Introduction to the mathematical theory of control:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Springfield, MO
American Institute of Mathematical Sciences
2007
|
| Schriftenreihe: | AIMS series on applied mathematics
2 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Includes bibliographical references (p. [305]-309) and index |
| Beschreibung: | XIII, 312 S. Ill. 25 cm |
| ISBN: | 9781601330024 1601330022 |
Internformat
MARC
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| 020 | |a 1601330022 |9 1-60133-002-2 | ||
| 035 | |a (OCoLC)180757015 | ||
| 035 | |a (DE-599)BVBBV039728418 | ||
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| 100 | 1 | |a Bressan, Alberto |d 1956- |e Verfasser |0 (DE-588)172009952 |4 aut | |
| 245 | 1 | 0 | |a Introduction to the mathematical theory of control |c Alberto Bressan and Benedetto Piccoli |
| 264 | 1 | |a Springfield, MO |b American Institute of Mathematical Sciences |c 2007 | |
| 300 | |a XIII, 312 S. |b Ill. |c 25 cm | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a AIMS series on applied mathematics |v 2 | |
| 500 | |a Includes bibliographical references (p. [305]-309) and index | ||
| 650 | 4 | |a Nonlinear control theory | |
| 650 | 4 | |a Control theory | |
| 650 | 0 | 7 | |a Kontrolltheorie |0 (DE-588)4032317-1 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Kontrolltheorie |0 (DE-588)4032317-1 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Piccoli, Benedetto |e Sonstige |4 oth | |
| 830 | 0 | |a AIMS series on applied mathematics |v 2 |w (DE-604)BV023094684 |9 2 | |
| 856 | 4 | 2 | |m Digitalisierung UB Passau - ADAM Catalogue Enrichment |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024576374&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-024576374 | ||
Datensatz im Suchindex
| _version_ | 1804148610072313856 |
|---|---|
| adam_text | Contents
1 Introduction........................................................ 1
2 Review of Differential Equations................................... 13
2.1 Fundamental theory.......................................... 14
2.2 Linear systems............................................... 21
2.3 Differentiability with respect to initial data............... 26
2.4 A transversality theorem..................................... 30
Problems ......................................................... 32
3 Control Systems.................................................... 35
3.1 An equivalent differential inclusion......................... 36
3.2 Fundamental properties of trajectories ...................... 37
3.3 Closure ..................................................... 44
3.4 Density...................................................... 47
3.5 Reachable sets............................................... 51
3.6 Linear systems............................................... 56
3.7 Local controllability of nonlinear systems................... 59
3.8 Lie brackets and controllability............................. 61
3.9 Chattering controls.......................................... 65
3.10 The Bang-Bang theorem ....................................... 67
Problems ......................................................... 69
4 Asymptotic stabilization........................................... 75
4.1 Lyapunov stability........................................... 75
4.2 Stabilization of linear control systems...................... 79
4.3 Stabilization of nonlinear systems........................... 83
Problems ......................................................... 85
5 Existence of Optimal Controls...................................... 87
5.1 Mayer problems............................................... 87
5.2 The problem of Bolza......................................... 93
Problems
95
6 Necessary conditions ........................................... 99
6.1 The Mayer problem with free terminal point.................100
6.2 Computation of optimal controls............................104
6.3 The Mayer problem with terminal constraints................110
6.4 Variable terminal time.....................................115
6.5 The problem of Bolza..................................... 119
6.6 Linear-quadratic optimal control...........................125
Problems........................................................127
7 Sufficient Conditions....................................... 133
7.1 Existence + PMP............................................134
7.2 Convexity + PMP............................................135
7.3 Dynamic Programming........................................137
7.4 Relations between the P.M.P.
and the P.D.E. of Dynamic Programming......................148
7.5 Linear-quadratic case......................................150
7.6 Optimal syntheses..........................................154
Problems........................................................161
8 Viscosity solutions for Hamilton-Jacobi equations...............165
8.1 The method of characteristics..............................166
8.2 One-sided differentials....................................170
8.3 Viscosity solutions........................................174
8.4 Stability properties.......................................176
8.5 Comparison theorems........................................178
8.6 Dynamic programming (revisited)............................185
8.7 The Hamilton-Jacobi-Bellman equation ......................189
8.8 Infinite horizon problems .................................192
Problems........................................................197
9 Patchy Feedbacks................................................199
9.1 Patchy vector fields..................................... 201
9.2 Asymptotic feedback stabilization..........................206
9.3 Robustness.................................................211
9.4 Nearly optimal patchy feedbacks ...........................219
Problems........................................................229
10 Impulsive Control Systems ......................................233
10.1 Mechanical systems controlled by moving constraints........235
10.2 Generalized trajectories for commuting vector fields.......241
10.3 The non-commutative case: graph completions................247
10.4 Systems with quadratic impulses............................252
10.5 Optimization problems for commutative impulsive systems. . . . 257
Problems
259
A Appendices......................................................263
A.l Normed spaces............................................263
A.2 Banach’s contraction mapping theorem......................265
A.3 Brouwer’s fixed point theorem ............................267
A.4 A compactness theorem.....................................273
A.5 Review of Lebesgue measure theory........................274
A.6 Differentiability of Lipschitz continuous functions.......277
A.7 Multifunctions............................................279
A.8 Convex sets..............................................283
A.9 Convex cones.............................................288
A. 10 Lie brackets and Frobenius’ theorem.....................294
Problems......................................................300
References........................................................305
Index
311
|
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| author | Bressan, Alberto 1956- |
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| dewey-ones | 515 - Analysis |
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| dewey-search | 515.642 |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV039728418 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T00:09:52Z |
| institution | BVB |
| isbn | 9781601330024 1601330022 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-024576374 |
| oclc_num | 180757015 |
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| owner | DE-384 DE-739 |
| owner_facet | DE-384 DE-739 |
| physical | XIII, 312 S. Ill. 25 cm |
| publishDate | 2007 |
| publishDateSearch | 2007 |
| publishDateSort | 2007 |
| publisher | American Institute of Mathematical Sciences |
| record_format | marc |
| series | AIMS series on applied mathematics |
| series2 | AIMS series on applied mathematics |
| spelling | Bressan, Alberto 1956- Verfasser (DE-588)172009952 aut Introduction to the mathematical theory of control Alberto Bressan and Benedetto Piccoli Springfield, MO American Institute of Mathematical Sciences 2007 XIII, 312 S. Ill. 25 cm txt rdacontent n rdamedia nc rdacarrier AIMS series on applied mathematics 2 Includes bibliographical references (p. [305]-309) and index Nonlinear control theory Control theory Kontrolltheorie (DE-588)4032317-1 gnd rswk-swf Kontrolltheorie (DE-588)4032317-1 s DE-604 Piccoli, Benedetto Sonstige oth AIMS series on applied mathematics 2 (DE-604)BV023094684 2 Digitalisierung UB Passau - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024576374&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Bressan, Alberto 1956- Introduction to the mathematical theory of control AIMS series on applied mathematics Nonlinear control theory Control theory Kontrolltheorie (DE-588)4032317-1 gnd |
| subject_GND | (DE-588)4032317-1 |
| title | Introduction to the mathematical theory of control |
| title_auth | Introduction to the mathematical theory of control |
| title_exact_search | Introduction to the mathematical theory of control |
| title_full | Introduction to the mathematical theory of control Alberto Bressan and Benedetto Piccoli |
| title_fullStr | Introduction to the mathematical theory of control Alberto Bressan and Benedetto Piccoli |
| title_full_unstemmed | Introduction to the mathematical theory of control Alberto Bressan and Benedetto Piccoli |
| title_short | Introduction to the mathematical theory of control |
| title_sort | introduction to the mathematical theory of control |
| topic | Nonlinear control theory Control theory Kontrolltheorie (DE-588)4032317-1 gnd |
| topic_facet | Nonlinear control theory Control theory Kontrolltheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024576374&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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