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arXiv · 2407.20366

Stackelberg-Nash null controllability for stochastic parabolic equations

Omar Oukdach·Said Boulite·Abdellatif Elgrou·Lahcen Maniar
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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.

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Omar Oukdach, Said Boulite, Abdellatif Elgrou, Lahcen Maniar. 2024-07-29. Stackelberg-Nash null controllability for stochastic parabolic equations. https://arxiv.org/abs/2407.20366

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