Control theory from the geometric viewpoint:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
2004
|
| Series: | Encyclopaedia of mathematical sciences
87 Encyclopaedia of mathematical sciences Control theory and optimization ; 2 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIV, 412 S. graph. Darst. |
| ISBN: | 3540210199 |
Staff View
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| 100 | 1 | |a Agračev, Andreij A. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Control theory from the geometric viewpoint |c Andrei A. Agrachev ; Yuri L. Sachkov |
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Record in the Search Index
| _version_ | 1804130554485932032 |
|---|---|
| adam_text | ANDREI A. AGRACHEV
YURI L. SACHKOV
CONTROL THEOR
Y
FROM TH
E GEOMETRIE
VIEWPOINT
SPRINGER
I
CONTENT
S
1 VECTO
R FIELD
S AN
D CONTRO
L SYSTEM
S O
N SMOOT
H MANIFOLD
S .
. 1
1.1 SMOOT
H MANIFOLDS 1
1.2 VECTOR FIELDS ON SMOOT
H MANIFOLDS 4
1.3 SMOOT
H DIFFERENTIAL EQUATION
S AN
D FLOWS ON MANIFOLDS 8
1.4 CONTRO
L SYSTEM
S 12
2 ELEMENT
S O
F CHRONOLOGICA
L CALCULU
S 21
2.1 POINTS
, DIFFEOMORPHISMS, AN
D VECTOR FIELDS 21
2.2 SEMINORM
S AN
D C (M)-TOPOLOG
Y 25
2.3 FAMILIES OF FUNCTIONAL
S AN
D OPERATOR
S 26
2.4 CHRONOLOGICAL EXPONENTIA
L 28
2.5 ACTIO
N OF DIFFEOMORPHISMS ON VECTOR FIELDS 37
2.6 COMMUTATIO
N OF FLOWS 40
2.7 VARIATION
S FORMUL
A 41
2.8 DERIVATIVE OF FLOW WIT
H RESPECT T
O PARAMETE
R 43
3 LINEA
R SYSTEM
S 47
3.1 CAUCHY
S FORMUL
A FOR LINEAR SYSTEM
S 47
3.2 CONTROLLABILIT
Y OF LINEA
R SYSTEM
S 49
4 STAT
E LINEARIZABILIT
Y O
F NONLINEA
R SYSTEM
S 53
4.
1 LOCAL LINEARIZABILIT
Y 53
4.2 GLOBA
L LINEARIZABILIT
Y 57
5 TH
E ORBI
T THEORE
M AN
D IT
S APPLICATION
S 63
5.1 FORMULATIO
N OF TH
E ORBI
T THEORE
M 63
5.2 IMMERSE
D SUBMANIFOLD
S 64
5.3 COROLLARIES OF TH
E ORBI
T THEORE
M 66
5.4 PROOF OF TH
E ORBI
T THEORE
M 67
5.5 ANALYTI
C CASE 72
5.6 FROBENIUS THEORE
M 74
XII CONTENTS
5.7 STAT
E EQUIVALENC
E OF CONTRO
L SYSTEMS 76
6 ROTATION
S O
F TH
E RIGI
D BOD
Y 81
6.1 STAT
E SPACE 81
6.2 EULER EQUATION
S 84
6.3 PHAS
E PORTRAI
T 88
6.4 CONTROLLE
D RIGI
D BODY
: ORBIT
S 90
7 CONTRO
L O
F CONFIGURATION
S 97
7.1 MODEL 97
7.2 TWO FREE POINT
S 100
7.3 THRE
E FREE POINT
S 101
7.4 BROKEN LINE 104
8 ATTAINABL
E SET
S 109
8.1 ATTAINABL
E SET
S OF FUELL-RAN
K SYSTEMS 109
8.2 COMPATIBL
E VECTOR FIELD
S AN
D RELAXATION
S 113
8.3 POISSON STABILIT
Y 116
8.4 CONTROLLED RIGID BODY
: ATTAINABL
E SETS , 118
9 FEEDBAC
K AN
D STAT
E EQUIVALENC
E O
F CONTRO
L SYSTEM
S 121
9.1 FEEDBACK EQUIVALENC
E 121
9.2 LINEAR SYSTEM
S 123
9.3 STATE-FEEDBAC
K LINEARIZABILIT
Y 131
1
0 OPTIMA
L CONTRO
L PROBLE
M 137
10.1 PROBLE
M STATEMEN
T 137
10.2 REDUCTIO
N T
O STUD
Y OF ATTAINABL
E SETS 138
10.3 COMPACTNES
S OF ATTAINABL
E SETS 140
10.4 TIME-OPTIMA
L PROBLE
M 143
10.5 RELAXATION
S 143
1
1 ELEMENT
S O
F EXTERIO
R CALCULU
S AN
D SYMPLECTI
C GEOMETR
Y . . 145
11.1 DIFFERENTIAL 1-FORMS 145
11.2 DIFFERENTIAL A;-FORMS 147
11.3 EXTERIO
R DIFFERENTIAL . 151
11.4 LIE DERIVATIV
E OF DIFFERENTIAL FORMS 153
11.5 ELEMENT
S OF SYMPLECTI
C GEOMETR
Y 157
1
2 PONTRYAGI
N MAXIMU
M PRINCIPL
E 167
12.1 GEOMETRI
E STATEMEN
T OF PM
P AN
D DISCUSSION 167
12.2 PROO
F OF PM
P 172
12.3 GEOMETRI
E STATEMEN
T OF PM
P FOR FREE TIM
E 177
12.4 PM
P FOR OPTIMA
L CONTRO
L PROBLEM
S 179
12.5 PM
P WIT
H GENERA
L BOUNDAR
Y CONDITION
S 182
CONTENTS XIII
1
3 EXAMPLE
S O
F OPTIMA
L CONTRO
L PROBLEM
S 191
13.1 TH
E FASTES
T STO
P OF A TRAI
N A
T A STATIO
N 191
13.2 CONTRO
L OF A LINEA
R OSCILLATOR 194
13.3 TH
E CHEAPES
T STO
P OF A TRAI
N 197
13.4 CONTRO
L OF A LINEA
R OSCILLATOR WIT
H COST 199
13.5 DUBIN
S CA
R 200
1
4 HAMILTONIA
N SYSTEM
S WIT
H CONVE
X HAMILTONIAN
S 207
1
5 LINEA
R TIME-OPTIMA
L PROBLE
M 211
15.1 PROBLE
M STATEMEN
T 211
15.2 GEOMETR
Y OF POLYTOPE
S 212
15.3 BANG-BAN
G THEORE
M 213
15.4 UNIQUENES
S OF OPTIMA
L CONTROL
S AN
D EXTREMAI
S 215
15.5 SWITCHINGS OF OPTIMA
L CONTRO
L 218
1
6 LINEAR-QUADRATI
C PROBLE
M 223
16.1 PROBLE
M STATEMEN
T 223
16.2 EXISTENC
E OF OPTIMA
L CONTRO
L 224
16.3 EXTREMAI
S 227
16.4 CONJUGAT
E POINT
S 229
17 SUFFICIEN
T OPTIMALIT
Y CONDITIONS
, HAMILTON-JACOB
I
EQUATION
, AN
D DYNAMI
C PROGRAMMIN
G 235
17.1 SUFFICIENT OPTIMALIT
Y CONDITION
S 235
17.2 HAMILTON-JACOB
I EQUATIO
N 242
17.3 DYNAMI
C PROGRAMMIN
G 244
18 HAMILTONIA
N SYSTEM
S FO
R GEOMETRI
E OPTIMA
L CONTRO
L
PROBLEM
S 247
18.1 HAMILTONIA
N SYSTEM
S ON TRIVIALIZED COTANGEN
T BUENDL
E 247
18.2 LIE GROUP
S 255
18.3 HAMILTONIA
N SYSTEM
S ON LIE GROUP
S 260
19 EXAMPLE
S O
F OPTIMA
L CONTRO
L PROBLEM
S O
N COMPAC
T LI
E
GROUP
S 265
19.1 RIEMANNIA
N PROBLE
M 265
19.2 A SUB-RIEMANNIA
N PROBLE
M 267
19.3 CONTRO
L OF QUANTU
M SYSTEMS 271
19.4 A TIME-OPTIMA
L PROBLE
M ON SO(3) 284
2
0 SECON
D ORDE
R OPTIMALIT
Y CONDITION
S 293
20.1 HESSIAN 293
20.2 LOCAL OPENNES
S OF MAPPING
S 297
20.3 DIFFERENTIATION OF TH
E ENDPOIN
T MAPPIN
G 304
20.4 NECESSARY OPTIMALIT
Y CONDITION
S 309
XIV CONTENTS
20.5 APPLICATION
S 318
20.6 SINGLE-INPU
T CASE 321
2
1 JACOB
I EQUATIO
N 333
21.1 REGULAE
R CASE
: DERIVATIO
N OF JACOB
I EQUATIO
N 334
21.2 SINGULA
R CASE
: DERIVATION OF JACOB
I EQUATIO
N 338
21.3 NECESSARY OPTIMALIT
Y CONDITION
S 342
21.4 REGULAE
R CASE
: TRANSFORMATIO
N OF JACOB
I EQUATIO
N 343
21.5 SUFFICIENT OPTIMALIT
Y CONDITION
S 346
2
2 REDUCTIO
N 355
22.1 REDUCTIO
N 355
22.2 RIGI
D BOD
Y CONTRO
L 358
22.3 ANGULA
R VELOCITY CONTRO
L .35
9
2
3 CURVATUR
E 363
23.1 CURVATUR
E OF 2-DIMENSIONAL SYSTEM
S 363
23.2 CURVATUR
E OF 3-DIMENSIONAL CONTROL-AFFINE SYSTEM
S 373
2
4 ROLLIN
G BODIE
S 377
24.1 GEOMETRI
E MODEL 377
24.2 TWO-DIMENSIONA
L RIEMANNIA
N GEOMETR
Y 379
24.3 ADMISSIBL
E VELOCITIES 383
24.4 CONTROLLABILIT
Y 384
24.5 LENGT
H MINIMIZATIO
N PROBLE
M 387
A APPENDI
X 393
A.
L HOMOMORPHISM
S AN
D OPERATOR
S IN C
CO
{M) 393
A.2 REMAINDE
R TER
M OF TH
E CHRONOLOGICAL EXPONENTIA
L 395
REFERENCE
S 399
LIS
T O
F FIGURE
S 407
INDE
X 409
|
| any_adam_object | 1 |
| author | Agračev, Andreij A. Sačkov, Jurij L. |
| author_facet | Agračev, Andreij A. Sačkov, Jurij L. |
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| building | Verbundindex |
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| ctrlnum | (OCoLC)633967705 (DE-599)BVBBV017889220 |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV017889220 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T19:22:53Z |
| institution | BVB |
| isbn | 3540210199 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-010729477 |
| oclc_num | 633967705 |
| open_access_boolean | |
| owner | DE-29T DE-19 DE-BY-UBM DE-384 DE-573 DE-20 DE-91G DE-BY-TUM DE-634 DE-11 |
| owner_facet | DE-29T DE-19 DE-BY-UBM DE-384 DE-573 DE-20 DE-91G DE-BY-TUM DE-634 DE-11 |
| physical | XIV, 412 S. graph. Darst. |
| publishDate | 2004 |
| publishDateSearch | 2004 |
| publishDateSort | 2004 |
| publisher | Springer |
| record_format | marc |
| series | Encyclopaedia of mathematical sciences |
| series2 | Encyclopaedia of mathematical sciences Encyclopaedia of mathematical sciences : Control theory and optimization |
| spelling | Agračev, Andreij A. Verfasser aut Control theory from the geometric viewpoint Andrei A. Agrachev ; Yuri L. Sachkov Berlin [u.a.] Springer 2004 XIV, 412 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Encyclopaedia of mathematical sciences 87 Encyclopaedia of mathematical sciences : Control theory and optimization 2 Kontrolltheorie (DE-588)4032317-1 gnd rswk-swf System von gewöhnlichen Differentialgleichungen (DE-588)4116671-1 gnd rswk-swf Differentialgeometrie (DE-588)4012248-7 gnd rswk-swf Gewöhnliche Differentialgleichung (DE-588)4020929-5 gnd rswk-swf Kontrolltheorie (DE-588)4032317-1 s System von gewöhnlichen Differentialgleichungen (DE-588)4116671-1 s Differentialgeometrie (DE-588)4012248-7 s DE-604 Gewöhnliche Differentialgleichung (DE-588)4020929-5 s 1\p DE-604 Sačkov, Jurij L. Verfasser aut Encyclopaedia of mathematical sciences 87 (DE-604)BV024126459 87 Encyclopaedia of mathematical sciences Control theory and optimization ; 2 (DE-604)BV019270591 2 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010729477&sequence=000001&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 | Agračev, Andreij A. Sačkov, Jurij L. Control theory from the geometric viewpoint Encyclopaedia of mathematical sciences Kontrolltheorie (DE-588)4032317-1 gnd System von gewöhnlichen Differentialgleichungen (DE-588)4116671-1 gnd Differentialgeometrie (DE-588)4012248-7 gnd Gewöhnliche Differentialgleichung (DE-588)4020929-5 gnd |
| subject_GND | (DE-588)4032317-1 (DE-588)4116671-1 (DE-588)4012248-7 (DE-588)4020929-5 |
| title | Control theory from the geometric viewpoint |
| title_auth | Control theory from the geometric viewpoint |
| title_exact_search | Control theory from the geometric viewpoint |
| title_full | Control theory from the geometric viewpoint Andrei A. Agrachev ; Yuri L. Sachkov |
| title_fullStr | Control theory from the geometric viewpoint Andrei A. Agrachev ; Yuri L. Sachkov |
| title_full_unstemmed | Control theory from the geometric viewpoint Andrei A. Agrachev ; Yuri L. Sachkov |
| title_short | Control theory from the geometric viewpoint |
| title_sort | control theory from the geometric viewpoint |
| topic | Kontrolltheorie (DE-588)4032317-1 gnd System von gewöhnlichen Differentialgleichungen (DE-588)4116671-1 gnd Differentialgeometrie (DE-588)4012248-7 gnd Gewöhnliche Differentialgleichung (DE-588)4020929-5 gnd |
| topic_facet | Kontrolltheorie System von gewöhnlichen Differentialgleichungen Differentialgeometrie Gewöhnliche Differentialgleichung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010729477&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV024126459 (DE-604)BV019270591 |
| work_keys_str_mv | AT agracevandreija controltheoryfromthegeometricviewpoint AT sackovjurijl controltheoryfromthegeometricviewpoint |