Elements of finite dimensional systems and control theory:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Harlow
Longman Scientific & Technical
1988
|
| Schriftenreihe: | Pitman monographs and surveys in pure and applied mathematics
37 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIII, 421 S. |
| ISBN: | 0582013739 |
Internformat
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| 100 | 1 | |a Ahmed, Nasir U. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Elements of finite dimensional systems and control theory |c N. U. Ahmed |
| 264 | 1 | |a Harlow |b Longman Scientific & Technical |c 1988 | |
| 300 | |a XIII, 421 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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| 490 | 1 | |a Pitman monographs and surveys in pure and applied mathematics |v 37 | |
| 650 | 4 | |a Calcul variation | |
| 650 | 4 | |a Commande optimale | |
| 650 | 4 | |a Commande, Théorie de la | |
| 650 | 7 | |a Commande, Théorie de la |2 ram | |
| 650 | 4 | |a Exercice analyse | |
| 650 | 4 | |a Filtrage | |
| 650 | 4 | |a Méthode Ljapunov | |
| 650 | 4 | |a Observabilité | |
| 650 | 4 | |a Principe Bellman | |
| 650 | 4 | |a Processus stochastique | |
| 650 | 4 | |a Stabilité | |
| 650 | 4 | |a Système dimmension finie | |
| 650 | 4 | |a Systèmes, Analyse de | |
| 650 | 7 | |a Systèmes, Analyse de |2 ram | |
| 650 | 4 | |a Control theory | |
| 650 | 4 | |a System analysis | |
| 650 | 0 | 7 | |a Kontrolltheorie |0 (DE-588)4032317-1 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Systemanalyse |0 (DE-588)4116673-5 |2 gnd |9 rswk-swf |
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Datensatz im Suchindex
| _version_ | 1804120832001179648 |
|---|---|
| adam_text | Contents
Preface xi
1 System models 1
1.0 Introduction 1
1.1 Linear, nonlinear and stochastic systems 2
1.2 Modelling of system dynamics 5
1.3 Some remarks on stochastic models 27
Exercises 28
2 Linear systems 30
2.0 Introduction 30
2.1 Some elements from real analysis 30
2.1.1 Linear space 30
2.1.2 Metric space 32
2.1.3 Normed vector space 34
2.1.4 Banach space 34
2.1.5 Hilbert space 34
2.1.6 Continuous functions 42
2.2 Existence and uniqueness of solutions of linear systems of
differential equations 46
2.2.1 Existence and uniqueness 47
2.2.2 State transition operator 54
2.3 Continuous dependence of solutions on system parameters and
sensitivity 58
2.3.1 Continuous dependence 59
2.3.2 Sensitivity 65
2.4 Input output stability (BIBO) 70
2.5 Linear integral equations arising from output feedback 76
Exercises 80
vii
viii CONTENTS
3 Nonlinear systems 83
3.0 Introduction 83
3.1 Existence and uniqueness of solutions of nonlinear systems of
differential equations 83
3.1.1 Existence and uniqueness of solutions based on the
Banach fixed point theorem 84
3.1.2 Existence of solutions based on the Schauder fixed point
theorem 90
3.2 Continuous dependence of solutions on system parameters,
nonlinear semigroup and sensitivity 101
3.2.1 Continuous dependence on initial data 101
3.2.2 Continuous dependence on parameters 103
3.3 Continuous dependence of solutions on controls (inputs) 106
3.4 Nonlinear integral equations arising from output feedback and
Lp stability 110
Exercises 115
4 Stability 117
4.0 Introduction 117
4.1 Definitions of Lyapunov stability 118
4.2 Asymptotic stability of linear systems 121
4.2.1 Time invariant systems 121
4.2.2 Time varying systems 125
4.3 Lyapunov s first method: stability of mildly nonlinear
systems 130
4.3.1 Time invariant system (nonlinear) 130
4.3.2 Time varying system (nonlinear) 134
4.4 Lyapunov s second method (fundamental stability
theorems) 136
4.5 Domain of stability, limit sets, invariant sets and stability of
sets 145
Exercises 161
5 Observability, controllability and stabilizability 165
5.0 Introduction 165
5.1 Observability 165
5.1.1 Linear time invariant systems 166
5.1.2 Linear time varying systems (observability) 171
5.2 Controllability without control constraints 173
5.2.1 Linear time invariant systems 173
5.2.2 Linear time varying systems 183
5.3 Controllability under control constraints 187
CONTENTS ix
5.4 Stabilizability of linear systems with state feedback and
observers 202
5.5 Controllability of nonlinear systems 221
Exercises 227
6 Optimal control 232
6.0 Introduction 232
6.1 Time optimal control of linear systems 232
6.1.1 The LaSalle bang bang principle 234
6.2 Calculus of variations and optimal control 244
6.2.1 The Euler Lagrange equation 244
6.2.2 Pontryagin s minimum principle and transversality
conditions 249
6.2.3 Existence of optimal controls 268
6.3 Bellman s principle of optimality and feedback controls 277
6.3.1 Bellman s equations for feedback controls 277
6.3.2 Linear systems with quadratic cost functions 284
6.3.3 Nonlinear regulators 291
6.4 Computation of optimal controls and system identification 300
6.4.1 Computation of optimal controls 301
6.4.2 System identification 306
Exercises 311
7 Elements of stochastic systems 317
7.0 Introduction 317
7.1 Basic concepts from probability theory 317
7.2 Stochastic integrals and differentials 326
7.2.1 Stochastic integrals based on the Wiener process 326
7.2.2 Stochastic integrals based on the Poisson process 335
7.2.3 Ito formula and stochastic differentials 337
7.3 Systems governed by linear stochastic differential
equations 342
7.3.1 Existence and uniqueness of solutions 342
7.3.2 Continuous dependence of solutions on parameters 349
7.4 Systems governed by nonlinear stochastic differential
equations 352
7.4.1 Existence and uniqueness of solutions 353
7.4.2 Continuous dependence of solutions on parameters 360
7.4.3 Solution of stochastic differential equations as Markov
processes 364
7.4.4 Kolmogorov s equations 368
7.4.5 Jump Markov processes 375
x CONTENTS
7.5 Filtering and identification 377
7.5.1 Linear filtering 378
7.5.2 Identification 382
7.5.3 Nonlinear filtering 384
7.6 Stability and optimal control 388
7.6.1 Stability 388
7.6.2 Optimal control 393
7.6.3 Reliability 405
Exercises 406
Bibliography 409
Index 419
|
| any_adam_object | 1 |
| author | Ahmed, Nasir U. |
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| author_sort | Ahmed, Nasir U. |
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| dewey-ones | 003 - Systems |
| dewey-raw | 003 |
| dewey-search | 003 |
| dewey-sort | 13 |
| dewey-tens | 000 - Computer science, information, general works |
| discipline | Informatik Mathematik |
| format | Book |
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| indexdate | 2024-07-09T16:48:21Z |
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| language | English |
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| series2 | Pitman monographs and surveys in pure and applied mathematics |
| spelling | Ahmed, Nasir U. Verfasser aut Elements of finite dimensional systems and control theory N. U. Ahmed Harlow Longman Scientific & Technical 1988 XIII, 421 S. txt rdacontent n rdamedia nc rdacarrier Pitman monographs and surveys in pure and applied mathematics 37 Calcul variation Commande optimale Commande, Théorie de la Commande, Théorie de la ram Exercice analyse Filtrage Méthode Ljapunov Observabilité Principe Bellman Processus stochastique Stabilité Système dimmension finie Systèmes, Analyse de Systèmes, Analyse de ram Control theory System analysis Kontrolltheorie (DE-588)4032317-1 gnd rswk-swf Systemanalyse (DE-588)4116673-5 gnd rswk-swf Stabilität (DE-588)4056693-6 gnd rswk-swf Stochastisches System (DE-588)4057635-8 gnd rswk-swf Kontrolltheorie (DE-588)4032317-1 s Stochastisches System (DE-588)4057635-8 s Stabilität (DE-588)4056693-6 s DE-604 Systemanalyse (DE-588)4116673-5 s 1\p DE-604 Pitman monographs and surveys in pure and applied mathematics 37 (DE-604)BV000022446 37 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=004185008&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Ahmed, Nasir U. Elements of finite dimensional systems and control theory Pitman monographs and surveys in pure and applied mathematics Calcul variation Commande optimale Commande, Théorie de la Commande, Théorie de la ram Exercice analyse Filtrage Méthode Ljapunov Observabilité Principe Bellman Processus stochastique Stabilité Système dimmension finie Systèmes, Analyse de Systèmes, Analyse de ram Control theory System analysis Kontrolltheorie (DE-588)4032317-1 gnd Systemanalyse (DE-588)4116673-5 gnd Stabilität (DE-588)4056693-6 gnd Stochastisches System (DE-588)4057635-8 gnd |
| subject_GND | (DE-588)4032317-1 (DE-588)4116673-5 (DE-588)4056693-6 (DE-588)4057635-8 |
| title | Elements of finite dimensional systems and control theory |
| title_auth | Elements of finite dimensional systems and control theory |
| title_exact_search | Elements of finite dimensional systems and control theory |
| title_full | Elements of finite dimensional systems and control theory N. U. Ahmed |
| title_fullStr | Elements of finite dimensional systems and control theory N. U. Ahmed |
| title_full_unstemmed | Elements of finite dimensional systems and control theory N. U. Ahmed |
| title_short | Elements of finite dimensional systems and control theory |
| title_sort | elements of finite dimensional systems and control theory |
| topic | Calcul variation Commande optimale Commande, Théorie de la Commande, Théorie de la ram Exercice analyse Filtrage Méthode Ljapunov Observabilité Principe Bellman Processus stochastique Stabilité Système dimmension finie Systèmes, Analyse de Systèmes, Analyse de ram Control theory System analysis Kontrolltheorie (DE-588)4032317-1 gnd Systemanalyse (DE-588)4116673-5 gnd Stabilität (DE-588)4056693-6 gnd Stochastisches System (DE-588)4057635-8 gnd |
| topic_facet | Calcul variation Commande optimale Commande, Théorie de la Exercice analyse Filtrage Méthode Ljapunov Observabilité Principe Bellman Processus stochastique Stabilité Système dimmension finie Systèmes, Analyse de Control theory System analysis Kontrolltheorie Systemanalyse Stabilität Stochastisches System |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=004185008&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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