F. Tröltzsch : Lipschitz stability of solutions to linear-quadratic parabolic control problems with respect to perturbations

Author(s) :

F. Tröltzsch

Title :

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

Electronic source :

[gzipped ps-file] 68 kB

Preprint series

Technische Universität Chemnitz-Zwickau, Fakultät für Mathematik (Germany). Preprint 97-12, 1997

Mathematics Subject Classification :

49K20 [ Optimal control problems with PDE (nec./ suff.) ]

49K40 [ Sensitivity of optimal solutions in the presence of perturbations ]

Abstract :

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 contains 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. Making use of parabolic regularity in the whole scale of $L^p$ the known Lipschitz stability in the $L^2$-norm is improved to the supremum-norm.

Keywords :

Boundary control, distributed control, linear parabolic equation, control constraints, Lipschitz continuity, supremum norm

Language :

english

Publication time :

4/1997