An ensemble optimal control problem governed by a semiclassical space-homogeneous Boltzmann equation for charge transport in graphene is formulated and analyzed. The control mechanism is an external time-dependent electric field having the purpose of driving the material density of electrons in graphene to follow a desired trajectory. For this purpose, an ensemble cost functional with quadratic H1 costs is considered. Well-posedness of the control problem is proved, and the characterization of optimal controls by an optimality system is discussed. This system is approximated by a discontinuous Galerkin scheme and solved using a nonlinear conjugate gradient method. Results of numerical experiments are presented that demonstrate the ability of the proposed control framework to design control fields.

Optimal control of a semiclassical Boltzmann equation for charge transport in graphene

Nastasi, Giovanni
;
Romano, Vittorio
2024-01-01

Abstract

An ensemble optimal control problem governed by a semiclassical space-homogeneous Boltzmann equation for charge transport in graphene is formulated and analyzed. The control mechanism is an external time-dependent electric field having the purpose of driving the material density of electrons in graphene to follow a desired trajectory. For this purpose, an ensemble cost functional with quadratic H1 costs is considered. Well-posedness of the control problem is proved, and the characterization of optimal controls by an optimality system is discussed. This system is approximated by a discontinuous Galerkin scheme and solved using a nonlinear conjugate gradient method. Results of numerical experiments are presented that demonstrate the ability of the proposed control framework to design control fields.
2024
Charge transport in graphene; Discontinuous Galerkin scheme; Ensemble optimal control problems; Optimal control theory; Semiclassical Boltzmann equation
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11769/606554
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