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The optimal control of magnetization dynamics in a ferromagnetic sample at amicroscopic scale is studied. The dynamics of this model is governed by theLandau-Lifshitz-Gilbert equation on a two-dimensional bounded domain with theexternal magnetic field (the control) applied through the effective field. Weprove the global existence and uniqueness of a regular solution in $\mathbbS^2$ under a smallness condition on control and initial data. We establish theexistence of optimal control and derive a first-order necessary optimalitycondition using the Fr\'echet derivative of the control-to-state operator andadjoint problem approach.

Optimal Control of the 2D Landau-Lifshitz-Gilbert Equation with Control Energy in Effective Magnetic Field