The control problems of $k$ -valued logical systems have gained a lot of research attention in recent years. In most existing works about the control problems of $k$ -valued logical systems, the controllers are injected to all the nodes or some randomly selected nodes. As a consequence, the control objectives, such as controllability and stabilization, can only be achieved when the logical system satisfies certain conditions. Motivated by this, in this article, a pinning controller design algorithm, including a constructive method to select the pinning nodes and Boolean sequence controller design, is proposed such that for any given $k$ -valued logical system, it is controllable. First, an algorithm for reconstructing the transition matrix for a $k$ -valued logical system is given such that it is controllable with the designed transition matrix. The selection of pinning nodes is considered according to the designed transition matrix and the properties of $k$ -valued logical systems. The logical relationship between the control input nodes and the system nodes is given by solving some logical matrix equations. The control sequence design algorithm is also provided. Finally, two numerical examples are presented to illustrate the effectiveness of the proposed results.

中文翻译：

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钉扎的可控性 $ k $值逻辑系统

控制问题 $ k $ 值逻辑系统近年来受到了很多研究关注。在大多数现有的关于控制问题的著作中$ k $ 值逻辑系统，将控制器注入所有节点或某些随机选择的节点。结果，只有当逻辑系统满足某些条件时，才能实现控制目标，例如可控性和稳定性。因此，本文提出了一种钉扎控制器设计算法，包括选择钉扎节点的构造方法和布尔序列控制器设计，从而对于任何给定$ k $ 值逻辑系统，它是可控制的。首先，一种算法用于重建$ k $ 给出了一个有价逻辑系统，使其可以使用设计的转换矩阵进行控制。根据设计的过渡矩阵和节点的特性来考虑固定节点的选择$ k $ 值逻辑系统。控制输入​​节点和系统节点之间的逻辑关系通过求解一些逻辑矩阵方程式给出。还提供了控制序列设计算法。最后，通过两个数值例子说明了所提出结果的有效性。