The Optimization of Solutions of the Dynamic Systems with Random Structure

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.