In this article, a hybrid method combining flip matrix approach and an open (or closed) loop control is proposed to study global controllability and stabilization of Boolean control networks (BCNs). First, the necessary and sufficient condition for global controllability of BCNs, by flipping some members of a perturbation set and under free control sequences, is proposed. After that, using a search algorithm, the minimal perturbation sets for global controllability (MS‐GCs) of the BCN are obtained. Next, we propose a necessary and sufficient criterion for global stabilization of BCNs by flipping some members of a perturbation set and under a state feedback control. Similarly, an algorithm is given to search for the minimal perturbation sets for global stabilization (MS‐GSs) of the BCN. Moreover, the time‐optimal MS‐GSs of the BCN are also obtained by an algorithm. Some examples are given to illustrate the effectiveness of the results.

中文翻译：

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通过翻转辅助功能实现布尔控制网络的可控性和稳定性

在本文中，提出了一种将翻转矩阵方法与开环（或闭环）控制相结合的混合方法，以研究布尔控制网络（BCN）的全局可控性和稳定性。首先，通过扰动集的某些成员并在自由控制序列下，提出了BCN全局可控性的充要条件。之后，使用搜索算法，获得BCN全局可控性（MS-GC）的最小扰动集。接下来，我们通过扰动集的某些成员并在状态反馈控制下，为BCN的全局稳定提出了一个必要和充分的标准。类似地，给出了一种算法来搜索BCN的全局稳定（MS-GSs）的最小扰动集。此外，BCN的时间最佳MS-GS也通过算法获得。给出了一些例子来说明结果的有效性。