Optimal control for stochastic nonlinear Schrodinger equation on graph
Optimization and Control
2022-09-13 v1 Numerical Analysis
Numerical Analysis
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.
Cite
@article{arxiv.2209.05346,
title = {Optimal control for stochastic nonlinear Schrodinger equation on graph},
author = {Jianbo Cui and Shu Liu and Haomin Zhou},
journal= {arXiv preprint arXiv:2209.05346},
year = {2022}
}