A Spectral Approach to Optimal Control of the Fokker–Planck Equation

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 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.