Optimal control: an introduction to the theory with applications
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Oxford
Clarendon Press
1997
|
| Edition: | Reprinted (with corr.) |
| Series: | Oxford applied mathematics and computing science series
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIV, 254 S. graph. Darst. |
| ISBN: | 0198596758 0198596820 |
Staff View
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Record in the Search Index
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| adam_text | LESLIE M. HOCKING DEPARTMENT OF MATHEMATICS, UNIVERSITY COLLEGE LONDON
OPTIMAL CONTROL AN INTRODUCTION TO THE THEORY WITH APPLICATIONS
CLARENDON PRESS * OXFORD CONTENTS 1 OPTIMAL CONTROL PROBLEMS 1.1
INTRODUCTION L 1.2 PLANT GROWTH 2 1.3 GENERAL FORMULATION 4 1.4 THE
POSITIONING PROBLEM 7 1.5 DIABETES MELLITUS 9 EXERCISES 1 12 2 SYSTEMS
OF DIFFERENTIAL EQUATIONS, MATRICES, AND SETS 2.1 ORDINARY DIFFERENTIAL
EQUATIONS 14 2.2 LINEAR DIFFERENTIAL EQUATIONS 16 2.3 AUTONOMOUS SYSTEMS
19 2.4 THE ADJOINT SYSTEM 20 2.5 VECTORS AND MATRICES 21 2.6 CONVEX SETS
24 EXERCISES 2 27 PART A TIME-OPTIMAL CONTROL OF LINEAR SYSTEMS 3
CONTROLLABILITY 3.1 THE CONTROLLABLE SET 30 3.2 CONTROLLABILITY FOR THE
LINEAR SYSTEM 33 3.3 THE CONTROLLABILITY MATRIX 35 3.4 THE REACHABLE SET
39 3.5 REDUNDANT CONTROLS 43 EXERCISES 3 44 4 TIME-OPTIMAL CONTROL 4.1 A
BALANCING PROBLEM 46 4.2 STATEMENT OF THE GENERAL TIME-OPTIMAL PROBLEM
47 4.3 THE TIME-OPTIMAL MAXIMUM PRINCIPLE (TOP) 48 XI XII CONTENTS 4.4
SIMPLE EXAMPLES OF TIME-OPTIMAL PROBLEMS 52 4.5 UNIQUENESS AND NORMALITY
55 4.6 CONVEX TARGET SETS 60 4.7 THE BANG-BANG PRINCIPLE 62 EXERCISES 4
64 FURTHER EXAMPLES 5.1 POSITIONING WITH TWO CONTROLS 66 5.2 THE
STEERING PROBLEM 69 5.3 THE HARMONIC OSCILLATOR 71 5.4 A PREDATOR-PREY
PROBLEM 75 EXERCISES 5 79 PART * THE PONTRYAGIN MAXIMUM PRINCIPLE THE
BASIC PONTRYAGIN MAXIMUM PRINCIPLE (PMP) 6.1 AN ILLUSTRATIVE EXAMPLE 82
6.2 STATEMENT OF THE PMP IN ITS BASIC FORM 85 6.3 SOME EXAMPLES 88 6.4
THE POSITIONING PROBLEM WITH A FUEL COST 93 EXERCISES 6 97 EXTENSIONS TO
THE PMP 7.1 GENERAL TARGETS 99 7.2 TERMINAL COST 103 7.3 NON-AUTONOMOUS
PROBLEMS 106 EXERCISES 7 111 LINEAR STATE EQUATIONS WITH QUADRATIC COSTS
8.1 THE ONE-DIMENSIONAL PROBLEM 115 8.2 THE N-DIMENSIONAL PROBLEM 120
8.3 THEK-METHOD 122 8.4 THE K-METHOD FOR A FIXED TARGET AT THE ORIGIN
125 8.5 DIABETES MELLITUS (CONTINUED FROM CHAPTER 1) 127 EXERCISES 8 130
CONTENTS ** 9 PROOF OF THE PONTRYAGIN MAXIMUM PRINCIPLE 9.1 TIME-OPTIMAL
LINEAR PROBLEMS 132 9.2 STATEMENT OF THE THEOREM 134 9.3 THE
PERTURBATION CONE 136 9.4 THE CO-STATE VARIABLES AND THE MAXIMUM
PRINCIPLE: CASE 1 139 9.5 CASE 2 143 9.6 CASE3 144 9.7 AN ILLUSTRATIVE
EXAMPLE OF THE PROOF OF THE PMP 146 EXERCISES 9 150 10 FURTHER
APPLICATIONS AND EXTENSIONS 10.1 THE MOON-LANDING PROBLEM 151 10.2 THE
HARMONIC OSCILLATOR WITH A FUEL COST 154 10.3 POSITIONING WITH SMOOTHLY
VARYING CONTROLS 157 10.4 OTHER CONTROL SETS 161 10.5 RESTRICTED STATE
VARIABLES 165 EXERCISES 10 169 PART * APPLICATIONS OF OPTIMAL CONTROL
THEORY 11 SOME APPLIED OPTIMAL CONTROL PROBLEMS 11.1 MAXIMIZING THE FISH
HARVEST 174 11.2 CONTROL OF EPIDEMICS 180 11.3 COMMODITY TRADING 187
11.4 CONTRACTION OF THE LEFT VENTRICLE OF THE HEART 191 EXERCISES 11 197
12 NUMERICAL METHODS FOR OPTIMAL CONTROL PROBLEMS 12.1 IMPLEMENTATION OF
THE PONTRYAGIN MAXIMUM PRINCIPLE 199 12.2 NUMERICAL TECHNIQUES 200 12.3
OPTIMAL CONTROLS DETERMINED EXPLICITLY: DISCRETIZATION 203 12.4 OPTIMAL
CONTROLS DETERMINED EXPLICITLY: RUNGE-KUTTA METHOD 207 12.5 OPTIMAL
CONTROLS DETERMINED CONDITIONALLY 208 12.6 CONCLUSION 211 EXERCISES 12
212 XIV CONTENTS BIBLIOGRAPHY 213 OUTLINE SOLUTIONS TO THE EXERCISES
EXERCISES EXERCISES EXERCISES EXERCISES EXERCISES EXERCISES EXERCISES
EXERCISES EXERCISES EXERCISES EXERCISES EXERCISES 1 2 3 4 5 6 7 8 9 10
11 12 217 217 219 222 224 226 229 233 236 237 242 247 INDEX 249
|
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| author | Hocking, Leslie M. |
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| dewey-full | 629.8312 |
| dewey-hundreds | 600 - Technology (Applied sciences) |
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| dewey-sort | 3629.8312 |
| dewey-tens | 620 - Engineering and allied operations |
| discipline | Mathematik Mess-/Steuerungs-/Regelungs-/Automatisierungstechnik / Mechatronik |
| edition | Reprinted (with corr.) |
| format | Book |
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| indexdate | 2024-07-09T18:14:52Z |
| institution | BVB |
| isbn | 0198596758 0198596820 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007915907 |
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| physical | XIV, 254 S. graph. Darst. |
| publishDate | 1997 |
| publishDateSearch | 1997 |
| publishDateSort | 1997 |
| publisher | Clarendon Press |
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| series2 | Oxford applied mathematics and computing science series |
| spelling | Hocking, Leslie M. Verfasser aut Optimal control an introduction to the theory with applications Leslie M. Hocking Reprinted (with corr.) Oxford Clarendon Press 1997 XIV, 254 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Oxford applied mathematics and computing science series Regelungstheorie (DE-588)4122327-5 gnd rswk-swf Kontrolltheorie (DE-588)4032317-1 gnd rswk-swf Optimale Kontrolle (DE-588)4121428-6 gnd rswk-swf Optimale Kontrolle (DE-588)4121428-6 s Kontrolltheorie (DE-588)4032317-1 s DE-604 Regelungstheorie (DE-588)4122327-5 s 1\p DE-604 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007915907&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 | Hocking, Leslie M. Optimal control an introduction to the theory with applications Regelungstheorie (DE-588)4122327-5 gnd Kontrolltheorie (DE-588)4032317-1 gnd Optimale Kontrolle (DE-588)4121428-6 gnd |
| subject_GND | (DE-588)4122327-5 (DE-588)4032317-1 (DE-588)4121428-6 |
| title | Optimal control an introduction to the theory with applications |
| title_auth | Optimal control an introduction to the theory with applications |
| title_exact_search | Optimal control an introduction to the theory with applications |
| title_full | Optimal control an introduction to the theory with applications Leslie M. Hocking |
| title_fullStr | Optimal control an introduction to the theory with applications Leslie M. Hocking |
| title_full_unstemmed | Optimal control an introduction to the theory with applications Leslie M. Hocking |
| title_short | Optimal control |
| title_sort | optimal control an introduction to the theory with applications |
| title_sub | an introduction to the theory with applications |
| topic | Regelungstheorie (DE-588)4122327-5 gnd Kontrolltheorie (DE-588)4032317-1 gnd Optimale Kontrolle (DE-588)4121428-6 gnd |
| topic_facet | Regelungstheorie Kontrolltheorie Optimale Kontrolle |
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