Mathematical Theory of Optimal Processes

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CRC Press, 1987. 3. 6. - 360페이지
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.
 

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목차

Introduction
1
The Maximum Principle
9
Statement of the Fundamental Problem
11
The Maximum Principle
17
Discussion of the Maximum Principle
21
Examples The Synthesis Problem
22
The Problem with Variable Endpoints and the Trans versality Conditions
45
The Maximum Principle for NonAutonomous Systems
58
Variations of Controls and Trajectories
86
Fundamental Lemmas
92
The Proof of the Maximum Principle
99
The Derivation of the Transversality Conditions
108
Linear TimeOptimal Processes
115
Uniqueness Theorems
123
Miscellaneous Problems 189
197
The Maximum Principle and the Calculus of Variations
239

Fixed Time Problems
66
The Relation of the Maximum Principle to the Method of Dynamic Programming
69
The Proof of the Maximum Principle
75
The Formulation of the Maximum Principle for an Arbi trary Class of Admissible Controls
79
The System of Variational Equations and its Adjoint System
83
Optimal Processes with Restricted Phase Coordinates
257
A Statistical Optimal Control Problem
317
References
354
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