Mathematical Theory of Optimal Processes 1st Edition by Pontryagin, Boltyanskii, Gamkrelidze, Mishchenko ISBN 0470693819 9780470693810

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Product details:
ISBN 10: 0470693819
ISBN 13: 9780470693810 
Author: Pontryagin, Boltyanskii, Gamkrelidze, Mishchenko

Mathematical Theory of Optimal Processes 1st Edition Table of contents:

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 Transversality 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 Arbitrary 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 / in the General Case

References

Index

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