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Abstract and Applied Analysis
Volume 2011 (2011), Article ID 486714, 18 pages
doi:10.1155/2011/486714
The Optimization of Solutions of the Dynamic Systems with Random Structure
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.