Computational Methods in Optimal Control Problems (Lecture Notes in Economics and Mathematical Systems, 27) - Softcover
Synopsis
The purpose of this modest report is to present in a simplified manner some of the computational methods that have been developed in the last ten years for the solution of optimal control problems. Only those methods that are based on the minimum (maximum) principle of Pontriagin are discussed here. The autline of the report is as follows: In the first two sections a control problem of Bolza is formulated and the necessary conditions in the form of the minimum principle are given. The method of steepest descent and a conjugate gradient-method are dis cussed in Section 3. In the remaining sections, the successive sweep method, the Newton-Raphson method and the generalized Newton-Raphson method (also called quasilinearization method) ar~ presented from a unified approach which is based on the application of Newton Raphson approximation to the necessary conditions of optimality. The second-variation method and other shooting methods based on minimizing an error function are also considered. TABLE OF CONTENTS 1. 0 INTRODUCTION 1 2. 0 NECESSARY CONDITIONS FOR OPTIMALITY •••••••• 2 3. 0 THE GRADIENT METHOD 4 3. 1 Min H Method and Conjugate Gradient Method •. •••••••••. . . . ••••••. ••••••••. • 8 3. 2 Boundary Constraints •••••••••••. ••••. • 9 3. 3 Problems with Control Constraints ••. •• 15 4. 0 SUCCESSIVE SWEEP METHOD •••••••••••••••••••• 18 4. 1 Final Time Given Implicitly ••••. •••••• 22 5. 0 SECOND-VARIATION METHOD •••••••••••••••••••• 23 6. 0 SHOOTING METHODS ••••••••••••••••••••••••••• 27 6. 1 Newton-RaphsonMethod ••••••••••••••••• 27 6.
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Computational Methods in Optimal Control Problems
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Springer, J.B. Metzler Jan 1970, 1970
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ISBN 13: 9783540049517
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Taschenbuch. Condition: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -The purpose of this modest report is to present in a simplified manner some of the computational methods that have been developed in the last ten years for the solution of optimal control problems. Only those methods that are based on the minimum (maximum) principle of Pontriagin are discussed here. The autline of the report is as follows: In the first two sections a control problem of Bolza is formulated and the necessary conditions in the form of the minimum principle are given. The method of steepest descent and a conjugate gradient-method are dis cussed in Section 3. In the remaining sections, the successive sweep method, the Newton-Raphson method and the generalized Newton-Raphson method (also called quasilinearization method) ar~ presented from a unified approach which is based on the application of Newton Raphson approximation to the necessary conditions of optimality. The second-variation method and other shooting methods based on minimizing an error function are also considered. TABLE OF CONTENTS 1. 0 INTRODUCTION 1 2. 0 NECESSARY CONDITIONS FOR OPTIMALITY -------- 2 3. 0 THE GRADIENT METHOD 4 3. 1 Min H Method and Conjugate Gradient Method -. ---------. . . . ------. --------. - 8 3. 2 Boundary Constraints -----------. ----. - 9 3. 3 Problems with Control Constraints --. -- 15 4. 0 SUCCESSIVE SWEEP METHOD -------------------- 18 4. 1 Final Time Given Implicitly ----. ------ 22 5. 0 SECOND-VARIATION METHOD -------------------- 23 6. 0 SHOOTING METHODS --------------------------- 27 6. 1 Newton-RaphsonMethod ----------------- 27 6. 56 pp. Englisch. Seller Inventory # 9783540049517
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Computational Methods in Optimal Control Problems (Lecture Notes in Economics and Mathematical Systems)
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Computational Methods in Optimal Control Problems
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Condition: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. The purpose of this modest report is to present in a simplified manner some of the computational methods that have been developed in the last ten years for the solution of optimal control problems. Only those methods that are based on the minimum (maximum) . Seller Inventory # 4878615
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Computational Methods in Optimal Control Problems (Lecture Notes in Economics and Mathematical Systems, 27)
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Computational Methods in Optimal Control Problems
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Taschenbuch. Condition: Neu. This item is printed on demand - Print on Demand Titel. Neuware -The purpose of this modest report is to present in a simplified manner some of the computational methods that have been developed in the last ten years for the solution of optimal control problems. Only those methods that are based on the minimum (maximum) principle of Pontriagin are discussed here. The autline of the report is as follows: In the first two sections a control problem of Bolza is formulated and the necessary conditions in the form of the minimum principle are given. The method of steepest descent and a conjugate gradient-method are dis cussed in Section 3. In the remaining sections, the successive sweep method, the Newton-Raphson method and the generalized Newton-Raphson method (also called quasilinearization method) ar~ presented from a unified approach which is based on the application of Newton Raphson approximation to the necessary conditions of optimality. The second-variation method and other shooting methods based on minimizing an error function are also considered. TABLE OF CONTENTS 1. 0 INTRODUCTION 1 2. 0 NECESSARY CONDITIONS FOR OPTIMALITY żżżżżżżż 2 3. 0 THE GRADIENT METHOD 4 3. 1 Min H Method and Conjugate Gradient Method ż. żżżżżżżżż. . . . żżżżżż. żżżżżżżż. ż 8 3. 2 Boundary Constraints żżżżżżżżżżż. żżżż. ż 9 3. 3 Problems with Control Constraints żż. żż 15 4. 0 SUCCESSIVE SWEEP METHOD żżżżżżżżżżżżżżżżżżżż 18 4. 1 Final Time Given Implicitly żżżż. żżżżżż 22 5. 0 SECOND-VARIATION METHOD żżżżżżżżżżżżżżżżżżżż 23 6. 0 SHOOTING METHODS żżżżżżżżżżżżżżżżżżżżżżżżżżż 27 6. 1 Newton-RaphsonMethod żżżżżżżżżżżżżżżżż 27 6.Springer-Verlag KG, Sachsenplatz 4-6, 1201 Wien 56 pp. Englisch. Seller Inventory # 9783540049517
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Computational Methods in Optimal Control Problems
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Taschenbuch. Condition: Neu. Druck auf Anfrage Neuware - Printed after ordering - The purpose of this modest report is to present in a simplified manner some of the computational methods that have been developed in the last ten years for the solution of optimal control problems. Only those methods that are based on the minimum (maximum) principle of Pontriagin are discussed here. The autline of the report is as follows: In the first two sections a control problem of Bolza is formulated and the necessary conditions in the form of the minimum principle are given. The method of steepest descent and a conjugate gradient-method are dis cussed in Section 3. In the remaining sections, the successive sweep method, the Newton-Raphson method and the generalized Newton-Raphson method (also called quasilinearization method) ar~ presented from a unified approach which is based on the application of Newton Raphson approximation to the necessary conditions of optimality. The second-variation method and other shooting methods based on minimizing an error function are also considered. TABLE OF CONTENTS 1. 0 INTRODUCTION 1 2. 0 NECESSARY CONDITIONS FOR OPTIMALITY -------- 2 3. 0 THE GRADIENT METHOD 4 3. 1 Min H Method and Conjugate Gradient Method -. ---------. . . . ------. --------. - 8 3. 2 Boundary Constraints -----------. ----. - 9 3. 3 Problems with Control Constraints --. -- 15 4. 0 SUCCESSIVE SWEEP METHOD -------------------- 18 4. 1 Final Time Given Implicitly ----. ------ 22 5. 0 SECOND-VARIATION METHOD -------------------- 23 6. 0 SHOOTING METHODS --------------------------- 27 6. 1 Newton-RaphsonMethod ----------------- 27 6. Seller Inventory # 9783540049517
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Taschenbuch. Condition: Neu. Computational Methods in Optimal Control Problems | I. H. Mufti | Taschenbuch | Lecture Notes in Economics and Mathematical Systems | iv | Englisch | Springer | EAN 9783540049517 | Verantwortliche Person für die EU: Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg, juergen[dot]hartmann[at]springer[dot]com | Anbieter: preigu. Seller Inventory # 105577337
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