1. Stackelberg-Nash null controllability for stochastic parabolic equations
- Author
-
Oukdach, Omar, Boulite, Said, Elgrou, Abdellatif, and Maniar, Lahcen
- Subjects
Mathematics - Optimization and Control ,Mathematics - Analysis of PDEs - 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., Comment: arXiv admin note: text overlap with arXiv:2405.15730
- Published
- 2024