Stackelberg-Nash null controllability for stochastic parabolic equations
Abstract
We study a hierarchical control problem for stochastic parabolic equations involving gradient terms. We employ the Stackelberg-Nash strategy with two leaders and two followers. The leaders are responsible for selecting the policy targeting null controllability, while the followers solve a bi-objective optimal control problem which consists of maintaining the solution process close to prefixed targets. Once the Nash equilibrium is determined, the problem reduces to achieving null controllability of a coupled forward-backward stochastic system. To solve this problem, via Carleman estimates, we establish a suitable observability inequality. Subsequently, we achieve the desired controllability result.
Cite
@article{arxiv.2407.20366,
title = {Stackelberg-Nash null controllability for stochastic parabolic equations},
author = {Omar Oukdach and Said Boulite and Abdellatif Elgrou and Lahcen Maniar},
journal= {arXiv preprint arXiv:2407.20366},
year = {2024}
}
Comments
arXiv admin note: text overlap with arXiv:2405.15730