A gradient method for solving the optimal control problem for the system of telegraph equations

Abstract

THE optimal control problem is considered for a process with a distributed parameter, the variation of which is described by the system of first-order linear partial differential equations known in electromagnetic theory as the system of telegraph equations. The optimal control problem will be considered for a process with a distributed parameter, the variation of which is described by the system of first-order linear partial differential equations known in electromagnetic theory as the system of telegraph equations. The control appears in the right-hand side of the equations. The optimization criterion is assumed to be a quadratic functional. We show that the functional is differentiable and write an expression for the gradient in the space of controls L 2[0, T]. As a preliminary, the system is shown to be solvable with a fixed control, and expressions are obtained for the solution by Mikasinski's operator method [1].