A Time Optimal Control Problem for Systems Described by Differential Difference Equations

Abstract

The aim of this paper is to establish the solution of an optimal time control problem for a physical system whose state is described by a linear differential-difference equation with retarded argument. We have obtained here a generalisation of the results of Bellman and his collaborators Glicksberg, Gross and Kalaba, and of LaSalie and Neustadt by using a technique due to LaSalle, with the help of the kernel matrix representation of Bellman and Cooke and also a new integral representation for the solutions of linear differential-difference equations.