On optimal control for linear distributed time-delay systems

Abstract

This article presents the solution to the infinite horizon optimal control problem for linear distributed time-delay systems. It is based on the use of the Cauchy solution for distributed time-delay systems. In contrast to previous results for systems with concentrated delays, the form of the functional and its properties are formally justified. An important property is demonstrated: the Bellman functional admits upper and lower bounds; thus, it is proved to be positive definite. Additionally, some experimental results of a temperature process are presented.