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The behavior of smart obstacles in electromagnetic scattering: mathematical models as optimal control problems

机译：智能障碍物在电磁散射中的行为：作为最佳控制问题的数学模型

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摘要

We consider a bounded obstacle characterized by a boundary electromagnetic impedance contained in the three dimensional real Euclidean space filled with a homogeneous isotropic medium. When an incoming electromagnetic field illuminates the obstacle a scattered field is generated. A smart obstacle is an obstacle that in the scattering process, circulating a surface electric current density on its boundary, tries to achieve a given goal. We consider four possible goals: making the obstacle undetectable (i.e.: furtivity problem), making the obstacle to appear with a shape and impedance different from its actual ones (i.e.: masking problem), making the obstacle to appear in a location different from its actual one eventually with a shape and impedance different from its actual ones (i.e.: ghost obstacle problem) and finally one of the previous goals limited to a given subset of the frequency space (i.e.: definite band problems). We consider the problem of determining the optimal electric current density to achieve the given goal. The relevance in many application fields (i.e. stealth technology, electromagnetic noise control, etc.) of these problems is well known. The previous problems are modelled as optimal control problems for the Maxwell equations. Some numerical results on test problems obtained solving the optimal control problems proposed are shown.
机译：我们考虑一个边界障碍物，其特征是在充满均匀各向同性介质的三维实际欧几里得空间中包含的边界电磁阻抗。当入射的电磁场照亮障碍物时，会产生散射场。智能障碍物是在散射过程中，在其边界上循环表面电流密度，试图达到给定目标的障碍物。我们考虑了四个可能的目标：使障碍物不可检测（即：肥力性问题）；使障碍物的形状和阻抗与实际障碍物不同（即，掩蔽问题）；使障碍物出现在与障碍物不同的位置最终，其形状和阻抗不同于其实际形状和阻抗（例如，重影障碍问题），并且最终将先前的目标之一限制到给定的频率空间子集（即，确定频带问题）。我们考虑确定最佳电流密度以实现给定目标的问题。这些问题在许多应用领域（即隐身技术，电磁噪声控制等）中的相关性是众所周知的。先前的问题被建模为麦克斯韦方程组的最优控制问题。给出了解决所提出的最优控制问题而获得的一些测试问题的数值结果。

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