Singular linear-quadratic control problem for systems with linear delay

A singular linear-quadratic optimization problem on the trajectories of non-autonomous linear differential equations with linear delay is considered. The peculiarity of this problem is the fact that this problem has no solution in the class of integrable controls. To ensure the existence of solutions is required to expand the class of controls including controls with impulse components. Dynamical systems with linear delay are used to describe the motion of pantograph from the current collector with electric traction, biology, etc. It should be noted that for practical problems fact singularity criterion of quality is quite commonly occurring, and therefore the study of these problems is surely important. For the problem under discussion optimal programming control contained impulse components at the initial and final moments of time is constructed under certain assumptions on the functional and the right side of the control system.