The Controllability of Parabolic Systems with Delay and Distributed Parameters on the Graph

The optimal boundary control problem for a differential system with delay and distributed parameters on the graph is considered. As a state-space systems and the space of boundary control and observation, the classes of integrable functions is used. The conditions of the unique solvability of the problem of optimal control are obtained. And finally, the existence conditions of a unique control action and the controllability system are obtained.