Computational Methods in Optimal Control Problems by I.H. Mufti

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  • Title: Computational Methods in Optimal Control Problems
  • Author: I.H. Mufti
  • Category: Mathematics
  • Date: December 2012
  • Lenguage: English
  • Pages: unknown
  • ISBN: 3642859607

 

Ebook description:

The objective of this modest report is to current in a simplified method among the computational strategies which were developed in the final ten years for the answer of optimum management issues. Only these strategies which might be primarily based on the minimal (most) precept of Pontriagin are mentioned right here. The autline of the report is as follows: In the primary two sections a management downside of Bolza is formulated and the required situations in the type of the minimal precept are given. The technique of steepest descent and a conjugate gradient-method are dis­ stubborn in Section 3. In the remaining sections, the successive sweep technique, the Newton-Raphson technique and the generalized Newton-Raphson technique (additionally referred to as quasilinearization technique) ar~ offered from a unified method which relies on the applying of Newton­ Raphson approximation to the required situations of optimality. The second-variation technique and different taking pictures strategies primarily based on minimizing an error operate are additionally thought-about. TABLE OF CONTENTS 1. zero INTRODUCTION 1 2. zero NECESSARY CONDITIONS FOR OPTIMALITY •••••••• 2 3. zero THE GRADIENT METHOD Four 3. 1 Min H Method and Conjugate Gradient Method •. •••••••••. . . . ••••••. ••••••••. • eight 3. 2 Boundary Constraints •••••••••••. ••••. • 9 3. 3 Problems with Control Constraints ••. •• 15 4. zero SUCCESSIVE SWEEP METHOD •••••••••••••••••••• 18 4. 1 Final Time Given Implicitly ••••. •••••• 22 5. zero SECOND-VARIATION METHOD •••••••••••••••••••• 23 6. zero SHOOTING METHODS ••••••••••••••••••••••••••• 27 6. 1 Newton-Raphson Method ••••••••••••••••• 27 6

 

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