Funnel control for Langevin dynamics

In this study, we apply concepts from control theory to stochastic differential equations of Langevin type, motivated by complex dynamical systems in computational statistical physics, learning, or uncertainty quantification. The objective is to guarantee the evolution of the mean value in a prescribed performance funnel around a given sufficiently smooth reference signal. To achieve this objective we design a novel funnel controller and show its feasibility under certain structural conditions on the potential energy. The control design does not require any specific knowledge of the shape of the potential energy. We illustrate the results by a numerical simulation for a metastable double-well potential.