As the backbone of Industrial 4.0, cyber‐physical systems (CPSs) are widely applicable in industrial processes. In this paper, a resilient control is designed for a class of two‐dimensional (2D) CPSs with the occurrence of Denial‐of‐Service (DoS) attacks. Firstly, we model the physical layer of CPSs as a 2D Fornasini‐Marchesini plant and set up the stability issue as preliminaries. Next, for CPSs suffering from DoS attacks, under which the controller operating in the fog layer is attacked by adversaries, sufficient conditions are established to guarantee the exponential stability of the underlying systems, and the corresponding switched control is designed to make a prescribed system performance is satisfied. Finally, an example is given to illustrate the effectiveness and potential of the proposed design methods.

中文翻译：

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拒绝服务攻击下的二维系统的主动弹性控制

作为工业4.0的骨干网络物理系统（CPS）广泛应用于工业过程。本文针对发生拒绝服务（DoS）攻击的一类二维（2D）CPS设计了一种弹性控制。首先，我们将CPS的物理层建模为2D Fornasini-Marchesini工厂，并将稳定性问题设置为初步模型。接下来，对于遭受DoS攻击的CPS，在其中攻击在雾层中的控制器受到对手的攻击，要建立足够的条件以保证基础系统的指数稳定性，并设计相应的开关控制以实现规定的系统性能。很满意。最后，给出一个例子来说明所提出的设计方法的有效性和潜力。