Nonlinear and adaptive control of complex systems

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Hauptverfasser: Fradkov, Aleksandr L. (VerfasserIn), Miroshnik, Iliya V. (VerfasserIn), Nikiforov, Vladimir O. (VerfasserIn)
Format: Buch
Sprache:English
Veröffentlicht: Dordrecht [u.a.] Kluwer 1999
Schriftenreihe:Mathematics and its applications 491
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Datensatz im Suchindex

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adam_text IMAGE 1 NONLINEAR AND ADAPTIVE CONTROL OF COMPLEX SYSTEMS BY ALEXANDER L. FRADKOV INSTITUTE FOR PROBLEMS OF MECHANICAL ENGINEERING OFTHE RUSSIAN ACADEMY OF SCIENCES, ST PETERSBURG, RUSSIA ILIYA V. MIROSHNIK ST PETERSBURG, STATE INSTITUTE OFFINE MECHANICS AND OPTICS, ST PETERSBURG, RUSSIA AND VLADIMIR O. NIKIFOROV ST PETERSBURG, STATE INSTITUTE OFFINE MECHANICS AND OPTICS, ST PETERSBURG, RUSSIA KLUWER ACADEMIC PUBLISHERS DORDRECHT / BOSTON / LONDON IMAGE 2 TABLE OF C O N T E N TS P R E F A CE XI N O T A T I O NS A ND D E F I N I T I O NS XV 1 F A C ES OF C O M P L E X I TY 1 1.1 COMPLEXITY AND DECOMPOSITION 1 1.2 MULTIVARIABLE CONTROL AND GEOMETRY 5 1.2.1 COORDINATING CONTROL 6 1.2.2 OSCILLATION SYNCHRONIZATION 8 1.2.3 SPATIAL MOTION CONTROL 10 1.2.4 TERMINAL CONTROL 15 1.2.5 STATE TRACKING SYSTEMS 16 1.3 UNCERTAINTY AND ADAPTATION 17 2 N O N L I N E AR S Y S T E M S: A N A L Y S IS A ND D E S I GN T O O LS 25 2.1 STABILITY OF NONLINEAR SYSTEMS 25 2.1.1 COMPLETENESS AND STABILITY 25 2.1.2 LYAPUNOV FUNCTIONS AND THEIR APPLICATIONS 32 2.1.3 PARTIAL STABILITY 37 2.2 EQUIVALENT MODELS A,ND COORDINATE CHANGES 44 2.2.1 AUTONOMOUS SYSTEMS 45 2.2.2 SINGLE-INPUT SYSTEMS AND CONTROLLABILITY 47 2.2.3 CANONICAL FORMS 49 2.3 BASIC CANONICAL FORM AND LINEARIZATION TECHNIQUES . . .. 52 2.3.1 BASIC CANONICAL FORM 52 2.3.2 EXACT LINEARIZATION 56 2.3.3 LINEAR APPROXIMATION 57 2.4 EQUIVALENCE OF MULTI-INPUT SYSTEMS 60 2.5 INPUT-OUTPUT CANONICAL FORMS AND STABILIZATION WITH RESPECT TO OUTPUT 63 2.5.1 MAIN TRANSLORINATION A/ND LINEARIZED DYNAMICS . . .. 64 2.5.2 SYSTEM ZERO DYNAMICS 67 V IMAGE 3 VI 2.5.3 NORMAL FORM AND LOCAL STABILIZATION 68 2.6 CONTROL OF TRIANGULAER SYSTEMS 71 2.7 PASSIVITY AND PASSIFICATION 76 2.7.1 PASSIVITY AND STABILITY 76 2.7.2 PASSIVITY AND DISSIPATIVITY 78 2.7.3 PASSIVITY AND KAIMAN-YAKUBOVICH LEMMA 80 2.7.4 PASSIFICATION AND FEEDBACK KAIMAN-YAKUBOVICH LEMMA 84 3 S P E E D - G R A D I E NT M E T H OD A ND P A R T I AL S T A B I L I Z A T I ON 91 3.1 GOAL-ORIENTED CONTROL PROBLEM STATEMENT 91 3.2 DESIGN OF SPEED-GRADIENT ALGORITHMS 94 3.2.1 SPEED-GRADIENT ALGORITHMS FOR LOCAL OBJECTIVE FUNCTIONALS 94 3.2.2 SPEED-GRADIENT ALGORITHMS FOR INTEGRAL OBJECTIVE FUNCTIONALS 95 3.2.3 SPEED-GRADIENT ALGORITHMS IN FINITE FORM 96 3.2.4 COMBINED ALGORITHMS 97 3.3 CONVERGENCE OF THE SPEED-GRADIENT ALGORITHMS 97 3.3.1 REGULATION A,ND TRACKING 97 3.3.2 PARTIAL STABILIZATION 105 3.4 IDENTIFYING PROPERTIES OF SPEED-GRADIENT ALGORITHMS . . .. 111 3.5 ROBUSTNESS OF SPEED-GRADIENL ALGORITHMS WITH RESPECT TO DISTURBANCES 113 3.6 SPEED-GRADIENT CONTROL OF HAMILTONIAN SYSTEMS 118 3.6.1 CONTROL OF ENERGY 118 3.6.2 CONTROL OF FIRST INTEGRALS 122 4 N O N L I N E AR C O N T R OL OF M U L T I V A R I A B LE S Y S T E MS 127 4.1 MULTIVARIABLE CONTROL AND GEOMETRIE APPROACH 127 4.2 EQUILIBRIUM STABILIZATION 129 4.2.1 STATE REGULATION PROBLEMS 129 4.2.2 STABILIZATION VIA EXAET LINEARIZATION 131 4.2.3 STABILIZATION VIA LINEAR APPROXIMATION 133 4.3 A T T R A C T I NG SETS 135 4.3.1 ATTRACTIVITY AND INVARIANCE 135 4.3.2 NEJGHBORHOOD PROPERTIES 140 4.3.3 EQUIVALENT DYNAMICS OF AUTONOMOUS SYSTEMS . . .. 146 4.3.4 CONDITIONS OF ATTRACTIVITY 148 4.4 SET STABILIZATION 153 4.4.1 CONTROL PROBLEMS AND INVARIANCE CONDITIONS 153 IMAGE 4 VLL 4.4.2 PROBLEM DECOMPO SITION AND INVARIANT CONTROL . . .. 157 4.4.3 EQUIVALENT DYNAMICS 163 4.4.4 SYSTEM STABILIZATION 167 4.5 STATE TRACKING CONTROL 173 4.5.1 TRA,CKING PROBLEM 173 4.5.2 INVARIANT CONTROL 175 4.5.3 SYSTEM STABILIZATION 177 5 N O N L I N E AR C O N T R OL OF M I MO S Y S T E MS 183 5.1 PROBLEMS OF OUTPUT CONTROL AND COORDINATION OF MIMO SYSTEMS 183 5.2 OUTPUT REGULATION 185 5.2.1 REGULATION PROBLEM 185 5.2.2 MAIN TRANSFORMATIONS 186 5.2.3 SYSTEMS WITHOUT ZERO DYNAMICS 191 5.2.4 ZERO DYNAMICS SUBMANIFOLD 193 5.2.5 SYSTEM EQUIVALENT DYNAMICS 194 5.2.6 ISSUES OF EQUIVALENCE AND STABILITY 199 5.3 OUTPUT COORDINATION 212 5.3.1 (KOORDINATION CONDITIONS 212 5.3.2 PROBLEMS OF COORDINATING CONTROL 216 5.3.3 TRANSFORMATION TO NORMAL FORM 219 5.3.4 TRANSFORMATION TO TASK-ORIENTED FORM 223 5.4 COORDINATING CONTROL 230 5.4.1 CONTROL PROBLEMS IN STATE SPACE 230 5.4.2 BASIC CONTROL LAW AND PARTIAL DECONPLING 231 5.4.3 CONTROL BY USING IMPLICIT MODEIS 232 5.4.4 CONTROL BY USING REFERENCE MODEL 237 5.5 SPATIAL MOTION CONTROL 242 5.5.1 SET STABILIZATION IN OUTPUT SPACE 243 5.5.2 CANONICAL REPRESENTATIONS AND DIFFERENTIAL FORMS . . . 246 5.5.3 SYSTEM EQUIVALENT DYNAMICS AND CONTROL DESIGN . . . 257 6 A D A P T I VE A ND R O B U ST C O N T R OL D E S I GN 265 6.1 STATE-FEEDBACK CONTROL 266 6.1.1 CERTAINTY EQUIVALENCE DESIGN 266 6.1.2 RECURSIVE DESIGN PROCEDURES 283 6.2 OUTPUT-FEEDBACK CONTROL 297 6.2.1 CONTROL OF STRICTLY PASSIVE ARID STRICTLY MINIMUM PHASE SYSTEMS 298 6.2.2 AUGMENTED ERROR BASED DESIGN 303 6.2.3 HIGH-ORDER TUNER BASED DESIGN 309 IMAGE 5 6.3 OUTPUT-FEEDBACK ADAPTIVE SYSTEMS WITH IMPLICIT REFERENCE MODEL 320 6.3.1 DESIGN OF ADAPTIVE CONTROLLER 320 6.3.2 SHUNTING METHOD 323 6.4 OUTPUT-FEEDBACK CONTROL OF UNCERTAIN LINEAR PLANTS UNDER IDEAL CONDITIONS 328 6.4.1 PROBLEM STATEMENT 329 6.4.2 PLANT MODEL PARAMETRIZATIONS 329 6.4.3 CERTAINTY EQUIVALENCE DESIGN 337 6.4.4 DYNAMIC CERTAINTY EQUIVALENCE DESIGN 342 6.4.5 NONLINEAR ADAPTIVE DESIGN FOR LINEAR PLANTS 349 6.4.6 DISCUSSION 369 6.5 OUTPUT-FEEDBACK CONTROL OF UNCERTAIN LINEAR PLANTS IN THE PRESENCE OF EXTERNA] DISTURBANC.ES 373 6.5.1 PLANT MODEL PARAMETRIZATIONS 373 6.5.2 ROBUST CONTROLLERS WITH HIGH-ORDER TUNERS 375 6.5.3 ROBUST CONTROLLER WITH NONLINEAR DAMPING TERMS . . 381 D E C O M P O S I T I ON OF A D A P T I VE S Y S T E MS 3 91 7.1 SEPARATION OF MOTIONS IN ADAPTIVE SYSTEMS 392 7.1.1 THE FIRST SCHEINE OF MOTION SEPARATION FOR CONTINUOUS TIME SYSTEMS 392 7.1.2 THE FIRST SCHEINE OF MOTION SEPARATION FOR DISCRETETIME SYSTEMS 399 7.1.3 THE SECOND SCHEME OF MOTION SEPARATION 401 7.2 CONDITIONS OF APPLICABILITY AND ESTIMATION OF ACCURACY OF THE MOTION SEPARATION SCHEINES IN ADAPTIVE SYSTEMS . . .. 403 7.2.1 APPLICABILITY OF THE SPEED-GRADIENT ALGORITHMS TO SINGULARLY PERTURBED SYSTEMS 405 7.2.2 DISCRETIZATION OF THE SPEED-GRADIENT ALGORITHMS . . . 417 7.3 ADAPTIVE DECENTRALIZED CONTROL OF INTERCONNECTED NONLINEAR SYSTEMS 419 7.3.1 PROBLEM STATEMENT AND CONTROL ALGORITHM 419 7.3.2 PROPERTIES OF THE CONTROL SYSTEM 421 C O N T R OL OF M E C H A N I C AL S Y S T E MS 4 29 8.1 SPATIAL MOTION CONTROL OF RIGID BODY 429 8.1.1 DYNAMICS AND KINEMATICAL PROPERTIES 429 8.1.2 MASS-POINT CONTROL 433 8.1.3 CONTROL OF ROTATION 436 8.2 ROBOT MOTION CONTROL 438 8.2.1 ROBOT MODEL AND THE PROBLEM STATEMENT 439 IMAGE 6 IX 8.2.2 DIFFERENTIAL RELATIONS AND THE MAIN APPROACH 442 8.2.3 TRAJECTORY CONTROL STRATEGY 446 8.3 MOBILE ROBOT CONTROL 449 8.3.1 ANALYSIS OF ROBOT DYNAMICS 449 8.3.2 CONTROL PROBLEM STATEMENT 453 8.3.3 CONTROL LAW DESIGN 455 8.4 CONTROL OF OSCILLATORY SYSTEMS 459 8.4.1 ENERGY CONTROL OF A PENDULUM WITH CONTROLLED PIVOT 459 8.4.2 WHEELING A RAR OUT OF A DITCH 464 9 P H Y S I CS A ND C O N T R OL 4 69 9.1 FEEDBACK RESONANCE IN A NONLINEAR OSCILLATOR 469 9.2 SUPEROPTIMAL ESCAPE FROM POTENTIAL WELLS 473 9.3 STABILIZATION OF UNSTABLE MODES 475 9.4 FEEDBACK SPECTROSCOPY 476 9.5 EXCITABILITY INDEX 477 9.6 SPEED-GRADIENT LAWS OF DYNAMICS 479 9.7 ONZAGGER EQUATIONS 482 9.8 DISCUSSION 483 A A P P E N D IX 4 85 R E F E R E N C ES 4 93 I N D EX 507
any_adam_object 1
author Fradkov, Aleksandr L.
Miroshnik, Iliya V.
Nikiforov, Vladimir O.
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Miroshnik, Iliya V.
Nikiforov, Vladimir O.
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physical XVIII, 510 S.
publishDate 1999
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publisher Kluwer
record_format marc
series Mathematics and its applications
series2 Mathematics and its applications
spellingShingle Fradkov, Aleksandr L.
Miroshnik, Iliya V.
Nikiforov, Vladimir O.
Nonlinear and adaptive control of complex systems
Mathematics and its applications
Adaptive control systems
Dynamics
Nonlinear control theory
Kontrolltheorie (DE-588)4032317-1 gnd
Komplexes System (DE-588)4114261-5 gnd
subject_GND (DE-588)4032317-1
(DE-588)4114261-5
title Nonlinear and adaptive control of complex systems
title_auth Nonlinear and adaptive control of complex systems
title_exact_search Nonlinear and adaptive control of complex systems
title_full Nonlinear and adaptive control of complex systems by Alexander L. Fradkov, Iliya V. Miroshnik, and Vladimir O. Nikoforov
title_fullStr Nonlinear and adaptive control of complex systems by Alexander L. Fradkov, Iliya V. Miroshnik, and Vladimir O. Nikoforov
title_full_unstemmed Nonlinear and adaptive control of complex systems by Alexander L. Fradkov, Iliya V. Miroshnik, and Vladimir O. Nikoforov
title_short Nonlinear and adaptive control of complex systems
title_sort nonlinear and adaptive control of complex systems
topic Adaptive control systems
Dynamics
Nonlinear control theory
Kontrolltheorie (DE-588)4032317-1 gnd
Komplexes System (DE-588)4114261-5 gnd
topic_facet Adaptive control systems
Dynamics
Nonlinear control theory
Kontrolltheorie
Komplexes System
url http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008889333&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
volume_link (DE-604)BV008163334
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