论文标题
布尔网络的一般控制框架
A General Control Framework for Boolean Networks
论文作者
论文摘要
本文着重于为大规模布尔网络(\ texttt {bns})提出一个通用控制框架。仅通过网络结构,\ texttt {bns}的结构可控性概念才被形式化。为\ texttt {bns}的结构可控性得出了必要和足够的标准;可以用$θ(n^2)$时间进行验证,其中$ n $是网络节点的数量。一个有趣的结论表明,只有在结构固定时可控时,就可以在结构上控制\ texttt {bn}。之后,关于结构可控性的最小节点控制问题被证明是结构\ texttt {bns}的NP-HARD。根据结构可控的标准,可以有效地解决三个困难的控制问题,并伴随一些优势。就固定控制器的设计而言,通过利用结构可控的标准生成可控制的\ texttt {bn},首次开发了固定节点集的选择过程,而不仅仅是在给定的固定控制形式下检查可控性;固定控制器的分布式形式为$θ(n2^{3d^{\ ast}}}}+2(n+m)^2)$,其中$ m $和$ d^\ ast $是生成器的数量和最大Verterex In-degree。关于稳定的控制设计,概率\ texttt {bns}(\ texttt {pbns})的概率,事实证明,一个重要的定理可以揭示几种类型的稳定性之间的等效性。然后,通过结构可控的标准在一定程度上解决了概率稳定的现有困难。
This paper focuses on proposing a general control framework for large-scale Boolean networks (\texttt{BNs}). Only by the network structure, the concept of structural controllability for \texttt{BNs} is formalized. A necessary and sufficient criterion is derived for the structural controllability of \texttt{BNs}; it can be verified with $Θ(n^2)$ time, where $n$ is the number of network nodes. An interesting conclusion is shown as that a \texttt{BN} is structurally controllable if and only if it is structurally fixed-time controllable. Afterwards, the minimum node control problem with respect to structural controllability is proved to be NP-hard for structural \texttt{BNs}. In virtue of the structurally controllable criterion, three difficult control issues can be efficiently addressed and accompanied with some advantages. In terms of the design of pinning controllers to generate a controllable \texttt{BN}, by utilizing the structurally controllable criterion, the selection procedure for the pinning node set is developed for the first time instead of just checking the controllability under the given pinning control form; the pinning controller is of distributed form, and the time complexity is $Θ(n2^{3d^{\ast}}+2(n+m)^2)$, where $m$ and $d^\ast$ are respectively the number of generators and the maximum vertex in-degree. With regard to the control design for stabilization in probability of probabilistic \texttt{BNs} (\texttt{PBNs}), an important theorem is proved to reveal the equivalence between several types of stability. The existing difficulties on the stabilization in probability are then solved to some extent via the structurally controllable criterion.