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Stabilization and set stabilization of switched Boolean control networks via flipping mechanism
Nonlinear Analysis: Hybrid Systems ( IF 3.7 ) Pub Date : 2021-05-06 , DOI: 10.1016/j.nahs.2021.101055
Qiliang Zhang , Jun-e Feng , Ying Zhao , Jianli Zhao

Stabilization and set stabilization of switched Boolean control networks are investigated by using flipping mechanism in this paper. Firstly, with the help of Warshall algorithm, an explicit criterion for the stabilization of switched Boolean control networks is derived. Secondly, the necessary and sufficient condition for the solvability of stabilization of switched Boolean control networks, by flipping some elements of perturbation set once, is presented. Thirdly, a search algorithm is proposed to calculate the minimum number of stabilization flipped nodes and what exactly they are. Furthermore, a necessary and sufficient condition is established for the solvability of set stabilization of switched Boolean control networks by flipping some elements of perturbation set once. Analogously, an algorithm is given to find the minimum number of set stabilization flipped nodes. Finally, examples are shown to demonstrate the feasibility of the above results.



中文翻译:

通过翻转机制对布尔布尔控制网络进行镇定和集镇定

利用翻转机制研究了交换布尔控制网络的镇定和集镇定。首先,借助Warshall算法,推导了布尔交换控制网络稳定的显式判据。其次,通过一次扰动集合的某些元素一次翻转,给出了交换布尔控制网络稳定化的可解性的充要条件。第三,提出了一种搜索算法来计算稳定翻转节点的最小数量以及它们的确切数目。此外,通过一次扰动集合的一些元素的一次翻转,为交换布尔控制网络的集合稳定的可解性建立了必要和充分的条件。类似地,给出了一种算法,以找到设置的稳定翻转节点的最小数量。最后,通过实例说明了上述结果的可行性。

更新日期:2021-05-06
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