Constrained Dirichlet Boundary Control in L2 for a Class of Evolution Equations

Optimal Dirichlet boundary control based on the very weak solution of a parabolic state equation is analysed. This approach allows to consider the boundary controls in L2 which has advantages over approaches which consider control in Sobolev involving (fractional) derivatives. Point-wise constraints on the boundary are incorporated by the primal-dual active set strategy. Its global and local super-linear convergence are shown. A discretization based on space-time finite elements is proposed and numerical examples are included.