Optimal syntheses for control systems on 2-D manifolds:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
Springer
2004
|
| Schriftenreihe: | Mathématiques & applications
43 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Literaturverz. S. 251 - 257 |
| Beschreibung: | XIII, 261 S. graph. Darst. |
| ISBN: | 3540203060 |
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Datensatz im Suchindex
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| adam_text | UGO BOSCAIN BENEDETTO PICCOLI OPTIMAL SYNTHESES FOR CONTROL SYSTEMS ON
2-D MANIFOLDS SPRINGER CONTENTS INTRODUCTION 1 OPTIMAL CONTROL PROBLEMS
AND SYNTHESES 2 THE MODEL PROBLEM 6 THE CLASSIFICATION PROGRAM 7
CHAPTERS OF THE BOOK 10 BIBLIOGRAPHICAL NOTE 13 1 GEOMETRIC CONTROL 15
1.1 CONTROL SYSTEMS 15 1.2 OPTIMAL CONTROL 19 1.2.1 EXISTENCE 20 1.2.2
PONTRYAGIN MAXIMUM PRINCIPLE 21 1.2.3 ABNORMAL EXTREMALS AND ENDPOINT
SINGULAR EXTREMALS 23 1.3 HIGH ORDER CONDITIONS 24 1.3.1 HIGH ORDER
MAXIMUM PRINCIPLE 24 1.3.2 ENVELOPE THEORY 26 1.4 GEOMETRIC CONTROL
APPROACH TO SYNTHESIS 27 BIBLIOGRAPHICAL NOTE 29 EXERCISES 30 2 TIME
OPTIMAL SYNTHESIS FOR 2*D SYSTEMS 33 2.1 INTRODUCTION 35 2.2 BASIC
DEFINITIONS 38 2.3 SPECIAL CURVES 40 2.4 BOUND ON THE NUMBER OF ARCS 48
2.4.1 PROOF OF THEOREM 13 51 2.5 EXISTENCE OF AN OPTIMAL SYNTHESIS 56
2.6 CLASSIFICATION OF SYNTHESIS SINGULARITIES 58 2.6.1 FRAME CURVES 58
2.6.2 FRAME POINTS 60 2.6.3 OTHER SPECIAL CURVES 62 XII CONTENTS 2.6.4
EXAMPLES OF FRAME CURVES AND FRAME POINTS 62 2.7 ON THE RELATION BETWEEN
THE SWITCHING STRATEGY AND THE FUNCTIONS AND D 1 83 2.7.1 THE Q 1
FUNCTION ON SINGULARITIES OF THE SYNTHESIS 85 2.8 STRUCTURAL STABILITY
AND CLASSIFICATION OF OPTIMAL FEEDBACKS .. 86 2.8.1 FEEDBACK EQUIVALENCE
88 2.8.2 AN ALGORITHM FOR THE SYNTHESIS 89 2.8.3 STRUCTURAL STABILITY
103 2.8.4 ^GRAPHS 104 2.8.5 ADMISSIBLE GRAPHS 108 2.8.6 CLASSIFICATION
ILL 2.9 SYSTEMS ON TWO DIMENSIONAL MANIFOLDS 113 2.9.1 GRAPHS, CELLULAR
EMBEDDINGS AND THE HEFFTER THEOREM. 114 2.9.2 ADMISSIBLE GRAPHS AND
SYNTHESES CLASSIFICATION 116 2.10 APPLICATIONS 118 2.10.1 APPLICATIONS
TO SECOND ORDER DIFFERENTIAL EQUATIONS . .. 118 2.10.2 EXAMPLE: THE
DUFFIN EQUATION 120 2.10.3 GENERALIZATION TO BOLZA PROBLEMS 121 2.10.4
THE NON-LOCALLY CONTROLLABLE CASE 122 BIBLIOGRAPHICAL NOTE 123 EXERCISES
124 3 GENERIC PROPERTIES OF THE MINIMUM TIME FUNCTION 127 3.1 BASIC
DEFINITIONS AND STATEMENTS OF RESULTS 129 3.2 PROPERTIES OF THE MINIMUM
TIME FRONT F T 132 3.2.1 DEFINITION OF STRIPS 132 3.2.2 F T IN A
NEIGHBORHOOD OF THE ORIGIN 134 3.2.3 F T IN A NEIGHBORHOOD OF 7+, U J~ P
135 3.2.4 THE MTF ON OTHER BASES 141 3.2.5 THE MTF ON OPEN STRIPS 141
3.2.6 F T ON OVERLAP CURVES 145 3.2.7 F T ON BORDERS 145 3.2.8 PROOF OF
THEOREM 27 149 3.3 PROOF OF THEOREM 26 149 3.4 TOPOLOGY OF THE REACHABLE
SET 151 EXERCISES 152 4 EXTREMAL SYNTHESIS 153 4.1 BASIC FACTS 156 4.1.1
GENERIC CONDITIONS 156 4.1.2 ANTI-TURNPIKES 157 4.1.3 NEW FRAME CURVES
158 4.1.4 THE SET OF EXTREMALS IN A NEIGHBORHOOD OF 7+ U 7 ... 159
4.1.5 NUMBER OF PRE*IMAGES 162 4.1.6 SINGULARITIES ALONG 7+1)7 164
CONTENTS XIII 4.1.7 SINGULARITIES ALONG SINGULAR TRAJECTORIES 164 4.2
EXTREMAL STRIPS AND THE ALGORITHM 167 4.2.1 EXTREMAL STRIP BORDERS: THE
FCS OF KIND 70 AND W 170 4.3 ABNORMAL EXTREMALS 171 4.3.1 GENERIC
PROPERTIES OF ABNORMAL EXTREMALS 171 4.3.2 SINGULARITIES 177 4.4
EXTREMAL STRIPS EVOLUTION AND FRAME POINTS 181 4.4.1 FRAME CURVES AND
FRAME POINTS ALONG C AND C 182 4.4.2 FRAME CURVES AND POINTS ALONG 70
184 4.4.3 FRAME CURVES AND POINTS ALONG W 18 7 4.5 EXISTENCE OF AN
EXTREMAL SYNTHESIS 189 4.6 CLASSIFICATION OF THE SINGULARITIES IN E 2 X
S L 195 5 PROJECTION SINGULARITIES 197 5.1 SINGULARITIES OF THE
PROJECTION 772 201 5.1.1 CLASSIFICATION OF PROJECTION SINGULARITIES 201
5.1.2 CLASSIFICATION OF ABNORMAL EXTREMALS 202 5.2 PROJECTION
SINGULARITIES FOR 77 3 209 5.2.1 THE EXTREMAL FRONT 211 A SOME TECHNICAL
PROOFS OF CHAPTER 2 219 A.I PROOF OF THEOREM 15, P. 60 219 A.2 PROOF OF
THEOREM 16, P. 60 221 A.3 PROOF OF PROPOSITION 3, P. 92 229 A.4 PROOF OF
PROPOSITION 4, P. 94 234 A.5 PROOF OF THEOREM 20, P. 113 236 B
BIDIMENSIONAL SOURCES 245 B.I LOCAL OPTIMAL SYNTHESIS AT THE SOURCE 246
B.2 THE LOCALLY CONTROLLABLE CASE AND SEMICONCAVITY OF THE MINIMUM TIME
FUNCTION 247 REFERENCES 251 INDEX 259
|
| adam_txt |
UGO BOSCAIN BENEDETTO PICCOLI OPTIMAL SYNTHESES FOR CONTROL SYSTEMS ON
2-D MANIFOLDS SPRINGER CONTENTS INTRODUCTION 1 OPTIMAL CONTROL PROBLEMS
AND SYNTHESES 2 THE MODEL PROBLEM 6 THE CLASSIFICATION PROGRAM 7
CHAPTERS OF THE BOOK 10 BIBLIOGRAPHICAL NOTE 13 1 GEOMETRIC CONTROL 15
1.1 CONTROL SYSTEMS 15 1.2 OPTIMAL CONTROL 19 1.2.1 EXISTENCE 20 1.2.2
PONTRYAGIN MAXIMUM PRINCIPLE 21 1.2.3 ABNORMAL EXTREMALS AND ENDPOINT
SINGULAR EXTREMALS 23 1.3 HIGH ORDER CONDITIONS 24 1.3.1 HIGH ORDER
MAXIMUM PRINCIPLE 24 1.3.2 ENVELOPE THEORY 26 1.4 GEOMETRIC CONTROL
APPROACH TO SYNTHESIS 27 BIBLIOGRAPHICAL NOTE 29 EXERCISES 30 2 TIME
OPTIMAL SYNTHESIS FOR 2*D SYSTEMS 33 2.1 INTRODUCTION 35 2.2 BASIC
DEFINITIONS 38 2.3 SPECIAL CURVES 40 2.4 BOUND ON THE NUMBER OF ARCS 48
2.4.1 PROOF OF THEOREM 13 51 2.5 EXISTENCE OF AN OPTIMAL SYNTHESIS 56
2.6 CLASSIFICATION OF SYNTHESIS SINGULARITIES 58 2.6.1 FRAME CURVES 58
2.6.2 FRAME POINTS 60 2.6.3 OTHER SPECIAL CURVES 62 XII CONTENTS 2.6.4
EXAMPLES OF FRAME CURVES AND FRAME POINTS 62 2.7 ON THE RELATION BETWEEN
THE SWITCHING STRATEGY AND THE FUNCTIONS AND D 1 83 2.7.1 THE Q 1
FUNCTION ON SINGULARITIES OF THE SYNTHESIS 85 2.8 STRUCTURAL STABILITY
AND CLASSIFICATION OF OPTIMAL FEEDBACKS . 86 2.8.1 FEEDBACK EQUIVALENCE
88 2.8.2 AN ALGORITHM FOR THE SYNTHESIS 89 2.8.3 STRUCTURAL STABILITY
103 2.8.4 ^GRAPHS 104 2.8.5 ADMISSIBLE GRAPHS 108 2.8.6 CLASSIFICATION
ILL 2.9 SYSTEMS ON TWO DIMENSIONAL MANIFOLDS 113 2.9.1 GRAPHS, CELLULAR
EMBEDDINGS AND THE HEFFTER THEOREM. 114 2.9.2 ADMISSIBLE GRAPHS AND
SYNTHESES CLASSIFICATION 116 2.10 APPLICATIONS 118 2.10.1 APPLICATIONS
TO SECOND ORDER DIFFERENTIAL EQUATIONS . . 118 2.10.2 EXAMPLE: THE
DUFFIN EQUATION 120 2.10.3 GENERALIZATION TO BOLZA PROBLEMS 121 2.10.4
THE NON-LOCALLY CONTROLLABLE CASE 122 BIBLIOGRAPHICAL NOTE 123 EXERCISES
124 3 GENERIC PROPERTIES OF THE MINIMUM TIME FUNCTION 127 3.1 BASIC
DEFINITIONS AND STATEMENTS OF RESULTS 129 3.2 PROPERTIES OF THE MINIMUM
TIME FRONT F T 132 3.2.1 DEFINITION OF STRIPS 132 3.2.2 F T IN A
NEIGHBORHOOD OF THE ORIGIN 134 3.2.3 F T IN A NEIGHBORHOOD OF 7+, U J~ P
135 3.2.4 THE MTF ON OTHER BASES 141 3.2.5 THE MTF ON OPEN STRIPS 141
3.2.6 F T ON OVERLAP CURVES 145 3.2.7 F T ON BORDERS 145 3.2.8 PROOF OF
THEOREM 27 149 3.3 PROOF OF THEOREM 26 149 3.4 TOPOLOGY OF THE REACHABLE
SET 151 EXERCISES 152 4 EXTREMAL SYNTHESIS 153 4.1 BASIC FACTS 156 4.1.1
GENERIC CONDITIONS 156 4.1.2 ANTI-TURNPIKES 157 4.1.3 NEW FRAME CURVES
158 4.1.4 THE SET OF EXTREMALS IN A NEIGHBORHOOD OF 7+ U 7" . 159
4.1.5 NUMBER OF PRE*IMAGES 162 4.1.6 SINGULARITIES ALONG 7+1)7" 164
CONTENTS XIII 4.1.7 SINGULARITIES ALONG SINGULAR TRAJECTORIES 164 4.2
EXTREMAL STRIPS AND THE ALGORITHM 167 4.2.1 EXTREMAL STRIP BORDERS: THE
FCS OF KIND 70 AND W 170 4.3 ABNORMAL EXTREMALS 171 4.3.1 GENERIC
PROPERTIES OF ABNORMAL EXTREMALS 171 4.3.2 SINGULARITIES 177 4.4
EXTREMAL STRIPS EVOLUTION AND FRAME POINTS 181 4.4.1 FRAME CURVES AND
FRAME POINTS ALONG C AND C 182 4.4.2 FRAME CURVES AND POINTS ALONG 70
184 4.4.3 FRAME CURVES AND POINTS ALONG W 18 7 4.5 EXISTENCE OF AN
EXTREMAL SYNTHESIS 189 4.6 CLASSIFICATION OF THE SINGULARITIES IN E 2 X
S L 195 5 PROJECTION SINGULARITIES 197 5.1 SINGULARITIES OF THE
PROJECTION 772 201 5.1.1 CLASSIFICATION OF PROJECTION SINGULARITIES 201
5.1.2 CLASSIFICATION OF ABNORMAL EXTREMALS 202 5.2 PROJECTION
SINGULARITIES FOR 77 3 209 5.2.1 THE EXTREMAL FRONT 211 A SOME TECHNICAL
PROOFS OF CHAPTER 2 219 A.I PROOF OF THEOREM 15, P. 60 219 A.2 PROOF OF
THEOREM 16, P. 60 221 A.3 PROOF OF PROPOSITION 3, P. 92 229 A.4 PROOF OF
PROPOSITION 4, P. 94 234 A.5 PROOF OF THEOREM 20, P. 113 236 B
BIDIMENSIONAL SOURCES 245 B.I LOCAL OPTIMAL SYNTHESIS AT THE SOURCE 246
B.2 THE LOCALLY CONTROLLABLE CASE AND SEMICONCAVITY OF THE MINIMUM TIME
FUNCTION 247 REFERENCES 251 INDEX 259 |
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| index_date | 2024-07-02T18:38:17Z |
| indexdate | 2024-07-09T21:06:08Z |
| institution | BVB |
| isbn | 3540203060 |
| language | English |
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| physical | XIII, 261 S. graph. Darst. |
| publishDate | 2004 |
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| publisher | Springer |
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| series | Mathématiques & applications |
| series2 | Mathématiques & applications |
| spelling | Boscain, Ugo Verfasser aut Optimal syntheses for control systems on 2-D manifolds Ugo Boscain ; Benedetto Piccoli Berlin [u.a.] Springer 2004 XIII, 261 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Mathématiques & applications 43 Literaturverz. S. 251 - 257 Control theory Geometry, Differential Mathematical optimization Topological manifolds Mannigfaltigkeit (DE-588)4037379-4 gnd rswk-swf Optimale Kontrolle (DE-588)4121428-6 gnd rswk-swf Dimension 2 (DE-588)4321721-7 gnd rswk-swf Geometrische Methode (DE-588)4156715-8 gnd rswk-swf Optimale Kontrolle (DE-588)4121428-6 s Geometrische Methode (DE-588)4156715-8 s Mannigfaltigkeit (DE-588)4037379-4 s Dimension 2 (DE-588)4321721-7 s DE-604 Piccoli, Benedetto Verfasser aut Mathématiques & applications 43 (DE-604)BV006642035 43 HEBIS Datenaustausch Darmstadt application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015991880&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Boscain, Ugo Piccoli, Benedetto Optimal syntheses for control systems on 2-D manifolds Mathématiques & applications Control theory Geometry, Differential Mathematical optimization Topological manifolds Mannigfaltigkeit (DE-588)4037379-4 gnd Optimale Kontrolle (DE-588)4121428-6 gnd Dimension 2 (DE-588)4321721-7 gnd Geometrische Methode (DE-588)4156715-8 gnd |
| subject_GND | (DE-588)4037379-4 (DE-588)4121428-6 (DE-588)4321721-7 (DE-588)4156715-8 |
| title | Optimal syntheses for control systems on 2-D manifolds |
| title_auth | Optimal syntheses for control systems on 2-D manifolds |
| title_exact_search | Optimal syntheses for control systems on 2-D manifolds |
| title_exact_search_txtP | Optimal syntheses for control systems on 2-D manifolds |
| title_full | Optimal syntheses for control systems on 2-D manifolds Ugo Boscain ; Benedetto Piccoli |
| title_fullStr | Optimal syntheses for control systems on 2-D manifolds Ugo Boscain ; Benedetto Piccoli |
| title_full_unstemmed | Optimal syntheses for control systems on 2-D manifolds Ugo Boscain ; Benedetto Piccoli |
| title_short | Optimal syntheses for control systems on 2-D manifolds |
| title_sort | optimal syntheses for control systems on 2 d manifolds |
| topic | Control theory Geometry, Differential Mathematical optimization Topological manifolds Mannigfaltigkeit (DE-588)4037379-4 gnd Optimale Kontrolle (DE-588)4121428-6 gnd Dimension 2 (DE-588)4321721-7 gnd Geometrische Methode (DE-588)4156715-8 gnd |
| topic_facet | Control theory Geometry, Differential Mathematical optimization Topological manifolds Mannigfaltigkeit Optimale Kontrolle Dimension 2 Geometrische Methode |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015991880&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV006642035 |
| work_keys_str_mv | AT boscainugo optimalsynthesesforcontrolsystemson2dmanifolds AT piccolibenedetto optimalsynthesesforcontrolsystemson2dmanifolds |