A spectral approach to optimal control of the Fokker–Planck equation
File(s)arxiv_version.pdf (484.26 KB)
Accepted version
Author(s)
Kalise, Dante
Moschen, Lucas M
Pavliotis, Grigorios A
Vaes, Urbain
Type
Journal Article
Abstract
In this letter, we present a spectral optimal control framework for Fokker-Planck equations based on the standard ground state transformation that maps the Fokker-Planck operator to a Schrödinger operator. Our primary objective is to accelerate convergence toward the (unique) steady state. To fulfill this objective, a gradient-based iterative algorithm with Pontryagin’s maximum principle and the Barzilai-Borwein update is developed to compute time-dependent controls. Numerical experiments on two-dimensional ill-conditioned normal distributions and double-well potentials demonstrate that our approach effectively targets slow-decaying modes, thus increasing the spectral gap.
Date Issued
2025-01-01
Date Acceptance
2025-05-01
Citation
IEEE Control Systems Letters, 2025, 9
ISSN
2475-1456
Publisher
Institute of Electrical and Electronics Engineers
Start Page
1
End Page
1
Journal / Book Title
IEEE Control Systems Letters
Volume
9
Copyright Statement
Copyright © 2025 IEEE. This is the author’s accepted manuscript made available under a CC-BY licence in accordance with Imperial’s Research Publications Open Access policy (www.imperial.ac.uk/oa-policy)
License URL
Publication Status
Published
Date Publish Online
2025-05-26