A Spectral Approach to Optimal Control of the Fokker-Planck Equation
arXiv:2503.15125 · doi:10.1109/LCSYS.2025.3573604
Abstract
In this paper, 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 Schrodinger 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.
7 pages, 4 figures. Published in IEEE Control Systems Letters (L-CSS): https://ieeexplore.ieee.org/document/11015582. This is the Author Accepted Manuscript