Boundary control for hyperbolic systems involving infinite-order operators with control constraints

Abstract

In this paper, a class of n × n hyperbolic boundary control problems with control constraints is investigated. We first establish the solvability of an n × n system with non-homogeneous mixed Neumann conditions involving hyperbolic operator of infinite order. Also a boundary control problem for this system is considered. The necessary and sufficient conditions for the control to be optimal are obtained. Two mathematical examples for derived optimality conditions are presented.