Mathematical Theory of Optimal Processes

Content: 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 Principle10. 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 Circuits23. 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 Coordinates31. 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 Equation41. 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