中文摘要：

细胞凋零是细胞受基因控制的生物学演化现象，在生物进化中起非常重要的作用．布尔网络的提出为人们研究基因控制问题提供了新方法．文章以矩阵半张量积作为主要工具，考虑周期时变布尔控制网络的能控性和能达性问题．首先将周期时变布尔控制网络转换为离散动态系统，定义系统的依时间输入一状态关联矩阵；其次由依时间输入一状态关联矩阵给出了一系列周期时变布尔控制网络的能控性和能达性的充要判定条件，并设计了寻找最优控制序列的算法；最后将所得结论应用到一类细胞凋零网络，验证了所提供方法的有效性．

英文摘要：

Apoptosis, playing an important role in biological evolution, is a biological evolutionary phenomenon of cell controlled by gene. The introduction of Boolean networks provides a new method of researching the problem of gene regulation. This paper investigates the reachability and controllability of periodically time-variant Boolean control networks （BCNs） mainly based on the technique of the semi-tensor product of matrices. First, logical dynamic equations of periodically time-variant BCNs are transformed into discrete-time dynamic systems using the semi-tensor product of matrices, and a kind of time-dependent input-state incidence matrix is defined according to the algebraic representation; then by using the method of the time-dependent input-state incidence matrix, several necessary and sufficient conditions are obtained for the reachability and controllability of periodically time- variant BCNs, and an algorithm is designed to find a time-dependent control scheme to reach the target in the shortest time; finally, the effectiveness and correctiveness are verified by using relevent conclusions to research a class of apoptosis network.