Funnel Control for Langevin Dynamics

TL;DR

This paper introduces a novel funnel control method for Langevin dynamics to ensure the mean value tracks a reference signal within a prescribed performance funnel, applicable without detailed knowledge of the potential energy shape.

Contribution

It presents a new funnel controller for Langevin systems that guarantees tracking performance without requiring potential energy shape knowledge.

Findings

Controller successfully maintains mean tracking within the funnel.

Feasibility shown under certain structural conditions on potential energy.

Numerical simulation demonstrates effectiveness for double-well potential.

Abstract

We study tracking control for stochastic differential equations of Langevin type and describe a new conceptual approach to the sampling problem for those systems. 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 double-well potential.