Optimal control and the calculus of variations:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Oxford [u.a.]
Oxford Univ. Press
2002
|
| Edition: | Reprinted |
| Series: | Oxford science publications
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | VIII, 234 S. graph. Darst. |
| ISBN: | 0198514891 |
Staff View
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Record in the Search Index
| _version_ | 1804141033491005440 |
|---|---|
| adam_text | Contents
1
Introduction
1
The maxima and minima of functions
1
The calculus of variations
4
Optimal control
9
2
Optimization In
IR
13
Functions of one variable
13
Critical points, end-points, and points of discontinuity
16
Functions of several variables
18
Minimization with constraints
22
Å
geometrical interpretation
25
Distinguishing maxima from minima
28
3
The calculus of variations
33
The fixed end-point problem
33
Problems in which the end-points are not fixed
41
Finding minimizing curves
46
Isoperimetric problems
54
Sufficiency conditions
58
Fields of extremals
59
Hubert s invariant integral
62
Semi-fields and the Jacobi condition
66
4
Optimal control I: Theory
70
Introduction
70
Control of a simple first-order system
70
Systems governed by ordinary differential equations
72
The optimal control problem
74
The Pontryagin maximum principle
80
Optimal control to target curves
100
5
Optimal control II: Applications
103
Introduction
103
Time-optimal control of linear systems
103
Optimal control to target curves
139
Singular controls
149
VIU
CONTENTS
Fuel-optimal control
151
Problems where the cost depends on x(tt)
159
Linear systems with quadratic cost
163
The steady-state Riccati equation
168
The calculus of variations revisited
170
6
Proof of the maximum principle of Pontryagin
175
Convex sets in R
176
The linearized state equations
182
The behaviour of
H on
an optimal path
184
Sufficiency conditions for optimal control
206
Appendix: Answers and hints for the exercises
208
Bibliography
231
Index
233
|
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| id | DE-604.BV036009174 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T22:09:26Z |
| institution | BVB |
| isbn | 0198514891 |
| language | English |
| lccn | 92027772 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-018901428 |
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| owner_facet | DE-703 DE-11 |
| physical | VIII, 234 S. graph. Darst. |
| publishDate | 2002 |
| publishDateSearch | 2002 |
| publishDateSort | 2002 |
| publisher | Oxford Univ. Press |
| record_format | marc |
| series2 | Oxford science publications |
| spelling | Pinch, Enid R. Verfasser aut Optimal control and the calculus of variations Enid R. Pinch Reprinted Oxford [u.a.] Oxford Univ. Press 2002 VIII, 234 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Oxford science publications Calculus of variations Control theory Variationsrechnung (DE-588)4062355-5 gnd rswk-swf Optimale Kontrolle (DE-588)4121428-6 gnd rswk-swf Variationsrechnung (DE-588)4062355-5 s Optimale Kontrolle (DE-588)4121428-6 s DE-604 Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018901428&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Pinch, Enid R. Optimal control and the calculus of variations Calculus of variations Control theory Variationsrechnung (DE-588)4062355-5 gnd Optimale Kontrolle (DE-588)4121428-6 gnd |
| subject_GND | (DE-588)4062355-5 (DE-588)4121428-6 |
| title | Optimal control and the calculus of variations |
| title_auth | Optimal control and the calculus of variations |
| title_exact_search | Optimal control and the calculus of variations |
| title_full | Optimal control and the calculus of variations Enid R. Pinch |
| title_fullStr | Optimal control and the calculus of variations Enid R. Pinch |
| title_full_unstemmed | Optimal control and the calculus of variations Enid R. Pinch |
| title_short | Optimal control and the calculus of variations |
| title_sort | optimal control and the calculus of variations |
| topic | Calculus of variations Control theory Variationsrechnung (DE-588)4062355-5 gnd Optimale Kontrolle (DE-588)4121428-6 gnd |
| topic_facet | Calculus of variations Control theory Variationsrechnung Optimale Kontrolle |
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