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Frontiers of Information Technology & Electronic Engineering
ISSN 2095-9184 (print), ISSN 2095-9230 (online)
2020 Vol.21 No.2 P.268-280
Bisimulation-based stabilization of probabilistic Boolean control networks with state feedback control
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.
Key words: Probabilistic Boolean control network, Bisimulation, Stabilization with probability one, State feedback control
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。
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DOI:
10.1631/FITEE.1900447
CLC number:
TP13
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On-line Access:
2020-03-04
Received:
2019-08-29
Revision Accepted:
2019-10-21
Crosschecked:
2019-12-11