Constrained Dirichlet Boundary Control in $L^2$ for a Class of Evolution Equations

K. Kunisch, B. Vexler
2007 SIAM Journal of Control and Optimization  
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 L 2 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.
doi:10.1137/060670110 fatcat:c2skytffkvbmfl75lzvwbygidq