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.
Multi-objective control for stochastic parabolic equations with dynamic boundary conditions
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abstract
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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math.OC 1years
2024 1verdicts
REJECT 1representative citing papers
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Insensitizing controls for stochastic parabolic equations with dynamic boundary conditions
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.