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arXiv · 2209.05346

Optimal control for stochastic nonlinear Schrodinger equation on graph

Jianbo Cui·Shu Liu·Haomin Zhou
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Abstract

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.

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Jianbo Cui, Shu Liu, Haomin Zhou. 2022-09-12. Optimal control for stochastic nonlinear Schrodinger equation on graph. https://arxiv.org/abs/2209.05346

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