The order of singularity of pulse optimal controls in degenerate linear-quadratic optimization problems with time delay

Abstract

In the paper, we study a problem of minimization of degenerate integral quadratic functional of special delayed structure (a subintegral function contains items concentrated at the moment and items with delay in phase coordinates) on trajectories of a linear system of differential equations with time delay in phase coordinates considered on a finite period of time. Sufficient conditions for the existence of optimal program control in space of generalized functions of the lth order of singularity are established and an optimal control is obtained. A special feature of the problem is that the optimal program contains pulse components concentrated at the ends of the control gap.