Explicit algorithms to solve a class of state constrained parabolic optimal control problems

Abstract

We consider an optimal control problem of a system governed by a linear parabolic equation with the following features: control is dis-tributed, observation is either distributed or nal, there are constraints on the state function and on its time derivative. Iterative solution methods are proposed and investigated for the nite di erence ap-proximations of these optimal control problems. Due to explicit in time approximation of the state equation and the appropriate choice of the preconditioners in the iterative methods, the implementation of all constructed methods is carried out by explicit formulaes. Computational experiments con rm the theoretical results.