Journal
SIAM JOURNAL ON CONTROL AND OPTIMIZATION
Volume 61, Issue 4, Pages 2021-2042Publisher
SIAM PUBLICATIONS
DOI: 10.1137/22M1524175
Keywords
optimal control; density manifold; stochastic nonlinear Schrodinger equation on graph; Wasserstein Hamiltonian flow
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We study the optimal control formulation for the stochastic nonlinear Schrodinger equation (SNLSE) on a finite graph. By treating the SNLSE as a stochastic Wasserstein Hamiltonian flow on the density manifold, we prove the global existence of a unique strong solution for SNLSE with a linear drift control or a linear diffusion control on the graph. Additionally, we provide the gradient formula, the existence of the optimal control, and a description of the optimal condition through the forward and backward stochastic differential equations.
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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