Year: 2026
Type: preprint
Abstract: This work provides a framework to treat optimal control problems on separable Banach spaces in the viscosity sense. First, it extends the notion of $B$-viscosity solutions to the Banach setting and relates the extension to the notions of viscosity solutions used in metric space settings. As the main results, the paper proves a strict comparison principle and characterizes the value function of an optimal control problem as the unique viscosity solution to an infinite-dimensional HJB equation.
Source: arXiv (Cornell University)
Author: Fuchs, Fabian
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7221751353