English

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 H1(Ω)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.

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