Optimal control of a system governed by volterra integral equations

摘要

This paper deals with an optimal control problem governed by volterra integral equations of the second kind with degenerate kernel.An equivalent representation of the problem is obtained as a system of differential equations, then the measure theoretical approach is extended and applied to the new representation. We show that the optimal solution of the problem can be obtained by summation of some measures in positive Radon measures space. The method is developed in a way that we reach to a linear programming problem which can be solved by variety of efficient numerical approaches.