A Stochastic Maximum Principle for Control Problems Constrained by the Stochastic Navier-Stokes Equations
Optimization and Control
2018-10-30 v1
Abstract
We consider the control problem of the stochastic Navier-Stokes equations in multidimensional domains introduced in \cite{ocpc} restricted to noise terms defined by Q-Wiener processes. Using a stochastic maximum principle, we derive a necessary optimality condition to design the optimal control based on an adjoint equation, which is given by a backward SPDE. Moreover, we show that the optimal control satisfies a sufficient optimality condition. As a consequence, we can solve uniquely control problems constrained by the stochastic Navier-Stokes equations especially for two-dimensional as well as for three-dimensional domains.
Cite
@article{arxiv.1810.12119,
title = {A Stochastic Maximum Principle for Control Problems Constrained by the Stochastic Navier-Stokes Equations},
author = {Peter Benner and Christoph Trautwein},
journal= {arXiv preprint arXiv:1810.12119},
year = {2018}
}
Comments
arXiv admin note: text overlap with arXiv:1809.00911