JZUS - Journal of Zhejiang University SCIENCE

Frontiers of Information Technology & Electronic Engineering 2020 Vol.21 No.2 P.268-280

http://doi.org/10.1631/FITEE.1900447

Bisimulation-based stabilization of probabilistic Boolean control networks with state feedback control

Author(s): Nan Jiang, Chi Huang, Yao Chen, J�rgen Kurths
Affiliation(s): School of Economic Information Engineering, Southwestern University of Finance and Economics, Chengdu 611130, China; more
Corresponding email(s): jangnan.chloe.1023@gmail.com, huangchi@swufe.edu.cn, chenyao@swufe.edu.cn, Juergen.Kurths@pik-potsdam.de
Key Words: Probabilistic Boolean control network, Bisimulation, Stabilization with probability one, State feedback control

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Abstract: This study is concerned with probabilistic Boolean control networks (PBCNs) with state feedback control. A novel definition of bisimilar PBCNs is proposed to lower computational complexity. To understand more on bisimulation relations between PBCNs, we resort to a powerful matrix manipulation called semi-tensor product (STP). Because stabilization of networks is of critical importance, the propagation of stabilization with probability one between bisimilar PBCNs is then considered and proved to be attainable. Additionally, the transient periods (the maximum number of steps to implement stabilization) of two PBCNs are certified to be identical if these two networks are paired with a bisimulation relation. The results are then extended to the probabilistic Boolean networks.

带状态反馈控制的概率布尔网络上基于互模拟的稳定性研究

蒋楠¹，黄迟^1,2，陈姚¹，Jürgen KURTHS^3,4,5
¹西南财经大学经济信息工程学院，中国成都市，611130
²东南大学数学学院，中国南京市，210096
³波茨坦气候影响研究所，德国波茨坦，14412
⁴柏林洪堡大学物理系，德国柏林，12489
⁵萨拉托夫州立大学，俄罗斯萨拉托夫，410012

摘要：研究具有状态反馈控制的概率布尔控制网络。为降低计算复杂度，定义一种新的互模拟概率布尔控制网络。为更好理解概率布尔控制网络之间的互模拟关系，使用一种半张量积的强大矩阵运算。由于网络稳定至关重要，考虑互模拟概率布尔控制网络之间的1-概率稳定传播，并证明可行性。如果两个概率布尔控制网络之间匹配互模拟关系，则它们的过渡阶段（实现稳定的最大步骤数）被证明相同。之后，将结果推广到概率布尔网络。

关键词：概率布尔控制网络；互模拟；1-概率稳定；状态反馈控制

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