Mathematical Theory of Optimal ProcessesThe 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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Contents
The Maximum Principle | 9 |
The Proof of the Maximum Principle | 75 |
Linear TimeOptimal Processes | 115 |
Miscellaneous Problems 189 | 191 |
The Maximum Principle and the Calculus of Variations | 239 |
Optimal Processes with Restricted Phase Coordinates | 257 |
A Statistical Optimal Control Problem | 317 |
| 354 | |
Common terms and phrases
addition admissible control arbitrary assume belongs boundary bounded called Chapter closed coincides condition cone Consequently consider constant constructed contains continuous control u(t coordinates corresponding curve defined definition denote depend derivatives described determined differential directed endpoint entire equal equation example exists fact Figure Finally fixed follows formula function Furthermore give given holds inequality initial initial condition integral interior interval Lemma let x(t lies linear manifold maximum principle motion moving necessary object obtain obvious optimal control optimal problem optimal trajectory origin parameters passes phase point piecewise plane position possible problem proof prove region regular relation respect right-hand satisfies side smooth solution solve space sufficiently suppose switching t₁ takes Theorem theory tion trajectory x(t transfers uniquely variable variations vector zero
Bibliographic information
| Title | Mathematical Theory of Optimal Processes Classics of Soviet Mathematics |
| Author | L.S. Pontryagin |
| Edition | reprint |
| Publisher | CRC Press, 1987 |
| ISBN | 2881240771, 9782881240775 |
| Length | 360 pages |
| Subjects | › Mathematics / Applied Mathematics / General |
| Export Citation | BiBTeX EndNote RefMan |