Mathematical Theory of Optimal Processes

Routledge (Verlag)
  • erschienen am 3. Mai 2018
  • |
  • 360 Seiten
E-Book | PDF ohne DRM | Systemvoraussetzungen
978-1-351-43307-5 (ISBN)
The fourth and final volume in this comprehensive set presents the maximum principle as a wide ranging solution to nonclassical, variational problems. This one mathematical method can be applied in a variety of situations, including linear equations with variable coefficients, optimal processes with delay, and the jump condition. As with the three preceding volumes, all the material contained with the 42 sections of this volume is made easily accessible by way of numerous examples, both concrete and abstract in nature.
  • Englisch
  • Boca Raton
  • |
  • USA
Taylor & Francis Ltd
  • Für höhere Schule und Studium
978-1-351-43307-5 (9781351433075)
weitere Ausgaben werden ermittelt
  • Cover
  • Half Title
  • Title Page
  • Copyright Page
  • Table of Contents
  • Editor's Preface
  • Preface to the English Translation
  • Introduction
  • Chapter I: The Maximum Principle
  • 1. Admissible Controls
  • 2. Statement of the Fundamental Problem
  • 3. The Maximum Principle
  • 4. Discussion of the Maximum Principle
  • 5. Examples. The Synthesis Problem
  • 6. The Problem with Variable Endpoints and the Trans-versality Conditions
  • 7. The Maximum Principle for Non-Autonomous Systems
  • 8. Fixed Time Problems
  • 9. The Relation of the Maximum Principle to the Method of Dynamic Programming
  • Chapter II: The Proof of the Maximum Principle
  • 10. Admissible Controls
  • 11. The Formulation of the Maximum Principle for an Arbi trary Class of Admissible Controls
  • 12. The System of Variational Equations and its Adjoint System
  • 13. Variations of Controls and Trajectories
  • 14. Fundamental Lemmas
  • 15. The Proof of the Maximum Principle
  • 16. The Derivation of the Transversality Conditions
  • Chapter III: Linear Time-Optimal Processes
  • 17. Theorems on the Number of Switchings
  • 18. Uniqueness Theorems
  • 19. Existence Theorems
  • 20. The Synthesis of the Optimal Control
  • 21. Examples
  • 22. A Simulation of Linear Time-Optimal Processes by Means of Relay Circuits
  • 23. Linear Equations with Variable Coefficients
  • Chapter IV: Miscellaneous Problems
  • 24. The Case Where the Functional is Given by an Improper Integral
  • 25. Optimal Processes with Parameters
  • 26. An Application of the Theory of Optimal Processes to Problems in the Approximation of Functions
  • 27. Optimal Processes with a Delay
  • 28. A Pursuit Problem
  • Chapter V: The Maximum Principle and the Calculus of Variations
  • 29. The Fundamental Problem of the Calculus of Variations
  • 30. The Problem of Lagrange
  • Chapter VI: Optimal Processes with Restricted Phase Coordinates
  • 31. Statement of the Problem
  • 32. Optimal Trajectories Which Lie on the Boundary of the Region
  • 33. The Proof of Theorem 22 (Fundamental Constructions)
  • 34. The Proof of Theorem 22 (Conclusion)
  • 35. Some Generalizations
  • 36. The Jump Condition
  • 37. Statement of the Fundamental Result. Examples
  • Chapter VII: A Statistical Optimal Control Problem
  • 38. The Concept of a Markov Process. The Kolmogorov Differential Equation
  • 39. The Precise Statement of the Statistical Problem
  • 40. The Reduction of the Evaluation of the Functional J to the Solution of a Boundary Value Problem for the Kolmogorov Equation
  • 41. The Evaluation of the Functional J in the Case Where the Kolmogorov Equation has Constant Coefficients . .
  • 42. The Evaluation of the Functional J in the General Case
  • References
  • Index

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