Differentiability of the Value Function on $H^1(\Omega)$ of Semilinear Parabolic Infinite Time Horizon Optimal Control Problems under Control Constraints
Optimization and Control
2023-11-28 v1 Analysis of PDEs
Abstract
An abstract framework guaranteeing the continuous differentiability of local value functions on 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.
Keywords
Cite
@article{arxiv.2311.15374,
title = {Differentiability of the Value Function on $H^1(\Omega)$ of Semilinear Parabolic Infinite Time Horizon Optimal Control Problems under Control Constraints},
author = {Karl Kunisch and Buddhika Priyasad},
journal= {arXiv preprint arXiv:2311.15374},
year = {2023}
}
Comments
arXiv admin note: text overlap with arXiv:2108.12888