The optimal control problems of stochastic heat equations with switching controls
Abstract
This study investigates the bang-bang property of maximal time-optimal controls, with a focus on controls governed by a forward stochastic heat equation in a bounded domain. These controls exhibit a switching behaviour, acting locally on two measurable subsets of positive measure. The proofs rely on an observability estimate associated with a positively measurable time set derived from the backward stochastic heat equation.
Fields of Study & Subjects
Stability and Controllability of Differential Equations
Stochastic processes and financial applications
Differential Equations and Boundary Problems
Publication details
- Journal / source
- Optimization
- Volume
- 75
- Issue
- 13
- Pages
- 3495–3509
- Publication date
- 11 January 2026
- Language
- EN