Optimal boundary control problem for n × n infinite-order parabolic lag system

Abstract

In this paper, we study the linear quadratic optimal boundary control problem for n × n coupled system of infinite-order parabolic partial differential equation, in which time-varying lags appear in the state equation and in the Neumann boundary condition simultaneously. By Lions scheme, necessary and sufficient condition of optimality for the Neumann problem with quadratic functional and constraint control is derived. Finally, several mathematical examples for derived optimality conditions are presented.