NECESSARY CONDITIONS FOR CONSTRAINED DISTRIBUTED-PARAMETER SYSTEMS WITH DEVIATING ARGUMENT

In this paper we consider an optimal control problem governed by a sys tem of nonlinear hyperbolic partial differential equations with deviat ing argument, Darboux-type boundary conditions and terminal state ineq uality constraints. The control variables are assumed to be measurable and the state variables are assumed to belong to a Sobolev space. We derive an integral representation of the increments of the functionals involved, and using separation theorems of functional analysis, obtai n necessary conditions for optimality in the form of a Pontryagin maxi mum principle. The approach presented here applies equally well to oth er nonlinear constrained distributed parameters with deviating argumen t.