The outputs robustness is a property where the outputs of a system are insensitive to disturbances, and the property plays an important role in biological systems or engineering design. This paper presents an approach to analyze the outputs robustness with respect to disturbances (w.r.t. disturbances) for Boolean control networks (BCNs). Based on the wiring digraph of a BCN rather than the state transition digraph, an algorithm is proposed to construct a corresponding permutation digraph and permutation system. Then, we prove that if there exists a pinning controller such that the outputs of a permutation system are robust w.r.t. disturbances, then there must also exist another pinning controller such that the outputs of the corresponding original systems achieve robustness. Furthermore, pinning controllers are designed based on the neighbors of the pinned-nodes rather than all of the nodes. Finally, the proposed method is well demonstrated by a reduced signal transduction network.

中文翻译：

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通过钉扎控制输出布尔控制网络的鲁棒性

输出鲁棒性是系统输出对干扰不敏感的属性，并且该属性在生物系统或工程设计中起着重要作用。本文提出了一种针对布尔控制网络（BCN）的关于扰动（wrt扰动）的输出鲁棒性分析方法。基于BCN的接线图而不是状态转移图，提出了一种构建对应的置换图和置换系统的算法。然后，我们证明如果存在一个钉扎控制器，使得排列系统的输出是鲁棒的wrt干扰，那么还必须存在另一个钉扎控制器，以使相应原始系统的输出达到鲁棒性。此外，固定控制器是根据固定节点的邻居而不是所有节点设计的。最后，通过减少的信号转导网络很好地证明了所提出的方法。