Stochastic nonlinear Schrödinger equation and its laser induced optimal feedback control
Journal Title: Discussiones Mathematicae Differential Inclusions Control and Optimization - Year 2017, Vol 37, Issue 2
Abstract
In this paper we consider a class of nonlinear stochastic Schrödinger equations and their optimal control through laser induced electro-magnetic field. These equations arise in the field of optics. We prove existence and uniqueness of mild solutions. We consider optimal control problems where the control is given by operator valued functions arising from the electric potential induced by the interaction of laser beam with the target material. We prove existence of optimal controls and present necessary conditions of optimality. Further, we also present some fundamental results on compactness (tightness) of the attainable set of regular Borel probability measures induced by the solutions of the stochastic system corresponding to the set of admissible controls. Using these results we prove existence of optimal controls for problems involving objective functionals defined on the space of Borel measures. Also we present the corresponding necessary conditions of optimality.
Authors and Affiliations
NasirUddin Ahmed
Keywords
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- EP ID EP481651
- DOI 10.7151/dmdico.1196
- Views 49
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