Optimal boundary control of a linear parabolic evolution system

Abstract

We consider the optimal boundary control of a linear parabolic boundary value problem. Firstly, the problem is formulated as an optimization problem with the system state governed by a parabolic partial differential equation. Based on the formulation for the variation of the cost functional, a gradient-type optimization technique utilizing the finite element method is then developed to solve the constrained optimization problem. Finally, a numerical example is given and the results show that the method of solution is robust.