In this paper we consider a state constrained differential inclusion ẋ ∈ Ax+ F(t; x), with A generator of a strongly continuous semigroup in an infinite dimensional separable Banach space. Under an “inward pointing condition” we prove a relaxation result stating that the set of trajectories lying in the interior of the constraint is dense in the set of constrained trajectories of the convexified inclusion (formula presented). Some applications to control problems involving PDEs are given.
A relaxation result for state constrained inclusions in infinite dimension
MARCHINI, ELSA MARIA;
2016-01-01
Abstract
In this paper we consider a state constrained differential inclusion ẋ ∈ Ax+ F(t; x), with A generator of a strongly continuous semigroup in an infinite dimensional separable Banach space. Under an “inward pointing condition” we prove a relaxation result stating that the set of trajectories lying in the interior of the constraint is dense in the set of constrained trajectories of the convexified inclusion (formula presented). Some applications to control problems involving PDEs are given.File in questo prodotto:
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