 91
Acknowledgments 92
REFERENCES 92
CHAPTER 13. NONLINEAR MULTI-POINT MODELING AND PARAMETER ESTIMATION OF DO 28 RESEARCH AIRCRAFT1 94
INTRODUCTION 94
NONLINEAR MULTI-POINT AIRCRAFT MODEL 94
MULTI-STAGE IDENTIFICATION METHOD 96
ESTIMATION RESULTS 97
CONCLUSION 97
REFERENCES 98
CHAPTER 14. OPTIMAL PERIODIC TRAJECTORIES OF AIRCRAFT WITH SINGULAR CONTROL 100
Nomenclature 100
Introduction 100
Problem Formulation 101
Optimality Conditions 101
Optimal Trajectories with Singular Control 102
Flight Mechanics Considerations 103
Conclusions 103
References 103
CHAPTER 15. OPTIMIZATION OF CONTROL OF SPACE INVESTIGATIONS IN "GAMMA" PROJECT 106
INTRODUCTION 106
SCIENTIFIC EQUIPMENT AND PROGRAM INVESTIGATIONS 106
OPERATION MODE OF THE MODULEELECTRIC POWER AND GYRODYNE SYSTEM 107
OPTIMIZATION OF PROGRAM OF INVESTIGATIONS 108
EXAMPLE OF OBSERVATION PROGRAM 109
OPERATIONAL CONTROL 110
CONCLUSION 110
REFERENCES 110
CHAPTER 16. ATTITUDE CONTROL SYSTEM OF THE X-RAY OBSERVATORY ASTRO-D 112
INTRODUCTION 112
SYSTEM DESCRIPTION 113
INITIAL ATTITUDE ACQUISITION 113
ONBOARD ATTITUDE DETERMINATION 114
ATTITUDE CONTROL 114
CONTINGENCY STRATEGY FOR ATTITUDE ANOMALY 115
CONCLUSION 115
REFERENCES 116
CHAPTER 17. ROBUSTNESS ANALYSIS AND DESIGN FOR AIRCRAFT LATERAL CONTROL SYSTEM 120
INTRODUCTION 120
SYSTEM DESCRIPTION 120
RFN DESIGN METHOD 121
NUNERICAL SOLUTION 121
CONCLUSION 123
REFERENCES 123
CHAPTER 18. NAVIGATION AND GUIDANCE PROBLEMS OF JAPANESE SPACE VLBI SATELLITE-VSOP 124
I. Introduction 124
II. Satellite System Configuration 125
III. Tlracking Orbit Determination and Clock Transfer 126
IV. Technical Innovations of VSOP 128
V. Guidance Problems in VSOP 128
VI. Conclusion 129
References 129
PART II: ROBUST CONTROL 130
CHAPTER 19. A TUTORIAL ON LOOP SHAPING USING H-INFINITY ROBUST STABILIZATION 130
1 Introduction 130
2 Problem Formulation 131
3 Problem Motivation 132
4 Problem Solution 135
5 Loop Shaping Design Procedure(LSDP) 135
References 138
CHAPTER 20. WEIGHTING FUNCTION SELECTION IN H8 DESIGN 140
INTRODUCTION 140
DISTURBANCE REJECTION 140
TRACKING 141
CONSTRAINED OPTIMIZATION 141
CHOICE OF WEIGHTS 142
A DESIGN EXAMPLE 144
CONCLUSIONS 144
REFERENCES 145
CHAPTER 21. A DEGREE BOUND OF THE H8-OPTIMALSOLUTIONS OF THE ROBUST REGULATOR PROBLEM 146
Abstract 146
1 Introduction 146
Nomenclatures 147
2 Preliminaries 147
3 Main Results 148
4 An Example 150
5 Conclusion 151
Reference 151
CHAPTER 22. ROBUST CONTROL OF UNCERTAIN SYSTEMS BY DECENTRALIZED CONTROL 152
INTRODUCTION 152
CONTROLLER DESIGN AND PERFORMANCE BOUNDS 153
CHARACTERIZATION OF FAMILIES OF CENTRALIZED H8 CONTROLLERS 156
CONCLUSION 157
REFERENCES 157
ACKNOWLEDGEMENTS 157
CHAPTER 23. PROGRESS IN THE POLYNOMIAL SOLUTION OF THE STANDARD H8 OPTIMAL CONTROL PROBLEM 158
1 INTRODUCTION 158
2 PARAMETRIZATION OF THE CLOSED-LOOP TRANSFER MATRIX 158
3 EQUALIZING COMPENSATORS 160
4 STRUCTURED EQUATIONS AND ASYMPTOTIC ANALYSIS 161
5 SOLUTION OF THE OPTIMIZATION PROBLEM 162
6 EXAMPLE 163
7 CONCLUSIONS 164
REFERENCES 164
CHAPTER 24. THE DISTANCE FROM STABILITY OR G-STABILITY BOUNDARIES 166
1 Introduction 166
2 A simple example 166
3 The largest hypersphere in parameter space 168
4 The extension to other eigenvalue regions 169
5 Example 169
6 Concluding remarks 170
CHAPTER 25. STABILIZABILITY OF UNCERTAIN DYNAMICAL SYSTEMS: THE CONTINUOUS AND THE DISCRETE CASE 172
INTRODUCTION 172
STABILIZABILITY — AN ALGORITHM 172
UNCERTAIN DISCRETE SYSTEMS 175
SOME NUMERICAL RESULTS 176
CONCLUSIONS 177
REFERENCES 177
CHAPTER 26. ROBUST CONTROLLER DESIGN FOR UNCERTAIN LINEAR TIME INVARIANT SISO PLANTS 178
INTRODUCTION 178
PRELIMINARIES 178
LINEAR PARAMETRIZATION OF ALL STABILIZING COMPENSATORS OF MAXIMUM ORDER v 179
ROBUST D-STABILITY TEST 180
ROBUST CONTROLLER DESIGN 181
EXAMPLE 182
CONCLUSIONS 183
REFERENCES 183
CHAPTER 27. FUTURE DIRECTIONS IN H8 ROBUST CONTROL THEORY 184
Abstract 184
1 Introduction 184
2 The Robust Control Problem 185
3 Some Future Research Directions 185
4 Conclusion 186
References 187
CHAPTER 28. CHARACTERIZATION OF ALL SOLUTIONS TO THE "STANDARD" H8 OPTIMALCONTROL PROBLEM 190
1 Introduction 190
2 ... optimal equalizing solutions 190
3 Parametrization and lowerbounds 191
4 All H8-optimal solutions 193
5 A worked example 193
6 Conclusion 195
References 195
CHAPTER 29. MIMIMAX CONTROLLERS FOR LTI PLANTS UNDER I1-BOUNDED DISTURBANCES 196
1. INTRODUCTION 196
2. TIME-DOMAIN FORMULATION FOR A DISTURBANCE ATTENUATION PROBLEM 197
3. A SATURATION-TYPE MINIMAX CONTROLLER 198
4. DISTURBANCE ATTENUATION WITH NONZEROINITIAL STATE 200
5. DISCUSSION AND CONCLUDING REMARKS 201
REFERENCES 201
ACKNOWLEDGEMENT 202
CHAPTER 30. LOW-ORDER ROBUST MODEL MATCHING CONTROLLER DESIGN FOR SISO PLANTS 204
1. INTRODUCTION 204
2. PROBLEM STATEMENT 204
3. CONTROLLER DESIGN 205
4. ROBUSTNESS 206
5. DESIGN PROCEDURES 208
6. AN EXAMPLE AND SIMULATION RESULTS 209
7. CONCLUSION 209
REFERENCES 209
CHAPTER 31. ROBUSTNESS OF DISCRETE SYSTEMS:A REVIEW 210
I INTRODUCTION 210
II. BACKGROUND MATERIAL 210
III. DISCRETE ANALOG AND COUNTERPART OF KHARITONOV'S THEOREM 211
IV. DISCRETE ASPECTS OF THE EDGE THEOREM 213
V. CONCLUSION AND OPEN PROBLEMS 213
VI. BIBLIOGRAPHY 214
ACKNOWLEDGEMENT 215
CHAPTER 32. STABILITY ROBUSTNESS OF PLANT-CONTROLLER FAMILIES 216
INTRODUCTION 216
PROBLEM FORMULATION 216
PRELIMINARY PROPOSITIONS 217
THE MAIN RESULTS 217
CONCLUSIONS 218
REFERENCES 218
APPENDIX A: Proof of Proposition 3.3 218
CHAPTER 33. ROBUSTNESS OF SAMPLED-DATA CONTROL SYSTEMS WITH UNCERTAIN PHYSICAL PLANT PARAMETERS 220
INTRODUCTION 220
IS THE SAMPLING INTERVAL AN ADDITIONAL PARAMETER? 221
STABILITY BOUNDARIES OF CONTINUOUS AND SAMPLED SYSTEMS IN A SCALED PARAMETER SPACE 223
CONCLUSIONS 225
ACKNOWLEDGEMENT 225
REFERENCES 225
CHAPTER 34. INTERVAL STABILITY OF TIME-DELAY SYSTEMS 226
INTRODUCTION 226
INTERVAL STABILITY WITH RESPECT TO GAIN 226
INTERVAL STABILITY WITH RESPECT TO DELAY 228
CONCLUDING REMARKS 230
REFERENCES 230
APPENDIX 230
CHAPTER 35. A PARAMETERIZATION OF ALL DECENTRALIZED STABILIZERS AND ITSAPPLICATIONS IN DECENTRALIZED CONTROL SYSTEMS 232
I. INTRODUCTION 232
II. D-COPRIME FACTORIZATION AND D-UNIMODULAR 232
III . PARAMETERIZATION OF ALL DECENTRALLY STABILIZING CONTROLLER 234
IV . SIMULTANEOUS STABILIZATION AND ROBUST STABILIZATION IN DECENTRALIZED SYSTEMS 235
V. CONCLUSION 236
REFERENCES 236
CHAPTER 36. ROBUST ABSOLUTE STABILITY OF LUR'E CONTROL SYSTEMS IN PARAMETER SPACE 238
1. INTRODUCTION 238
2. PROBLEM FORMULATION AND BASIC RESULTS 239
3. ROBUST STABILITY AGAINST SCALAR PERTURBATIONS 240
4. ROBUST ABSOLUTE STABILITY FOR PLANAR UNCERTAINTY SETS 241
5. NUMERICAL EXAMPLES 242
6. CONCLUSIONS 243
REFERENCES 243
CHAPTER 37. ANALYTICAL DESIGN OF PREDICTIVE CONTROL FOR A CLASS OF INDUSTRIAL PROCESSES 244
INTRODUCTION 244
GENERALIZED DYNAMIC MATRIX CONTROL 244
PERFORMANCE ANALYSIS OF GDMC INIMC STRUCTURE 245
GDMC ANALYSIS FOR A CLASS OF INDUSTRIAL PROCESSES 246
COMPUTER-AIDED DESIGN OF GDMC SYSTEM FOR TYPICAL PROCESSE 247
SIMULATION EXAMPLE 248
CONCLUSION 248
REFERENCES 248
CHAPTER 38. VARIOUS UNITARY BASED ROBUSTNESS STUDIES ON MULTIVARIABLE SYSTEMS WITH TUNING CONTROLLERS 250
INTRODUCTION 250
PRINCIPLE OF ANALYSIS 250
AN ILLUSTRATIVE EXAMPLE 251
ROBUSTNESS STUDIES 252
CONCLUSIONS 254
REFERENCES 254
CHAPTER 39. DESIGN OF DISCRETE TIME REPETITIVE CONTROLLERS WITH APPLICATIONS TO MECHANICAL SYSTEMS 256
INTRODUCTION 256
INTERNAL MODEL BASED DISCRETE-TIMEREPETITIVE CONTROLLERS 256
ROBUSTNESS OF PROTOTYPE REPETITIVE CONTROL SYSTEMS 257
EXTERNAL MODEL BASED DISCRETE-TIME REPETITIVE CONTROLLER 258
CONCLUSIONS 261
REFERENCES 261
CHAPTER 40. MODEL BASED PREDICTIVE CONTROL OF EXOTIC SYSTEMS 262
INTRODUCTION 262
THE PPC TECHNIQUE 263
CONTROL STRATEGY FOR UNSTABLE SYSTBC5 264
CONTROL OF FLEXIBLE SYSTEMS 266
CONCLUSION 268
References 268
CHAPTER 41. H8/LTR PROCEDURE WITH SPECIFIED DEGREE OF RECOVERY 270
INTRODUCTION 270
PROBLEM FORMULATION II < MINIMAL ORDER OBSERVER>
SOLUTION OF H8 OPTIMAL CONTROL PROBLEM 272
SOLUTION OF PROBLEMS I AND II 273
COMPARISON WITH LQG/LTR PROCEDURE 273
NUMERICAL EXAMPLE 274
REFERENCES 274
CHAPTER 42. OPTIMIZATION BASED ROBUST DESIGN OF UNCERTAIN SISO SYSTEMS 276
1. Introduction 276
2. System Description 276
3. Controller and Closed Loop 277
4. Design of Feedback 277
5. Optimization Issues 279
6· Design of Feedforward 280
7. Examples 280
8. Conclusions 281
PART III: NONLINEAR CONTROL 282
CHAPTER 43. NONLINEAR CRONEKKER'S CHARACTERISTICS AND ITS APPLICATION 282
INTRODUCTION 282
THE CRONECKER CHARACTERISTIC 282
CONTROLLABILITY 283
STABILIZABILITY 284
REFERENCES 285
CHAPTER 44. GEOMETRIC THEORY OF DYNAMIC SYSTEMS WITH CONTROL 286
INTRODUCTION 286
BASIC NOTIONS OF CDS PHASE PORTRAIT METHOD 286
APPLICATION OF THE POLIATION TECHNIQUE TO CDS DECOMPOSITION 287
SINGULAR SETS OF THE CDS PHASE PORTRAIT ON THE PLANE 289
NOETHER THEOREM AMD INVARIANCE OF THE CDS PHASE PORTRAIT 291
REFERENCES 293
CHAPTER 45. IDENTIFIABILITY FOR NONLINEAR MULTIVARIABLE SYSTEMS IN OUTPUT INJECTION FORM 294
INTRODUCTION 294
OUTPUT INJECTION SYSTEMS 295
IDENTIFIABILITY FOR OUTPUT INJECTION SYSTEM 296
CONCLUSIONS 299
REFERENCES 299
CHAPTER 46. INPUT-OUTPUT DECOUPLING AND LINEARIZATION VIA RESTRICTED STATIC-STATE FEEDBACK 300
INTRODUCTION 300
FORMULATION OF THE PROBLEM AND NOTATIONS 300
MAIN RESULTS 302
EXAMPLES 304
CONCLUSION 304
ACKNOWLEDGEMENT 305
REFERENCES 305
CHAPTER 47. NEW IMPROVED CRITERIA OF ABSOLUTE STABILITY FOR NONLINEAR DYNAMICALSYSTEMS 306
INTRODUCTION 306
MAIN RESULTS 306
EXAMPLES 308
CONCLUSIONS 308
REFERENCES 309
APPENDIX 309
CHAPTER 48. ROBUST STABILITY AGAINST STRUCTURED AND UNSTRUCTURED PERTURBATIONS: NEW RESULTS 312
1.INTRODUCTION 312
2. PRELIMINARIES 313
3. ON STRICT POSITIVE REALNESS OF INTERVAL PLANTS 314
4. EXTENSION OF THE SMALL GAIN THEOREM TO INTERVAL PLANTS 315
5. CONCLUDING REMARKS 316
6. REFERENCES 316
CHAPTER 49. SAMPLE RATE SELECTION FOR DISCRETE TIME SWITCHING CONTROLS 318
BACKGROUND AND MOTIVATION 318
ANALYSIS 318
EXTENSION TO NONLINEAR SYSTEMS 320
APPLICATION TO DUAL-MODE CONTROLS 321
EXAMPLE 3 321
REFERENCES 321
CHAPTER 50. THE NEW RESULTS IN THE THEORY OF PERIODIC OSCILLATION IN NONLINEAR CONTROL SYSTEMS 324
1. THE EXISTENCE OF SELF-EXITING OSCILLATIONS 324
2. SYSTEMS WITH HYSTERESIS 325
3. HYSTERESIS WITH VARIABLE CHARACTERISTICS 325
4. SELF-OSCILLATIONS IN SYSTEMS WITH HYSTERESIS 326
5. THE ESTIMATE OF THE NUMBER OF CYCLES 326
6. ON FORCED OSCILLATIONS 327
7. COLLOCATIONS METHOD IN PROBLEMS OF PERIODICOSCILLATIONS 328
REFERENCES 329
CHAPTER 51. PARAMETRIZATION OF NONLINEAR MODEL STRUCTURES AS LINEAR REGRESSIONS 330
1. INTRODUCTION 330
2. MODEL SET 330
3. SOME DIFFERENTIAL ALGEBRAIC FACTS 331
4. PROBLEM FORMULATION 332
5. MAIN RESULTS 332
6. EXAMPLES 333
7. CONCLUSIONS 333
8. ACKNOWLEDGEMENTS 333
REFERENCES. 333
CHAPTER 52. STRONG INVARIANT SETS AND STABILITY OF POSITIONAL STRATEGIES IN (M,N)GAME ENCOUNTER PROBLEMS 336
INTRODUCTION 336
STRONG INVARIANT SETS 336
THE STABILITY OF POSITIONAL STRATEGIES 337
CONCLUSION 338
REFERENCES 338
CHAPTER 53. DESIGN OF NONLINEAR CONTROLLERS FOR NONLINEAR PLANTS 340
INTRODUCTION 340
DESIGN PROCEDURE 340
INVERSE DESCRIBING FUNCTION 340
DESCRIPTION OF DESIGN METHODS 341
EXAMPLES 342
CONCLUSION 343
References 343
CHAPTER 54. STABILITY AND DESIGN OF SINGLE LOOPSTATE CONTROL SYSTEMS WITH ACTUATOR SATURATIONS 348
THE PROBLEM 348
THE CONTROL SYSTEM 348
NONLINEAR STABILITY ANALYSIS 351
QUANTITATIVE EXAMPLES 353
CONCLUSIONS 356
REFERENCES 356
CHAPTER 55. INTEGRAL INDICES OF DYNAMIC SYSTEM STATE AND THEIR APPLICATION 358
INTRODUCTION 358
INTEGRAL INDICES IN STABILIZATION PROBLEM 359
MANUAL CONTROL 361
AUTONOMOUS CONTROL OF INTEGRAL INDICES 362
DISCUSSION 362
REFERENCES 363
CHAPTER 56. STABILIZATION OF A CLASS OF NONLINEAR SYSTEMS BY OUTPUT FEEDBACK 364
I. INTRODUCTION 364
II. PROBLEM FORMULATION AND MATHEMATICAL PRELIMINARIES 364
III. SOLUTION OF THE OUTPUT STABILIZING CONTROL LAWS 365
IV. AN EXAMPLE 367
REFERENCES 368
CHAPTER 57. A GENERAL METHODOLOGY FOR BILINEAR SYSTEM STABILITY WITH OUTPUT FEEDBACK 370
INTRODUCTION 370
NOTATION AND PRELIMINARIES 370
CONTINUOUS BILINEAR SYSTEM 371
DISCRETE BILINEAR SYSTEM 372
REFERENCES 373
CHAPTER 58. NONLINEAR OBSERVERS FOR FLEXIBLE ROBOTS 374
INTRODUCTION 374
EXACT OBSERVER DESIGN 375
APPROXIMATE OBSERVER DESIGN 376
CONCLUSIONS 378
ACKNOWLEDGEMENT 379
REFERENCES 379
CHAPTER 59. MODELING AND SLIDING MODE TEMPERATURE CONTROL OF A SEMI-BATCH POLYMERIZATION REACTOR IMPLEMENTED AT THE MIXER 380
INTRODUCTION 380
NOMENCLATURE 380
MODELING OF A SEMI-BATCH POLYMERIZATION REACTOR 381
SLIDING MODE TEMPERATÜRE CONTROL 383
RESULTS OF EXPERIMENT 385
CONCLUSIONS 385
REFERENCES 385
CHAPTER 60. CHAOS FROM PWM ELECTROHYDRAULIC SERVO 386
INTRODUCTION 386
SUFFICIENT CONDITIONS FOR THE EXISTENCE OF CHAOS 387
SBR ON PWM ELECTROHIDRAULIC SERVO 388
CONCLUSIONS 389
REFERENCES 390
APPENDIX 390
CHAPTER 61. STABILIZATION OF A CHAOTIC PREDATORPREY SYSTEM CONSIDERING FRACTAL BOUNDARIES 392
1. INTRODUCTION 392
2. CONTROL SCHEME FOR STABILIZATION 393
3. FRACTAL BOUNDARY OF AN INVARIANT DOMAIN 394
4. NUMERICAL EXPERIMENTS 396
5. CONCLUSIONS 397
REFERENCES 397
PART IV: CONTROL APPLICATIONS OF OPTIMIZATION 398
CHAPTER 62. A GENERAL APPROACH TO THE CONSTRUCTION OF ALGORITHMS OF OPTIMIZATION OF NONLINEAR CONTROL SYSTEMS WITH NONSMOOTH CHARACTERISTICS 398
I.NONLINEAR PROGRAMMING 398
2,NONSMOOTH NETWORK PROBLEMS 400
3.NONSMOOTH PIECE-WISE LINEAR PROBLEMS 400
4.REGULARLY AND SINGULARLY PERTURBED SYSTEM 400
5. THE AVERAGING METHOD 402
Conclusion 402
REFERENCES 403
CHAPTER 63. DECOMPOSITION OF DYNAMIC PROGRAMMING BY NONLINEAR PROGRAMMING AND PARALLEL PROCESSING 404
INTRODUCTION 404
GENERALIZED TIME INTERVAL ITERATION TECHNIQUE 405
CONVERGENCE OF THE ALGORITHM 406
MULTICRITERIA OPTIMIZATION 408
REFERENCES 409
CHAPTER 64. THE SUPERLINEAR CONVERGENCE OF SUCCESSIVE QUADRATIC PROGRAMMING ALGORITHMS 410
INTRODUCTION 410
Q - SUPERLINEAR RATE CONDITIONS 412
CONCLUDING REMARKS 415
ACKNOWLEDGEMENT 415
REFERENCES 415
CHAPTER 65. SOFTWARE TOOLS FOR NONLINEAR PROGRAMMING 416
INTRODUCTION 416
CLASSES OF SOLVABLE PROBLEMS AND OPTIMIZATION METHODS USED 416
STRUCTURE OF THE PACKAGE 418
USER INTERFACE 419
CONCLUSION 419
REFERENCES 420
CHAPTER 66. COMPUTATIONAL SINGULAR PERTURBATION METHOD FOR DYNAMIC SYSTEMS 422
INTRODUCTION 422
TRANSFORMATION OF DYNAMIC SYSTEMS 422
COMPUTATIONAL SINGULAR PERTURBATIONALGORITHM 424
EXAMPLES 425
CONCLUDING REMARKS 425
References 426
CHAPTER 67. GEOMETRICAL THEORY OF SINGULARLY PERTURBED CONTROL SYSTEMS 428
INTRODUCTION 428
OPTIMAL LINEAR STATE REGULATOR 428
TEMPERATURE FIELD CONTROL 430
NONLINEAR OPTIMAL CONTROL 430
SINGULAR SINGULARLY PERTURBED SYSTEMS 431
CHEAP CONTROL 431
FILTERING OF GYROSCOPIC SYSTEMS 431
HIGH-GAIN SYSTEM 432
CONCLUSION 432
REFERENCES 433
CHAPTER 68. SOME COMPUTATIONAL ASPECTS OF THE PERTURBATION THEORY IN OPTIMIZATION PROBLEMS 434
INTRODUCTION 434
DEGESNERCY, SINGULARITY AND QUASIAGGREGATABLE PROGRAMS · 434
UNCONTRAINED QUASIAGGREGATABLES PROBLEM AND "VALLEY EFFECT" 435
CONCLUSION 438
REFERENCES 438
CHAPTER 69. NEAR-OPTIMAL INCENTIVE STACKELBERG STRATEGIES FOR SINGULARLY PERTURBED SYSTEMS 440
INTRODUCTION 440
PROBLEM FORMULATION 440
COMPOSITE TEAM SOLUTIONS 441
CONSTRUCTION OF THE NEAR-OPTIMAL INCENTIVE STRATEGY 442
CONCLUSION 444
REFERENCES 444
CHAPTER 70. TEAM DIFFERENTIAL GAMES 446
INTRODUCTION 446
ONE-VERSUS-TWO TWO-STAGE TEAM DIFFERENTIAL GAMES 446
MULTI-PERSON TWO-TEAM DIFFERENTIAL GAMES 449
EXAMPLES 449
CONCLUSION 450
REFERENCES 450
CHAPTER 71. A COMPARISON OF CONSTRAINED OPTIMAL CONTROL ALGORITHMS 452
INTRODUCTION 452
IMPLEMENTED ALGORITHMS 453
GENERAL REMARKS 454
STATE INEQUALITY CONSTRAINT 454
BANG-BANG CONTROL PROBLEM 456
FIXED FINAL STATES PROBLEM 457
CONCLUSIONS 459
ACKNOWLEDGEMENT 459
REFERENCES 459
CHAPTER 72. PERIODIC ARMA MODELS: OPTIMAL PREDICTION AND MINIMUM-PHASE CONDITION 462
INTRODUCTION 462
PRELIMINARIES 463
CONCLUDING REMARKS 467
ACKNOWLEDGEMENT. 467
REFERENCES 467
CHAPTER 73. AN ALGORITHM AND A PROGRAM FOR SOLVING LINEAR NON-STATIONARY OPTIMAL CONTROL PROBLEMS 468
INTRODUCTION 468
PROBLEM STATEMENT 468
ALGORITHM 469
NUMERICAL EXPERIMENT 469
CONCLUSION 470
REFERENCES 471
PART V: DISTRIBUTED PARAMETER SYSTEMS 472
CHAPTER 74. POLE ASSIGNMENT OF DISTRIBUTED PARAMETER SYSTEMS 472
§1. INTRODUCTION 472
§2 ASSIGNMENT OF FINITELY MANY EIGENVALUES 472
§3 ASSIGNMENT OF INFINITELY MANY EIGENVALUES 474
§4 EXAMPLE 476
REFERENCES 477
CHAPTER 75. ITERATIVE PROCESSES IN OPTIMIZATION OF SEMILINEAR HYPERBOLIC SYSTEMS 478
INTRODUCTION 478
MAXIMUM PRINCIPLE 480
ITERATIVE METHODS 481
CONCLUSIONS 482
REFERENCES 482
CHAPTER 76. IDENTIFICATION OF SYSTEM PARAMETERSIN DISTRIBUTED PARAMETER SYSTEMS 484
INTRODUCTION 484
PROBLEM OF SYSTEM PARAMETER IDENTIFICATION 484
LINEAR INTEGRAL FILTER AND ITS EXTENSION 485
IDENTIFICATION IN THE NOISE-FREE CASE 486
IDENTIFICATION IN THE NOISY CASE 487
CONCLUDING REMARKS 489
CHAPTER 77. TRANSIENT FLOW CONTROL IN OPEN CHANNELS BY DISCRETE TIME LQR METHODS 490
1. INTRODUCTION 490
2. OPEN CHANNEL TRANSIENT MODELS 490
3. WAVE EQUATION DYNAMICS 491
4. REGULATION 492
5. EXAMPLE APPLICATION 493
6. CONCLUSIONS 494
REFERENCES 495
PART VI: THEORY OF DISCRETE EVENT SYSTEMS 496
CHAPTER 78. ALGEBRAIC CHARACTERISTICS AND STRUCTURE DECOMPOSITION FOR "LINEAR" DISCRETE EVENT DYNAMICSY STEMS 496
INTRODUCTION 496
SYSTEMS AND MODELS 496
ESTIMATION AND DETERMINATION OF EIGENVALUE AND EIGENVECTOR BY USING OUTPUT DATA 499
CONCLUSION 501
ACKNOWLEDGMENT 501
REFERENCES 501
CHAPTER 79. OPTIMAL CONTROL OF ASYNCHRONOUS DISCRETE EVENT SYSTEMS 502
1. INTRODUCTION 502
2. MULTICRITERIA OPTIMIZATION PROBLEM STATEMENT 503
3. QUALITATIVE PREFERENCE STRUCTURE IN THE SETS OF STATES AND TRAJECTORIES 504
4. AGGREGATED OPTIMAL CONTROL PROBLEM FORMULATION AND SOLUTION 504
CONCLUSIONS 508
REFERENCES 508
CHAPTER 80. SOME RESULTS ON NEAR-COMPLETE DECOMPOSABILITY OF DISCRETE EVENT SYSTEMS 510
INTRODUCTION 510
MODELLING AND ANALYSIS 511
SOLUTION TO THE SYSTEM 512
REFERENCE 512
CHAPTER 81. ON-LINE CONTROL OF DISCRETE EVENT SYSTEMS: SOME EXTENSIONS OF PERTURBATION ANALYSIS 514
INTRODUCTION 514
ON-LINE STOCHASTIC GRADIENT ESTIMATORS 514
CONSTRUCTION OF DEDS SAMPLE PATHS 515
PERTURBATION ANALYSIS WITH RESCHEDULING 516
CONCLUSIONS AND FUTURE WORK 518
REFERENCES 518
CHAPTER 82. FINITE AUTOMATA ON PARTIALLY ORDERED SETS 520
INTRODUCTION 520
0-SETS 520
0-FUNCTIONS 520
0-AUTOMATA 521
CONCLUSION 522
REFERENCES 522
CHAPTER 83. ANALYSIS AND SYNTHESIS OF DISCRETE-EVENT DISTRIBUTED SYSTEMS USING PETRI-NETS 524
INTRODUCTION 524
PETRI-NETS 525
DERIVATION OF THE CONTROL TASKS 526
MODIFICATION OF THE NET 527
CONCLUSIONS 528
REFERENCES 529
SYMBOLS 529
CHAPTER 84. OPTIMAL SCHEDULING FOR LINEAR AND NONLINEAR DYNAMIC PROCESSES 530
INTRODUCTION 530
LINEAR SCHEDULING PROBLEMS 530
NONLINEAR SCHEDULING PROBLEMS 532
EXAMPLE 532
REFERENCES 534
CHAPTER 85. DISCRETE EVENT SYSTEMS: DEADLOCK, LIVELOCK, AND LIVEDEADLOCK 536
INTRODUCTION 536
LOCKED PROCESSES 538
DETECTING LIVEDEADLOCK 539
LIVEDEADLOCK FREE CONNECTIONS 540
CONCLUSIONS 541
REFERENCES 541
CHAPTER 86. STABILIZATION, TRACKING, AND HIERARCHICAL MODELING OF DISCRETE-EVENT DYNAMIC SYSTEMS 542
INTRODUCTION 542
PRELIMINARIES 542
OUTPUT COMPENSATORS AND OUTPUT STABILIZATION 543
FURTHER TOPICS 545
CONCLUSIONS 546
REFERENCES 546
AUTHOR INDEX 548
KEYWORD INDEX 550