Global methods in optimal control theory:
This outstanding resource systematically describes all basic equations and inequalities that form the necessary and sufficient optimality conditions of variational calculus and the theory of optimal control - addressing the latest developments in the investigation of optimality conditions, new class...
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York [u.a.]
Dekker
1996
|
| Series: | Pure and applied mathematics
195 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Summary: | This outstanding resource systematically describes all basic equations and inequalities that form the necessary and sufficient optimality conditions of variational calculus and the theory of optimal control - addressing the latest developments in the investigation of optimality conditions, new classes of solutions, analytical and computation methods, and applications. Written by a world renowned scientist, Global Methods in Optimal Control Theory is an indispensable reference for pure and applied mathematicians; control, systems, aerospace, electrical and electronics, mechanical, and computer engineers; physicists; econometricians; statisticians; and upper-level undergraduate and graduate students in these disciplines. |
| Physical Description: | XIV, 384 S. |
| ISBN: | 0824793293 |
Staff View
MARC
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| 245 | 1 | 0 | |a Global methods in optimal control theory |c Vadim F. Krotov |
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| 490 | 1 | |a Pure and applied mathematics |v 195 | |
| 520 | 3 | |a This outstanding resource systematically describes all basic equations and inequalities that form the necessary and sufficient optimality conditions of variational calculus and the theory of optimal control - addressing the latest developments in the investigation of optimality conditions, new classes of solutions, analytical and computation methods, and applications. Written by a world renowned scientist, Global Methods in Optimal Control Theory is an indispensable reference for pure and applied mathematicians; control, systems, aerospace, electrical and electronics, mechanical, and computer engineers; physicists; econometricians; statisticians; and upper-level undergraduate and graduate students in these disciplines. | |
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| 650 | 7 | |a théorie commande optimale |2 inriac | |
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| 650 | 4 | |a Global analysis (Mathematics) | |
| 650 | 4 | |a Mathematical optimization | |
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Record in the Search Index
| _version_ | 1804125749696790528 |
|---|---|
| adam_text | Contents
Preface
1. CONTROL PROCESSES. OPTIMAL CONTROL PROBLEM 1
1.1 Preliminary Description of the Problem 1
1.2 Controlled Processes 3
1.3 Optimal Control of Ordinary Process. Problem Statement
and Some Applications 5
1.4 Optimal Control of Multistage Processes 15
1.5 Optimal Control of Multiargument Processes. Problem
Statement and Some Applications 16
Commentary and Bibliography 18
References 18
2. BOUNDING AND SOLVING FUNCTIONS. SUFFICIENT
CONDITIONS OF OPTIMALITY 21
2.1 Some Preliminary Theses. Extension Principle 21
2.2 Principle of Decomposition with Respect to Time 23
2.3 Equivalent Representations 25
2.4 Direct Application of Equivalent Representations of Some
Optimal Control Problems 28
xi
xii Contents
2.5 Global Bounds 35
2.6 Sufficient Optimality Conditions 43
2.7 Sufficient Optimality Conditions. Nonfixed Boundary State 47
2.8 Control Synthesis 49
2.9 Estimations of Achievability Regions. Strengthened Lower
Bounds and Sufficient Optimality Conditions 50
2.10 Principle of Optimality 52
Commentary and Bibliography 54
References 58
3. SOME SPECIAL OPTIMAL CONTROL PROBLEMS.
DIRECT APPLICATION OF THE SUFFICIENT
OPTIMALITY CONDITIONS 61
3.1 Some Generalizations of the Degenerate Euler s Problem 62
3.2 Simplest Macromodel of Optimal Economic Development 71
3.3 Two Dimensional Autonomous Problem Linear with
Respect to Control 81
3.4 Optimal Control for Vertical Maneuvers of Aircraft 90
3.5 Multidimensional Degenerate Problem 111
3.6 Applied Physics Problem: Maximization of Atomic
Excitement by Resonance Field 117
Commentary and Bibliography 121
References 128
4. SUFFICIENT OPTIMALITY CONDITIONS AND BASIC
EQUATIONS OF THE VARIATIONAL CALCULUS
AND OPTIMAL CONTROL THEORY 133
4.1 Some Useful Formulas 133
4.2 Sufficient Optimality Conditions and Maximum Principle 134
4.3 General Boundary Conditions 138
4.4 Absolute Minimum Problem in Lagrange s Method 139
4.5 Optimal Control for Linear Systems 141
4.6 Strong Local Minimum 146
4.7 Local Minimum Conditions for Euler s Problem of
Variational Calculus 149
4.8 Principle of Least Action 154
4.9 Second Order Conditions for Degenerate Problems 157
4.10 Processes with Discrete Argument 160
4.11 Multiargument Systems 168
Commentary and Bibliography 177
References 178
Contents xiii
5. OPTIMAL FEEDBACK POLICY. HAMILTON JACOBI
METHOD 181
5.1 Equations for Optimal Control Synthesis 184
5.2 Algorithmic Features of the Method 188
5.3 Synthesis of Controllers for Linear Systems with a
Quadratic Criterion 189
5.4 Approximate Optimal Synthesis 194
5.5 Descent of Spacecraft into Atmosphere Using the
Engine: Approximate Optimal Control Synthesis 201
5.6 Approximate Optimal Controllers for Linear Systems with
Restricted Control 207
5.7 Analytical Synthesis of Optimal Control for Nonlinear
Systems 219
Commentary and Bibliography 234
References 234
6. COMPUTER METHODS FOR SUCCESSIVE
IMPROVEMENTS IN A CONTROL PROGRAM 237
6.1 Infinitesimal Methods of Control Improvement 239
6.2 Global Methods of Successive Improvements of Control 242
6.3 Control of Observation Process 249
6.4 Some Special Problems 252
6.5 Optimal Control of Quantum Systems by Laser Radiation 253
6.6 Knapsack Multivariate Problem 259
6.7 Comparative Discussion of the Iterative Methods 261
References 262
7. DUAL COMPUTATIONAL ALGORITHMS FOR SOLVING
AND OPTIMIZING CONTROLLABLE SYSTEMS OF
EQUATIONS 265
7.1 Problem Statement. Basic Idea of the Method 265
7.2 Method of Improvement 269
7.3 Methods of Realization of an Elementary Operation 273
7.4 Convergence 277
7.5 Examples 281
Appendix: Some Auxiliary Results 287
Commentary and Bibliography 291
References 291
xiv Contents
8. EXTENSION OF THE CLASS OF SOLVING FUNCTIONS.
THEOREMS OF EXISTENCE OF SOLVING FUNCTIONS 293
8.1 Global Necessary and Sufficient Conditions of Optimality
for Multistage Processes 295
8.2 Necessary and Sufficient Optimality Conditions for
Ordinary Processes Free of State Restrictions 298
8.3 Weak Solving Functions 303
8.4 Global Necessary and Sufficient Conditions of Optimality
for Ordinary Controlled Processes with State Constraints 306
8.5 Global Necessary and Sufficient Conditions of Optimality
for Multiargument Controlled Processes 312
8.6 Some Concluding Observations 317
References 319
9. OPTIMAL CONTROL UNDER CONDITIONS OF
INCOMPLETE INFORMATION 323
9.1 Problem Statement 323
9.2 Global Bounds and Conditions of Optimality 328
9.3 Differential Games with Complete Information on the
State. Optimal Synthesis 338
9.4 Differential Games with Complete Information on the
State. Equations of Optimal Trajectory 344
9.5 Incomplete Information on State. Conditions for Lack of
Information Price 350
9.6 Information Differential Games. Discrete Sufficient
Information Operator 353
9.7 Information Differential Games. Optimal Control for
Insufficient Information 358
9.8 Invariance Problem. Conditions of Invariance 366
9.9 Invariance of a Linearly Quadratic Functional in a
Quasilinear System 369
9.10 Absolute Invariance 370
9.11 Synthesis of Invariant Systems 371
9.12 Invariant Control of Spacecraft Descent in a Planetary
Atmosphere 372
Commentary and Bibliography 376
References 378
Index 381
|
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| id | DE-604.BV011247818 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:06:31Z |
| institution | BVB |
| isbn | 0824793293 |
| language | English |
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| physical | XIV, 384 S. |
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| series | Pure and applied mathematics |
| series2 | Pure and applied mathematics |
| spelling | Krotov, Vadim F. Verfasser aut Global methods in optimal control theory Vadim F. Krotov New York [u.a.] Dekker 1996 XIV, 384 S. txt rdacontent n rdamedia nc rdacarrier Pure and applied mathematics 195 This outstanding resource systematically describes all basic equations and inequalities that form the necessary and sufficient optimality conditions of variational calculus and the theory of optimal control - addressing the latest developments in the investigation of optimality conditions, new classes of solutions, analytical and computation methods, and applications. Written by a world renowned scientist, Global Methods in Optimal Control Theory is an indispensable reference for pure and applied mathematicians; control, systems, aerospace, electrical and electronics, mechanical, and computer engineers; physicists; econometricians; statisticians; and upper-level undergraduate and graduate students in these disciplines. Commande, Théorie de la ram Optimisation mathématique ram analyse globale inriac optimisation mathématique inriac système dynamique inriac théorie commande optimale inriac Control theory Global analysis (Mathematics) Mathematical optimization Optimale Kontrolle (DE-588)4121428-6 gnd rswk-swf Kontrolltheorie (DE-588)4032317-1 gnd rswk-swf Analysis (DE-588)4001865-9 gnd rswk-swf Optimale Kontrolle (DE-588)4121428-6 s Kontrolltheorie (DE-588)4032317-1 s DE-604 Analysis (DE-588)4001865-9 s 1\p DE-604 Pure and applied mathematics 195 (DE-604)BV000001885 195 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007549773&sequence=000002&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 | Krotov, Vadim F. Global methods in optimal control theory Pure and applied mathematics Commande, Théorie de la ram Optimisation mathématique ram analyse globale inriac optimisation mathématique inriac système dynamique inriac théorie commande optimale inriac Control theory Global analysis (Mathematics) Mathematical optimization Optimale Kontrolle (DE-588)4121428-6 gnd Kontrolltheorie (DE-588)4032317-1 gnd Analysis (DE-588)4001865-9 gnd |
| subject_GND | (DE-588)4121428-6 (DE-588)4032317-1 (DE-588)4001865-9 |
| title | Global methods in optimal control theory |
| title_auth | Global methods in optimal control theory |
| title_exact_search | Global methods in optimal control theory |
| title_full | Global methods in optimal control theory Vadim F. Krotov |
| title_fullStr | Global methods in optimal control theory Vadim F. Krotov |
| title_full_unstemmed | Global methods in optimal control theory Vadim F. Krotov |
| title_short | Global methods in optimal control theory |
| title_sort | global methods in optimal control theory |
| topic | Commande, Théorie de la ram Optimisation mathématique ram analyse globale inriac optimisation mathématique inriac système dynamique inriac théorie commande optimale inriac Control theory Global analysis (Mathematics) Mathematical optimization Optimale Kontrolle (DE-588)4121428-6 gnd Kontrolltheorie (DE-588)4032317-1 gnd Analysis (DE-588)4001865-9 gnd |
| topic_facet | Commande, Théorie de la Optimisation mathématique analyse globale optimisation mathématique système dynamique théorie commande optimale Control theory Global analysis (Mathematics) Mathematical optimization Optimale Kontrolle Kontrolltheorie Analysis |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007549773&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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