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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 (Lecture Notes in Economics and Mathematical Systems 27)
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Springer, 1970
ISBN 10 : 3540049517
ISBN 13 : 9783540049517
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Computational Methods in Optimal Control Problems
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Springer Berlin Heidelberg, 1970
ISBN 10 : 3540049517
ISBN 13 : 9783540049517
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Etat : 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) . N° de réf. du vendeur 4878615
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Computational Methods in Optimal Control Problems
Edité par
Springer Berlin Heidelberg, 1970
ISBN 10 : 3540049517
ISBN 13 : 9783540049517
Neuf
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Taschenbuch. Etat : 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. N° de réf. du vendeur 9783540049517
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Computational Methods in Optimal Control Problems
Edité par
Springer Berlin Heidelberg, Springer Berlin Heidelberg Jan 1970, 1970
ISBN 10 : 3540049517
ISBN 13 : 9783540049517
Neuf
Taschenbuch
Vendeur : buchversandmimpf2000, Emtmannsberg, BAYE, Allemagne
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Taschenbuch. Etat : 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 ¿¿¿¿¿¿¿¿ 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.Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 56 pp. Englisch. N° de réf. du vendeur 9783540049517
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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 (Lecture Notes in Economics and Mathematical Systems)
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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
Edité par
Springer Berlin Heidelberg Jan 1970, 1970
ISBN 10 : 3540049517
ISBN 13 : 9783540049517
Neuf
Taschenbuch
Vendeur : BuchWeltWeit Ludwig Meier e.K., Bergisch Gladbach, Allemagne
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Taschenbuch. Etat : 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-Raphson Method ----------------- 27 6. 56 pp. Englisch. N° de réf. du vendeur 9783540049517
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Computational Methods in Optimal Control Problems
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Computational Methods in Optimal Control Problems (Lecture Notes in Economics and Mathematical Systems, 27)
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