Title: Differentiability of the value function on $ H^1(\Omega) $ of semilinear parabolic infinite time horizon optimal control problems under control constraints.
Authors: Kunisch, Karl; Priyasad, Buddhika
Abstract: An abstract framework guaranteeing the continuous differentiability of local value functions on $ H^1(\Omega) $ associated with optimal stabilization problems subject to abstract semilinear parabolic equations in the presence of norm constraints on the control is established. It guarantees the local well-posedness of the associated Hamilton-Jacobi-Bellman equation in the classical sense. Examples illustrate that the assumptions imposed on the dynamical system are satisfied for practically relevant semilinear equations.
Subjects: PARABOLIC differential equations; OPTIMAL control theory; TIME perspective; DYNAMICAL systems; EQUATIONS
Publication: Mathematical Control & Related Fields, 2024, Vol 14, Issue 4, pN.PAG
ISSN: 2156-8472
Publication type: Academic Journal
DOI: 10.3934/mcrf.2024020

Differentiability of the value function on $ H^1(\Omega) $ of semilinear parabolic infinite time horizon optimal control problems under control constraints.

Kunisch, Karl; Priyasad, Buddhika