Optimal control for stochastic nonlinear Schrodinger equation on graph

We study the optimal control formulation for stochastic nonlinear Schrodinger equation (SNLSE) on a finite graph. By viewing the SNLSE as a stochastic Wasserstein Hamiltonian flow on density manifold, we show the global existence of a unique strong solution for SNLSE with a linear drift control or a...

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Bibliographic Details
Published inarXiv.org
Main Authors Cui, Jianbo, Liu, Shu, Zhou, Haomin
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 12.09.2022
Subjects
Differential equations
Nonlinear control
Optimal control
Schrodinger equation
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Summary:We study the optimal control formulation for stochastic nonlinear Schrodinger equation (SNLSE) on a finite graph. By viewing the SNLSE as a stochastic Wasserstein Hamiltonian flow on density manifold, we show the global existence of a unique strong solution for SNLSE with a linear drift control or a linear diffusion control on graph. Furthermore, we provide the gradient formula, the existence of the optimal control and a description on the optimal condition via the forward and backward stochastic differential equations.
ISSN:2331-8422