Control of the Landau-Lifshitz Equation

TL;DR

This paper develops a control method for the nonlinear Landau-Lifshitz equation governing ferromagnetic magnetization, enabling transition between arbitrary states and stable equilibria, with proven stability and simulation validation.

Contribution

It introduces a control strategy for the Landau-Lifshitz equation that guarantees convergence to a desired equilibrium, a novel approach for this nonlinear system.

Findings

Control moves system between arbitrary states and equilibria

Proven asymptotic stability of the target equilibrium

Simulation results validate the control method

Abstract

The Landau--Lifshitz equation describes the dynamics of magnetization inside a ferromagnet. This equation is nonlinear and has an infinite number of stable equilibria. It is desirable to control the system from one equilibrium to another. A control that moves the system from an arbitrary initial state, including an equilibrium point, to a specified equilibrium is presented. It is proven that the second point is an asymptotically stable equilibrium of the controlled system. The results are illustrated with some simulations.