一般动态边界条件下热方程的Stackelberg-Nash零可控性

IF 1.3 4区数学 Q1 MATHEMATICS

Evolution Equations and Control Theory Pub Date : 2021-09-06 DOI:10.3934/eect.2021044

I. Boutaayamou, L. Maniar, O. Oukdach

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引用次数: 4

摘要

研究了具有动态边界条件和漂移项的各向异性热方程的层次控制问题。我们使用Stackelberg-Nash策略，一个领导者和两个追随者。对于每个固定的领导者，我们找到了一个纳什均衡，对应于一个双目标最优控制问题。然后，通过一些新的Carleman估计，证明了零可控性的结果。

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Stackelberg-Nash null controllability of heat equation with general dynamic boundary conditions

This paper deals with the hierarchical control of the anisotropic heat equation with dynamic boundary conditions and drift terms. We use the Stackelberg-Nash strategy with one leader and two followers. To each fixed leader, we find a Nash equilibrium corresponding to a bi-objective optimal control problem for the followers. Then, by some new Carleman estimates, we prove a null controllability result.

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来源期刊

Evolution Equations and Control Theory MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

3.10

自引率

6.70%

发文量

期刊介绍： EECT is primarily devoted to papers on analysis and control of infinite dimensional systems with emphasis on applications to PDE''s and FDEs. Topics include: * Modeling of physical systems as infinite-dimensional processes * Direct problems such as existence, regularity and well-posedness * Stability, long-time behavior and associated dynamical attractors * Indirect problems such as exact controllability, reachability theory and inverse problems * Optimization - including shape optimization - optimal control, game theory and calculus of variations * Well-posedness, stability and control of coupled systems with an interface. Free boundary problems and problems with moving interface(s) * Applications of the theory to physics, chemistry, engineering, economics, medicine and biology