探讨概率布尔网络的控制问题可以加深对生物系统内部机能的理解, 并有助于制定合理的措施实现复杂生物系统的有效调控. 文章考虑概率布尔网络的集合镇定控制问题, 以矩阵的半张量积作为主要的研究工具, 建立了概率布尔网络可全局镇定至给定目标状态集合的充分必要条件, 并进一步在网络可镇定时提出了镇定控制器的设计方法, 解决了概率布尔网络的集合镇定问题.

Addressing control-related problems in probabilistic Boolean networks may reveal new insights into the intrinsic functions of complex biological systems and enable us to develop strategies for manipulating biological systems using exogenous inputs. This paper investigates the problem of global stabilization of a probabilistic Boolean network to a given set of states using a state feedback law. The discussion is based on the recently developed technique of the semi-tensor product of matrices. A simple necessary and sufficient condition is derived for the existence of such a stabilizing feedback law, and a control design method is proposed when global stabilization via state feedback is feasible.