Bilinear optimal stabilization of a non-homogeneous Fokker-Planck equation

TL;DR

This paper investigates the bilinear optimal control strategies for stabilizing a non-homogeneous Fokker-Planck equation over finite and infinite time horizons, ensuring system stability with numerical validation.

Contribution

It introduces a novel approach to stabilizing non-homogeneous Fokker-Planck equations using bilinear optimal control methods for both finite and infinite time horizons.

Findings

Optimal control guarantees strong stability of the system.

The approach is validated through a numerical example.

Stability is achieved over both finite and infinite horizons.

Abstract

In this work, we study the bilinear optimal stabilization of a non-homogeneous Fokker-Planck equation. We first study the problem of optimal control in a finite-time interval and then focus on the case of the infinite time horizon. We further show that the obtained optimal control guarantees the strong stability of the system at hand. An illustrating numerical example is given.