ON THE CHARACTERIZATION OF PROPERLY RELAXED DELAYED CONTROLS
J. Rosenblueth, J. Warga and Q. J. Zhu
Abstract: In previous papers Warga and Zhu
have proven the conjecture of Rosenblueth and Vinter
that a particular abstract model characterizes the set $\bar{\Re}$ of relaxed controls that are limits of ordinary controls with
(possibly time-dependent) delays. Rosenblueth and Vinter
have also provided a simple and concrete
characterization of $\bar{\Re}$ for the case of constant delays
that are consecutive multiples of a common divisor $h$.
In the present paper we provide a concrete characterization of
$\bar \Re$ for the case of delays
that are arbitrary (and not necessarily consecutive) multiples
of some $h$. We also exhibit a simple compactification of the set of solutions
of controlled differential equations with such delays in the control.