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- 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