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 analyzed. This approach allows us to consider the boundary controls in L², which has advantages over approaches which consider control in Sobolev spaces involving (fractional) derivatives. Pointwise constraints on the boundary are incorporated by the primal-dual active set strategy. Its global and local superlinear convergences are shown. A discretization based on space-time finite elements is proposed and numerical examples axe included.