Necessary Conditions for the Existence of a Saddle Point in one Optimal Control Problem for Systems of Hyperbolic Equations

Abstract

In this paper, we consider one optimal control problem with a multipoint quality functional described by a system of nonlinear hyperbolic equations with Goursat boundary conditions. Using a modified version of the increment method, various necessary first-order optimality conditions such as the Pontryagin maximum principle and the linearized maximum condition are proved.