Work

Optimal control for stochastic nonlinear Schrodinger equation on graph

Year: 2022

Type: preprint

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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2209.05346

Authors: Cui, Jianbo, Liu, Shu, Zhou, Haomin

Institutions: Hong Kong Polytechnic University, Georgia Institute of Technology

Language: English

Topic: Advanced Mathematical Physics Problems

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: National Science Foundation, Hong Kong Polytechnic University, Office of Naval Research

Awards: G1357208708, G1872973553, G3015612576, G4353487559, G4819451180, G4847921658, ATD: Algorithm, Analysis, and Prediction for Nonlinear and Non-Stationary Signals via Data-Driven Iterative Filtering Methods, G549782230, G7306578966, G7489405649, G8876996369

OpenAlex ID: W4297811884

Cites:

Cited by: 1

Related to: 10