Full Text:   <400>

Summary:  <62>

CLC number: TP183

On-line Access: 2020-03-04

Received: 2019-05-07

Revision Accepted: 2019-07-11

Crosschecked: 2019-09-12

Cited: 0

Clicked: 892

Citations:  Bibtex RefMan EndNote GB/T7714

 ORCID:

Yang Liu

http://orcid.org/0000-0002-9005-9166

-   Go to

Article info.
Open peer comments

Frontiers of Information Technology & Electronic Engineering  2020 Vol.21 No.2 P.247-259

http://doi.org/10.1631/FITEE.1900229


Output feedback stabilizer design of Boolean networks based on network structure


Author(s):  Jie Zhong, Bo-wen Li, Yang Liu, Wei-hua Gui

Affiliation(s):  College of Mathematics and Computer Science, Zhejiang Normal University, Jinhua 321004, China; more

Corresponding email(s):   zhongjie0615@gmail.com, qfhxjy@126.com, liuyang@zjnu.edu.cn, gwh@csu.edu.cn

Key Words:  Boolean networks, Output feedback stabilizer, Network structure, Semi-tensor product of matrices


Jie Zhong, Bo-wen Li, Yang Liu, Wei-hua Gui. Output feedback stabilizer design of Boolean networks based on network structure[J]. Frontiers of Information Technology & Electronic Engineering, 2020, 21(2): 247-259.

@article{title="Output feedback stabilizer design of Boolean networks based on network structure",
author="Jie Zhong, Bo-wen Li, Yang Liu, Wei-hua Gui",
journal="Frontiers of Information Technology & Electronic Engineering",
volume="21",
number="2",
pages="247-259",
year="2020",
publisher="Zhejiang University Press & Springer",
doi="10.1631/FITEE.1900229"
}

%0 Journal Article
%T Output feedback stabilizer design of Boolean networks based on network structure
%A Jie Zhong
%A Bo-wen Li
%A Yang Liu
%A Wei-hua Gui
%J Frontiers of Information Technology & Electronic Engineering
%V 21
%N 2
%P 247-259
%@ 2095-9184
%D 2020
%I Zhejiang University Press & Springer
%DOI 10.1631/FITEE.1900229

TY - JOUR
T1 - Output feedback stabilizer design of Boolean networks based on network structure
A1 - Jie Zhong
A1 - Bo-wen Li
A1 - Yang Liu
A1 - Wei-hua Gui
J0 - Frontiers of Information Technology & Electronic Engineering
VL - 21
IS - 2
SP - 247
EP - 259
%@ 2095-9184
Y1 - 2020
PB - Zhejiang University Press & Springer
ER -
DOI - 10.1631/FITEE.1900229


Abstract: 
In genetic regulatory networks, a stable configuration can represent the evolutionary behavior of cell death or unregulated growth in genes. We present analytical investigations on output feedback stabilizer design of boolean networks (BNs) to achieve global stabilization via the semi-tensor product method. Based on network structure information describing coupling connections among nodes, an output feedback stabilizer is designed to achieve global stabilization. Compared with the traditional pinning control design, the output feedback stabilizer design is not based on the state transition matrix of BNs, which can efficiently determine pinning control nodes and reduce computational complexity. Our proposed method is efficient in that the calculation of the state transition matrix with dimension 2n×2n is avoided; here n is the number of nodes in a BN. Finally, a signal transduction network and a D. melanogaster segmentation polarity gene network are presented to show the efficiency of the proposed method. Results are shown to be simple and concise, compared with traditional pinning control for BNs.

基于网络结构的布尔网络输出反馈镇定器设计

钟杰1,李博文2,3,刘洋1,桂卫华4
1浙江师范大学数学与计算机科学学院,中国金华市,321004
2东南大学信息科学与工程学院,中国南京市,210096
3东南大学网络空间安全学院,中国南京市,210096
4中南大学自动化学院,中国长沙市,410083

摘要:在基因调控网络中,稳态结构可以用来表示细胞死亡或基因不受调控生长的进化行为。本文利用矩阵半张量积工具,分析与研究布尔网络输出反馈镇定器的设计。基于描述节点间耦合关系的网络结构信息,设计了输出反馈镇定器以实现全局稳定。与传统牵制控制器设计相比,输出反馈镇定器设计不再基于布尔网络的状态转移矩阵,可以有效确定牵制节点,降低计算复杂度。本文所提方法有效避免了计算2n×2n维的状态转移矩阵,这里n是布尔网络的节点数。最后,分别在一个信号转导网络和一个黑腹果蝇极性基因网络进行仿真模拟,证明该方法有效。结果表明,与传统布尔网络牵制控制相比,该方法更为简单、简洁。

关键词:布尔网络;输出反馈镇定器;网络结构;矩阵半张量积

Darkslateblue:Affiliate; Royal Blue:Author; Turquoise:Article

Reference

[1]Aracena J, 2008. Maximum number of fixed points in regulatory Boolean networks. Bull Math Biol, 70(5):1398-1409.

[2]Ay F, Xu F, Kahveci T, 2009. Scalable steady state analysis of Boolean biological regulatory networks. PLoS ONE, 4(12):e7992.

[3]Bang-Jensen J, Gutin G, 2008. Digraphs: Theory, Algorithms and Applications. Springer New York, USA.

[4]Bof N, Fornasini E, Valcher ME, 2015. Output feedback stabilization of Boolean control networks. Automatica, 57:21-28.

[5]Campbell C, Albert R, 2014. Stabilization of perturbed Boolean network attractors through compensatory interactions. BMC Syst Biol, 8, Article 53.

[6]Cheng DZ, Liu T, 2016. A survey on logical control systems. Unman Syst, 4(1):97-116.

[7]Cheng DZ, Qi HS, Li ZQ, 2010. Analysis and Control of Boolean Networks: a Semi-tensor Product Approach. Springer London, UK.

[8]Cheng DZ, Qi HS, Li ZQ, et al., 2011. Stability and stabilization of Boolean networks. Int J Robust Nonlin Contr, 21(2):134-156.

[9]Fan HB, Feng JE, Meng M, et al., 2018 General decomposition of fuzzy relations: semi-tensor product approach. Fuzzy Sets Syst, in press,

[10]Fornasini E, Valcher ME, 2013. Observability, reconstructibility and state observers of Boolean control networks. IEEE Trans Autom Contr, 58(6):1390-1401.

[11]Guo Y, Wang P, Gui W, et al., 2015. Set stability and set stabilization of Boolean control networks based on invariant subsets. Automatica, 61:106-112.

[12]Kauffman S, 1969. Metabolic stability and epigenesis in randomly constructed genetic nets. J Theor Biol, 22(3): 437-467.

[13]Kauffman S, Peterson C, Samuelsson B, et al., 2003. Random Boolean network models and the yeast transcriptional network. PNAS, 100(25):14796-14799.

[14]Kobayashi K, Hiraishi K, 2017. Design of probabilistic Boolean networks based on network structure and steady-state probabilities. IEEE Trans Neur Netw Learn Syst, 28(8):1966-1971.

[15]Laschov D, Margaliot M, 2012. Controllability of Boolean control networks via the Perron-Frobenius theory. Automatica, 48(6):1218-1223.

[16]Li BW, Lu JQ, Zhong J, et al., 2019a. Fast-time stability of temporal Boolean networks. IEEE Trans Neur Netw Learn Syst, 30(8):2285-2294.

[17]Li BW, Lu JQ, Liu Y, et al., 2019b. The outputs robustness of Boolean control networks via pinning control. IEEE Trans Contr Netw Syst, in press.

[18]Li BW, Lou JG, Liu Y, et al., 2019c. Robust invariant set analysis of Boolean networks. Complexity, 2019, Article 2731395.

[19]Li FF, 2015. Pinning control design for the stabilization of Boolean networks. IEEE Trans Neur Netw Learn Syst, 27(7):1585-1590.

[20]Li FF, 2016. Pinning control design for the synchronization of two coupled Boolean networks. IEEE Trans Circ Syst II, 63(3):309-313.

[21]Li HT, Wang YZ, 2013. Output feedback stabilization control design for Boolean control networks. Automatica, 49(12):3641-3645.

[22]Li HT, Wang YZ, 2017. Further results on feedback stabilization control design of Boolean control networks. Automatica, 83:303-308.

[23]Li R, Yang M, Chu TG, 2013. State feedback stabilization for Boolean control networks. IEEE Trans Autom Contr, 58(7):1853-1857.

[24]Li XD, Ho DWC, Cao JD, 2019. Finite-time stability and settling-time estimation of nonlinear impulsive systems. Automatica, 99:361-368.

[25]Li YY, Zhong J, Lu JQ, et al., 2017. On robust synchronization of drive-response Boolean control networks with disturbances. Math Probl Eng, 2018, Article 1737685.

[26]Li YY, Li BW, Liu Y, et al., 2018a. Set stability and stabilization of switched Boolean networks with state-based switching. IEEE Access, 6:35624-35630.

[27]Li YY, Lou JG, Wang Z, et al., 2018b. Synchronization of dynamical networks with nonlinearly coupling function under hybrid pinning impulsive controllers. J Franklin Inst, 355(14):6520-6530.

[28]Liu Y, Li BW, Lu JQ, et al., 2017. Pinning control for the disturbance decoupling problem of Boolean networks. IEEE Trans Autom Contr, 62(12):6595-6601.

[29]Lu JQ, Li ML, Liu Y, et al., 2018a. Nonsingularity of Grain-like cascade FSRs via semi-tensor product. Sci China Inform Sci, 61:010204.

[30]Lu JQ, Sun LJ, Liu Y, et al., 2018b. Stabilization of Boolean control networks under aperiodic sampled-data control. SIAM J Contr Optim, 56(6):4385-4404.

[31]Lu JQ, Li ML, Huang TW, et al., 2018c. The transformation between the Galois NLFSRs and the Fibonacci NLFSRs via semi-tensor product of matrices. Automatica, 96:393-397.

[32]Mao Y, Wang L, Liu Y, et al., 2018. Stabilization of evolutionary networked games with length- r information. Appl Math Comput, 337:442-451.

[33]Meng M, Lam J, Feng J, et al., 2018. Stability and guaranteed cost analysis of time-triggered Boolean networks. IEEE Trans Neur Netw Learn Syst, 29(8):3893-3899.

[34]Mori F, Mochizuki A, 2017. Expected number of fixed points in Boolean networks with arbitrary topology. Phys Rev Lett, 119:028301.

[35]Murrugarra D, Veliz-Cuba A, Aguilar B, et al., 2016. Identification of control targets in Boolean molecular network models via computational algebra. BMC Syst Biol, 10, Article 94.

[36]Pan J, Feng J, Meng M, 2019. Steady-state analysis of probabilistic Boolean networks. J Franklin Inst, 356(5):2994-3009.

[37]Paulevé L, Richard A, 2012. Static analysis of Boolean networks based on interaction graphs: a survey. Electron Notes Theor Comput Sci, 284:93-104.

[38]Robert F, 1986. Discrete Iterations: a Metric Study. Springer New York, USA.

[39]Saadatpour A, Albert I, Albert R, 2010. Attractor analysis of asynchronous Boolean models of signal transduction networks. J Theor Biol, 266(4):641-656.

[40]Saadatpour A, Wang R, Liao A, et al., 2011. Dynamical and structural analysis of a T cell survival network identifies novel candidate therapeutic targets for large granular lymphocyte leukemia. PLoS Comput Biol, 7(11):e1002267.

[41]Tong LY, Liu Y, Li YY, et al., 2018. Robust control invariance of probabilistic Boolean control networks via event-triggered control. IEEE Access, 6:37767-37774.

[42]Wang B, Feng J, 2019. On detectability of probabilistic Boolean networks. Inform Sci, 483:383-395.

[43]Wu Y, Shen T, 2018. Policy iteration algorithm for optimal control of stochastic logical dynamical systems. IEEE Trans Neur Netw Learn Syst, 29(5):2031-2036.

[44]Xiao YF, Dougherty ER, 2007. The impact of function perturbations in Boolean networks. Bioinformatics, 23(10):1265-1273.

[45]Yang M, Li R, Chu TG, 2013. Controller design for disturbance decoupling of Boolean control networks. Automatica, 49(1):273-277.

[46]Yu Y, Feng J, Pan J, et al., 2019. Block decoupling of Boolean control networks. IEEE Trans Autom Contr, 64(8):3129-3140.

[47]Zhang K, Zhang L, 2016. Observability of Boolean control networks: a unified approach based on finite automata. IEEE Trans Autom Contr, 61(9):2733-2738.

[48]Zhao Y, Ghosh BK, Cheng D, 2016. Control of large-scale Boolean networks via network aggregation. IEEE Trans Neur Netw Learn Syst, 27(7):1527-1536.

[49]Zhu QX, Lin W, 2019. Stabilizing Boolean networks by optimal event-triggered feedback control. Syst Contr Lett, 126:40-47.

[50]Zhu QX, Liu Y, Lu J, et al., 2018. On the optimal control of Boolean control networks. SIAM J Contr Optim, 56(2): 1321-1341.

[51]Zhu QX, Liu Y, Lu J, et al., 2019. Further results on the controllability of Boolean control networks. IEEE Trans Autom Contr, 64(1):440-442.

[52]Zhu SY, Lou JG, Liu Y, et al., 2018. Event-triggered control for the stabilization of probabilistic Boolean control networks. Complexity, 2018, Article 9259348.

Open peer comments: Debate/Discuss/Question/Opinion

<1>

Please provide your name, email address and a comment





Journal of Zhejiang University-SCIENCE, 38 Zheda Road, Hangzhou 310027, China
Tel: +86-571-87952783; E-mail: cjzhang@zju.edu.cn
Copyright © 2000 - Journal of Zhejiang University-SCIENCE