International Conference «Mathematical and Informational Technologies, MIT-2013»
(X Conference «Computational and Informational Technologies for Science,
Engineering and Education»)

Vrnjacka Banja, Serbia, September, 5–8, 2013

Budva, Montenegro, September, 9-14, 2013

Jainakov A.J.   Иманалиев З.К.   Аширбаев Б.Ы.  

On a discrete optimal control problems with a small step

Reporter: Jainakov A.J.

ON A discrete optimal control problems with a small step

Imanaliev ZK, Zhaynakov A., Ashirbaev B.Y.
Kyrgyz State Technical University. I.Razzakova.

Many problems in the management of economic and technical objects are reduced to the solution of the discrete optimal control [1-4], and the discrete step is small or very large number of steps. Construction of exact analytical solutions of such problems, in many cases is not yet possible.
This paper presents a method for constructing a discrete algorithm for the optimal control problem with a small step.
In the proof of the existence of solutions, revealed a special case, which is related to insufficient boundary conditions of the adjoint equations for use "maximum principle".
 

Literature
1. F Sharshenaliev., ZK Imanaliev. On the application of the moment problem in optimization of discrete systems // Proceedings of the FPI. Technical kibernetika.Frunze. 1976. Vyp.95. Pp. 15-29.
2. Glizer VJ, MG Dmitriev Asymptotics of the solution of some discrete optimal control problems with a small step // Differ. equation. 1979. V.15. Number 9. Pp. 116-122.
3. Glizer VJ On an optimal control problem of a difference with a small step // Differ. equation. 1985. T.21. Number 8. Pp. 1440-1442.
4. Glizer VJ Asymptotics of the solution of a difference with a small step optimal control problem with moving the right end of the trajectory // Differ. equation. 1988. T.24. Number 8. Pp. 1457-1459.


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