Landau-Lifshitz Equation with Affine Control

The Landau-Lifshitz equation is a coupled set of nonlinear partial differential equations that describes the dynamics of magnetization in a ferromagnet. This equation has an infinite number of stable equilibria. Steering the system from one equilibrium to another is a problem of both theoretical and practical interest. Since the objective is to steer between equilibria, approaches based on linearization are not appropriate. It is proven that affine proportional control can be used to steer the system from an arbitrary initial state, including an equilibrium point, to a specified equilibrium point. The second point becomes a globally asymptotically stable equilibrium of the controlled system. The control also removes hysteresis from the Landau-Lifshitz equation. These results are illustrated with simulations.