THE DISCRETE CLASSICAL OPTIMAL CONTROL PROBLEM OF A NONLINEAR HYPERBOLIC PARTIAL DIFFERENTIAL EQUATION (DCOCP)

Abstract

In this paper, we consider a continuous classical optimal control for systems of nonlinearhyperbolic partial differential equations, with several equality and inequality state constraints. First,the considered continuous classical optimal control problem is discretized into a discrete classicaloptimal control problem by using the Galerkin finite element method in space and the implicit finitedifference scheme in time. The classical continuous controls are approximated by picewiseconstants. Second the existence of a unique solution of the discrete state equations for fixed discreteclassical control is studied. Third, we develop the existence theory for optimality of the discreteclassical problem, and the discrete adjoint equations are developed corresponding to the discretestate equations. Finally the necessary conditions and a picewise minimum principle are developedfor optimality of the discrete classical problem