Dynamic optimization for beginners: with prerequisites and applications
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin
EMS Press
[2021]
|
| Series: | EMS textbooks in mathematics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | xi, 345 Seiten Illustrationen 23.5 cm x 16.5 cm |
| ISBN: | 9783985470129 398547012X |
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MARC
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| 020 | |a 9783985470129 |c Hb.: EUR 49.00 (DE), EUR 50.40 (AT) |9 978-3-98547-012-9 | ||
| 020 | |a 398547012X |9 3-98547-012-X | ||
| 024 | 3 | |a 978-3-98547-012-9 | |
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| 100 | 1 | |a Cannarsa, Piermarco |d 1957- |e Verfasser |0 (DE-588)17369361X |4 aut | |
| 245 | 1 | 0 | |a Dynamic optimization for beginners |b with prerequisites and applications |c Piermarco Cannarsa, Filippo Gazzola |
| 264 | 1 | |a Berlin |b EMS Press |c [2021] | |
| 300 | |a xi, 345 Seiten |b Illustrationen |c 23.5 cm x 16.5 cm | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a EMS textbooks in mathematics | |
| 650 | 0 | 7 | |a Dynamische Optimierung |0 (DE-588)4125677-3 |2 gnd |9 rswk-swf |
| 653 | |a optimal control | ||
| 653 | |a dynamic optimization | ||
| 653 | |a calculus of variations | ||
| 653 | |a Pontryagin minimum principle | ||
| 653 | |a Hamilton–Jacobi–Bellman equation | ||
| 653 | |a dynamic programming | ||
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Record in the Search Index
| _version_ | 1804182860608831488 |
|---|---|
| adam_text | CONTENTS
PREFACE
.....................................................................................................................
VII
1
ORDINARY
DIFFERENTIAL
EQUATIONS
....................................................................
1
1.1
DEFINITIONS
AND
MOTIVATIONS
.....................................................................
1
1.2
EXISTENCE
AND
UNIQUENESS
.......................................................................
3
1.3
SEPARABLE
EQUATIONS
................................................................................
4
1.4
FIRST-ORDER
LINEAR
EQUATIONS
....................................................................
6
1.5
BERNOULLI
EQUATIONS
....................................................................................
8
1.6
EXTENSION
OF
THE
SOLUTIONS
.......................................................................
10
1.7
SECOND-ORDER
LINEAR
EQUATIONS
WITH
CONSTANT
COEFFICIENTS
.......................
11
1.8
EULER
AND
RICCATI
EQUATIONS
....................................................................
16
1.9
LINEAR
DIFFERENTIAL
SYSTEMS
.......................................................................
18
1.10
LINEAR
HOMOGENEOUS
SYSTEMS
..................................................................
20
1.11
HOMOGENEOUS
SYSTEMS
WITH
CONSTANT
COEFFICIENTS
................................
22
1.12
NONHOMOGENEOUS
SYSTEMS
.......................................................................
24
2
FUNCTIONAL
ANALYSIS
..........................................................................................
27
2.1
VECTOR
SPACES
AND
NORMS
.........................................................................
27
2.2
BANACH
SPACES
..........................................................................................
31
2.3
LINEAR
OPERATORS
AND
DUAL
SPACES
.............................................................
34
2.4
HILBERT
SPACES
..........................................................................................
37
2.5
ORTHOGONAL
PROJECTIONS
IN
A
HILBERT
SPACE
..............................................
41
2.6
SEPARABLE
SPACES
.....................................................................................
46
2.7
L
P
SPACES
AND
DISTRIBUTIONS
....................................................................
50
2.8
FOURIER
SERIES
.............................................................................................
58
2.9
FIXED
POINTS
AND
DISCRETE
DYNAMICAL
SYSTEMS
.......................................
62
2.10
THE
PEANO-PICARD
EXISTENCE
AND
UNIQUENESS
THEOREM
...........................
67
3
FIRST-ORDER
PARTIAL
DIFFERENTIAL
EQUATIONS
...................................................
71
3.1
A
PHYSICAL
MODEL
LEADING
TO
TRANSPORT
EQUATIONS
..................................
71
3.2
MORE
GENERAL
LINEAR
EQUATIONS
...............................................................
74
3.3
CAUCHY PROBLEMS
FOR
A CLASS
OF
NONLINEAR
EQUATIONS
.............................
79
3.4
CLASSICAL
SOLUTIONS
OF
NONLINEAR
CONSERVATION
LAW
EQUATIONS
...............
80
3.5
WEAK
SOLUTIONS
OF
NONLINEAR
CONSERVATION
LAW
EQUATIONS
......................
84
3.6
CHARACTERISTICS
FOR
THE
HAMILTON-JACOBI-BELLMAN
EQUATION
.................
92
X
CONTENTS
4
CALCULUS
OF
VARIATIONS
......................................................................................
97
4.1
EXAMPLES
OF
FUNCTIONALS
IN
THE
CALCULUS
OF
VARIATIONS
............................
97
4.2
THE FRECHET
AND
GATEAUX
DERIVATIVES
.........................................................
100
4.3
CONVEX
FUNCTIONALS
......................................................................................
102
4.4
THE
EULER-LAGRANGE
EQUATION
.....................................................................
106
4.5
PARTICULAR
CASES
OF
THE
EULER-LAGRANGE
EQUATION
.....................................
109
4.6
EXTREMALS
IN
THE
SPACE
OF
PIECEWISE
SMOOTH
FUNCTIONS
...........................
112
4.7
SUFFICIENT
CONDITIONS
FOR
LOCAL
OPTIMALITY
.................................................
116
4.8
CONSTRAINED
OPTIMIZATION
............................................................................
122
4.9
HIGHER
ORDER
PROBLEMS
AND
SYSTEMS
...........................................................
125
4.10
HAMILTONIAN
MECHANICS
AND
POINTWISE
CONSTRAINTS
..................................
129
5
LINEAR
CONTROL
THEORY
........................................................................................
131
5.1
SOME
IL
LUSTRATIVE
EXAMPLES
..........................................................................
131
5.2
GEOMETRIC
SOLUTIONS
OF
CONTROL
PROBLEMS:
A
RAILROAD
ROCKET
CAR
............
135
5.3
THE
BANG-BANG
PRINCIPLE
FOR LINEAR
CONTROL
PROBLEMS
..............................
137
5.4
LINEAR
PROBLEMS
WITH
UNRESTRICTED
CONTROL
SPACE
.....................................
143
5.5
OPTIMAL
CONTROLS
WITH
TIME
PAYOFF
FOR
LINEAR
PROBLEMS
...........................
149
5.6
THE
PONTRYAGIN
MINIMUM
PRINCIPLE
FOR LINEAR
PROBLEMS
..........................
151
5.7
HAMILTONIANS
AND
THE
PONTRYAGIN
MINIMUM
PRINCIPLE
..............................
156
6
NONLINEAR
CONTROL
PROBLEMS
...............................................................................
161
6.1
THREE
PROBLEMS
IN
OPTIMAL
CONTROL
...........................................................
161
6.2
PMP
FOR
THE
MAYER
PROBLEM WITH
FIXED
HORIZON
.......................................
164
6.3
PMP
FOR
THE
BOLZA
PROBLEM
.......................................................................
171
6.4
SOME
EXAMPLES
AND
APPLICATIONS
OF
THE
PMP
..........................................
174
6.5
CURRENT
VALUE
PMP
......................................................................................
179
6.6
PMP
WITH
FREE
HORIZON
...............................................................................
181
6.7
PMP
WITH
TRANSVERSALITY
CONDITIONS
...........................................................
184
6.8
ROAD
ON
A
MOUNTAIN
....................................................................................
191
6.9
THE
MINIMAL
FUEL
MOON
LANDER
CONTROL
PROBLEM
.......................................
192
6.10
OPTIMAL
LOCKDOWN
STRATEGIES
FOR
PANDEMIC
VIRUSES
..................................
204
7
DYNAMIC
PROGRAMMING
......................................................................................
215
7.1
FROM
THE
PMP
TO
DYNAMIC
PROGRAMMING
.................................................
215
7.2
THE
VALUE
FUNCTION
......................................................................................216
7.3
THE
HAMILTON-JACOBI-BELLMAN
EQUATION
.................................................
220
7.4
SOME
APPLICATIONS
OF
THE
DYNAMIC
PROGRAMMING
METHOD
......................
225
7.5
POSSIBLE
FAILURES
OF
THE
DYNAMIC
PROGRAMMING
METHOD
...........................234
7.6
LINEAR
QUADRATIC
REGULATORS
.......................................................................
236
CONTENTS
XI
8
SOLVED
EXERCISES
.................................................................................................
241
8.1
ORDINARY
DIFFERENTIAL
EQUATIONS
..................................................................
241
8.2
FUNCTIONAL
ANALYSIS
.....................................................................................
257
8.3
FIRST-ORDER
PARTIAL
DIFFERENTIAL
EQUATIONS
...................................................
274
8.4
CALCULUS
OF
VARIATIONS
................................................................................
278
8.5
CONTROL
THEORY
............................................................................................
299
8.6
DYNAMIC
PROGRAMMING
..............................................................................
324
APPENDIX
...................................................................................................................
335
A.L
THE
LAGRANGE
MULTIPLIER
METHOD
IN
R
2
...................................................
335
A.2
POWER
SERIES
EXPANSION
OF
SOME
ANALYTIC
FUNCTIONS
...............................
338
A.3
THE
CAYLEY-HAMILTON
THEOREM
.................................................................
339
A.4
BIBLIOGRAPHICAL
NOTES
...............................................................................340
REFERENCES
...................................................................................................................
341
INDEX
..........................................................................................................................
343
|
| adam_txt |
CONTENTS
PREFACE
.
VII
1
ORDINARY
DIFFERENTIAL
EQUATIONS
.
1
1.1
DEFINITIONS
AND
MOTIVATIONS
.
1
1.2
EXISTENCE
AND
UNIQUENESS
.
3
1.3
SEPARABLE
EQUATIONS
.
4
1.4
FIRST-ORDER
LINEAR
EQUATIONS
.
6
1.5
BERNOULLI
EQUATIONS
.
8
1.6
EXTENSION
OF
THE
SOLUTIONS
.
10
1.7
SECOND-ORDER
LINEAR
EQUATIONS
WITH
CONSTANT
COEFFICIENTS
.
11
1.8
EULER
AND
RICCATI
EQUATIONS
.
16
1.9
LINEAR
DIFFERENTIAL
SYSTEMS
.
18
1.10
LINEAR
HOMOGENEOUS
SYSTEMS
.
20
1.11
HOMOGENEOUS
SYSTEMS
WITH
CONSTANT
COEFFICIENTS
.
22
1.12
NONHOMOGENEOUS
SYSTEMS
.
24
2
FUNCTIONAL
ANALYSIS
.
27
2.1
VECTOR
SPACES
AND
NORMS
.
27
2.2
BANACH
SPACES
.
31
2.3
LINEAR
OPERATORS
AND
DUAL
SPACES
.
34
2.4
HILBERT
SPACES
.
37
2.5
ORTHOGONAL
PROJECTIONS
IN
A
HILBERT
SPACE
.
41
2.6
SEPARABLE
SPACES
.
46
2.7
L
P
SPACES
AND
DISTRIBUTIONS
.
50
2.8
FOURIER
SERIES
.
58
2.9
FIXED
POINTS
AND
DISCRETE
DYNAMICAL
SYSTEMS
.
62
2.10
THE
PEANO-PICARD
EXISTENCE
AND
UNIQUENESS
THEOREM
.
67
3
FIRST-ORDER
PARTIAL
DIFFERENTIAL
EQUATIONS
.
71
3.1
A
PHYSICAL
MODEL
LEADING
TO
TRANSPORT
EQUATIONS
.
71
3.2
MORE
GENERAL
LINEAR
EQUATIONS
.
74
3.3
CAUCHY PROBLEMS
FOR
A CLASS
OF
NONLINEAR
EQUATIONS
.
79
3.4
CLASSICAL
SOLUTIONS
OF
NONLINEAR
CONSERVATION
LAW
EQUATIONS
.
80
3.5
WEAK
SOLUTIONS
OF
NONLINEAR
CONSERVATION
LAW
EQUATIONS
.
84
3.6
CHARACTERISTICS
FOR
THE
HAMILTON-JACOBI-BELLMAN
EQUATION
.
92
X
CONTENTS
4
CALCULUS
OF
VARIATIONS
.
97
4.1
EXAMPLES
OF
FUNCTIONALS
IN
THE
CALCULUS
OF
VARIATIONS
.
97
4.2
THE FRECHET
AND
GATEAUX
DERIVATIVES
.
100
4.3
CONVEX
FUNCTIONALS
.
102
4.4
THE
EULER-LAGRANGE
EQUATION
.
106
4.5
PARTICULAR
CASES
OF
THE
EULER-LAGRANGE
EQUATION
.
109
4.6
EXTREMALS
IN
THE
SPACE
OF
PIECEWISE
SMOOTH
FUNCTIONS
.
112
4.7
SUFFICIENT
CONDITIONS
FOR
LOCAL
OPTIMALITY
.
116
4.8
CONSTRAINED
OPTIMIZATION
.
122
4.9
HIGHER
ORDER
PROBLEMS
AND
SYSTEMS
.
125
4.10
HAMILTONIAN
MECHANICS
AND
POINTWISE
CONSTRAINTS
.
129
5
LINEAR
CONTROL
THEORY
.
131
5.1
SOME
IL
LUSTRATIVE
EXAMPLES
.
131
5.2
GEOMETRIC
SOLUTIONS
OF
CONTROL
PROBLEMS:
A
RAILROAD
ROCKET
CAR
.
135
5.3
THE
BANG-BANG
PRINCIPLE
FOR LINEAR
CONTROL
PROBLEMS
.
137
5.4
LINEAR
PROBLEMS
WITH
UNRESTRICTED
CONTROL
SPACE
.
143
5.5
OPTIMAL
CONTROLS
WITH
TIME
PAYOFF
FOR
LINEAR
PROBLEMS
.
149
5.6
THE
PONTRYAGIN
MINIMUM
PRINCIPLE
FOR LINEAR
PROBLEMS
.
151
5.7
HAMILTONIANS
AND
THE
PONTRYAGIN
MINIMUM
PRINCIPLE
.
156
6
NONLINEAR
CONTROL
PROBLEMS
.
161
6.1
THREE
PROBLEMS
IN
OPTIMAL
CONTROL
.
161
6.2
PMP
FOR
THE
MAYER
PROBLEM WITH
FIXED
HORIZON
.
164
6.3
PMP
FOR
THE
BOLZA
PROBLEM
.
171
6.4
SOME
EXAMPLES
AND
APPLICATIONS
OF
THE
PMP
.
174
6.5
CURRENT
VALUE
PMP
.
179
6.6
PMP
WITH
FREE
HORIZON
.
181
6.7
PMP
WITH
TRANSVERSALITY
CONDITIONS
.
184
6.8
ROAD
ON
A
MOUNTAIN
.
191
6.9
THE
MINIMAL
FUEL
MOON
LANDER
CONTROL
PROBLEM
.
192
6.10
OPTIMAL
LOCKDOWN
STRATEGIES
FOR
PANDEMIC
VIRUSES
.
204
7
DYNAMIC
PROGRAMMING
.
215
7.1
FROM
THE
PMP
TO
DYNAMIC
PROGRAMMING
.
215
7.2
THE
VALUE
FUNCTION
.216
7.3
THE
HAMILTON-JACOBI-BELLMAN
EQUATION
.
220
7.4
SOME
APPLICATIONS
OF
THE
DYNAMIC
PROGRAMMING
METHOD
.
225
7.5
POSSIBLE
FAILURES
OF
THE
DYNAMIC
PROGRAMMING
METHOD
.234
7.6
LINEAR
QUADRATIC
REGULATORS
.
236
CONTENTS
XI
8
SOLVED
EXERCISES
.
241
8.1
ORDINARY
DIFFERENTIAL
EQUATIONS
.
241
8.2
FUNCTIONAL
ANALYSIS
.
257
8.3
FIRST-ORDER
PARTIAL
DIFFERENTIAL
EQUATIONS
.
274
8.4
CALCULUS
OF
VARIATIONS
.
278
8.5
CONTROL
THEORY
.
299
8.6
DYNAMIC
PROGRAMMING
.
324
APPENDIX
.
335
A.L
THE
LAGRANGE
MULTIPLIER
METHOD
IN
R
2
.
335
A.2
POWER
SERIES
EXPANSION
OF
SOME
ANALYTIC
FUNCTIONS
.
338
A.3
THE
CAYLEY-HAMILTON
THEOREM
.
339
A.4
BIBLIOGRAPHICAL
NOTES
.340
REFERENCES
.
341
INDEX
.
343 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Cannarsa, Piermarco 1957- Gazzola, Filippo |
| author_GND | (DE-588)17369361X (DE-588)123905133 |
| author_facet | Cannarsa, Piermarco 1957- Gazzola, Filippo |
| author_role | aut aut |
| author_sort | Cannarsa, Piermarco 1957- |
| author_variant | p c pc f g fg |
| building | Verbundindex |
| bvnumber | BV047517664 |
| classification_rvk | SK 880 |
| ctrlnum | (OCoLC)1275377393 (DE-599)DNB1242488685 |
| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| format | Book |
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| id | DE-604.BV047517664 |
| illustrated | Illustrated |
| index_date | 2024-07-03T18:23:35Z |
| indexdate | 2024-07-10T09:14:16Z |
| institution | BVB |
| institution_GND | (DE-588)1066118477 |
| isbn | 9783985470129 398547012X |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-032918391 |
| oclc_num | 1275377393 |
| open_access_boolean | |
| owner | DE-634 DE-706 DE-739 DE-703 DE-188 |
| owner_facet | DE-634 DE-706 DE-739 DE-703 DE-188 |
| physical | xi, 345 Seiten Illustrationen 23.5 cm x 16.5 cm |
| publishDate | 2021 |
| publishDateSearch | 2021 |
| publishDateSort | 2021 |
| publisher | EMS Press |
| record_format | marc |
| series2 | EMS textbooks in mathematics |
| spelling | Cannarsa, Piermarco 1957- Verfasser (DE-588)17369361X aut Dynamic optimization for beginners with prerequisites and applications Piermarco Cannarsa, Filippo Gazzola Berlin EMS Press [2021] xi, 345 Seiten Illustrationen 23.5 cm x 16.5 cm txt rdacontent n rdamedia nc rdacarrier EMS textbooks in mathematics Dynamische Optimierung (DE-588)4125677-3 gnd rswk-swf optimal control dynamic optimization calculus of variations Pontryagin minimum principle Hamilton–Jacobi–Bellman equation dynamic programming Dynamische Optimierung (DE-588)4125677-3 s DE-604 Gazzola, Filippo Verfasser (DE-588)123905133 aut European Mathematical Society Publishing House ETH-Zentrum SEW A27 (DE-588)1066118477 pbl Erscheint auch als Online-Ausgabe 978-3-98547-512-4 (DE-604)BV047500374 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=032918391&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p vlb 20211005 DE-101 https://d-nb.info/provenance/plan#vlb |
| spellingShingle | Cannarsa, Piermarco 1957- Gazzola, Filippo Dynamic optimization for beginners with prerequisites and applications Dynamische Optimierung (DE-588)4125677-3 gnd |
| subject_GND | (DE-588)4125677-3 |
| title | Dynamic optimization for beginners with prerequisites and applications |
| title_auth | Dynamic optimization for beginners with prerequisites and applications |
| title_exact_search | Dynamic optimization for beginners with prerequisites and applications |
| title_exact_search_txtP | Dynamic optimization for beginners with prerequisites and applications |
| title_full | Dynamic optimization for beginners with prerequisites and applications Piermarco Cannarsa, Filippo Gazzola |
| title_fullStr | Dynamic optimization for beginners with prerequisites and applications Piermarco Cannarsa, Filippo Gazzola |
| title_full_unstemmed | Dynamic optimization for beginners with prerequisites and applications Piermarco Cannarsa, Filippo Gazzola |
| title_short | Dynamic optimization for beginners |
| title_sort | dynamic optimization for beginners with prerequisites and applications |
| title_sub | with prerequisites and applications |
| topic | Dynamische Optimierung (DE-588)4125677-3 gnd |
| topic_facet | Dynamische Optimierung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=032918391&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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