Department of Mathematics, Tongji University, Shanghai, 200092, PR China.
Neural Netw. 2013 Mar;39:12-7. doi: 10.1016/j.neunet.2012.12.004. Epub 2012 Dec 23.
Using the semi-tensor product, the global control problem of the higher order Boolean control network with avoiding set is considered. First, the number of different control sequences that drive the higher order Boolean control network from the initial state to the destination state while avoiding undesirable set is provided. Then, the definition of global controllability of higher order Boolean control network is given. Third, by using the classical theory of nonnegative matrices, the necessary and sufficient condition for the global controllability of higher order Boolean control network with avoiding set is presented. Furthermore, a sufficient condition for k fixed-time global controllability of the system is also obtained. At last, an example is given to illustrate the main results.
利用张量积方法研究了具有避区的高阶布尔控制网络的全局控制问题。首先，给出了在避区的情况下，驱动高阶布尔控制网络从初始状态到达目标状态的不同控制序列的数量。然后，给出了高阶布尔控制网络的全局可控性定义。第三，利用非负矩阵的经典理论，给出了具有避区的高阶布尔控制网络全局可控性的充要条件。此外，还得到了系统 k 固定时间全局可控性的充分条件。最后，通过一个实例说明了主要结果。
