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Multi-objective control for stochastic parabolic equations with dynamic boundary conditions

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arxiv 2405.15730 v1 pith:V2FF7ZZH submitted 2024-05-24 math.OC math.AP

Omar Oukdach , Said Boulite , Abdellatif Elgrou , Lahcen Maniar This is my paper · ORCID
classification math.OCmath.AP
keywords controlboundaryconditionsdynamicequationsfollowersleadersmulti-objective
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This paper deals with a hierarchical multi-objective control problem for forward stochastic parabolic equations with dynamic boundary conditions. The controls are divided into two classes: leaders and followers. The goal of the leaders is of null controllability type while the followers are in charge of letting the state close to prescribed targets in fixed observation regions. To solve the problem, Nash and Stackelberg strategies are used. To implement these strategies, we combine some appropriate Carleman estimates and the well-known control duality approach.

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  1. Insensitizing controls for stochastic parabolic equations with dynamic boundary conditions

    math.OC 2024-11 reject novelty 6.0 of 10

    The authors attempt to prove existence of insensitizing controls for a stochastic heat equation with dynamic boundary conditions, but a key Carleman-to-observability step in the proof is invalid.

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