Abstract and Applied Analysis
Volume 2011 (2011), Article ID 486714, 18 pages
http://dx.doi.org/10.1155/2011/486714
Research Article

The Optimization of Solutions of the Dynamic Systems with Random Structure

Miroslava Růžičková1 and Irada Dzhalladova2

1University of Žilina, Žilina, Slovakia
2Vadim Getman Kyjew National Economic University, Kyjew, Ukraine

Received 31 January 2011; Accepted 31 March 2011

Academic Editor: Josef Diblík

Copyright © 2011 Miroslava Růžičková and Irada Dzhalladova. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The paper deals with the class of jump control systems with semi-Markov coefficients. The control system is described as the system of linear differential equations. Every jump of the random process implies the random transformation of solutions of the considered system. Relations determining the optimal control to minimize the functional are derived using Lyapunov functions. Necessary conditions of optimization which enables the synthesis of the optimal control are established as well.