Technical comments on the optimal control for linear distributed time-delay

Abstract: The solution to the infinite horizon optimal control problem for linear distributed time-delay systems is presented. The proposal is based on the use of the Cauchy solution for distributed time-delay systems. In contrast with previous results (for punctual time delay systems), 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 on a temperature process are presented.