Lipschitz stability of solutions of linear-quadratic parabolic control problems with respect to perturbations

摘要

We consider a class of control problems governed by a linear parabolic initial-boundary value problem with linear-quadratic objective and pointwise constraints on the control. The control system is subject to different types of perturbations. They appear in the linear part of the objective functional, in the right hand side of the equation, in its boundary condition, and in the initial value. Employing results on parabolic regularity in the whole scale of L~p-spaces the known Lipschitz stability in the L~2-norm is strengthened to the supremum-norm.