Variational optimality condition in a control problem of a linear first-order hyperbolic system with boundary delay

In this paper, we examine a linear optimal-control problem for a first-order hyperbolic system in which a boundary condition at one of the ends is determined from a controlled system of ordinary differential equations with constant state lag. The approach proposed is based on the use of an exact formula for the increment of the cost functional. The reduced problem can be solved by various effective methods used for optimization problems in systems of ordinary differential equations.