This paper investigates the controllability and reachability of periodically time-variant mixed-valued logical control networks (PTMLCNs). The PTMLCN considered in this paper consists of several mixed-valued logical control networks with periodically switching signals, which circulates among different mixed-valued logical control networks. First, a PTMLCN is transformed into a discrete dynamic system by the semi-tensor product. Based on this algebraic expression, the time-dependent input-state incident matrix and the time-dependent state transition matrix are defined and the relationship between these two matrices is given. Secondly, the controllability and reachability of PTMLCNs are defined. Subsequently, by virtue of the proposed matrices, a series of necessary and sufficient conditions are given for checking controllability and reachability, and the algorithm for finding the optimal control sequence to reach the target state in the shortest time is designed. Finally, the effectiveness of the proposed method is verified by an example.

本文研究了周期性时变混合值逻辑控制网络 (PTMLCN) 的可控性和可达性。本文考虑的 PTMLCN 由多个混合值逻辑控制网络组成，这些网络具有周期性切换信号，在不同的混合值逻辑控制网络之间循环。首先，通过半张量积将 PTMLCN 转换为离散动态系统。基于该代数表达式，定义了瞬态输入状态事件矩阵和瞬态状态转移矩阵，并给出了这两个矩阵之间的关系。其次，定义了PTMLCNs的可控性和可达性。随后，凭借所提出的矩阵，给出了一系列检验可控性和可达性的充要条件，并设计了寻找最优控制序列以在最短的时间内达到目标状态的算法。最后通过算例验证了所提方法的有效性。