Complete synchronization of coupled Boolean networks with arbitrary finite delays

LIU Jie; LI Lulu; FARDOUN Habib M.

doi:10.1631/FITEE.1900438

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Complete synchronization of coupled Boolean networks with arbitrary finite delays

Special Issue on Complex Systems and Networks with Their Applications | Updated：2022-05-19

- Complete synchronization of coupled Boolean networks with arbitrary finite delays
- 具有任意有限延迟耦合布尔网络的完全同步
- Frontiers of Information Technology & Electronic Engineering Vol. 21, Issue 2, Pages: 281-293(2020)
- Affiliations：
  
  School of Mathematics, Hefei University of Technology, Hefei 230009, China
  Department of Information Systems, Faculty of Computing and Information Technology, King Abdulaziz University, Jeddah 21589, Saudi Arabia
- Author bio：
  
  [ "Jie LIU, E-mail: PYSF_JL@163.com" ]
  Lulu LI, E-mail: lululima@hfut.edu.cn
  [ "Habib M. FARDOUN, E-mail: hfardoun@kau.edu.sa" ]
- Funds：
- DOI：10.1631/FITEE.1900438
  CLC： O233
- Received：26 August 2019，
  
  Revised：2019-12-13，
  
  Published：2020-02
- Accepted：
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LIU Jie, LI Lulu, FARDOUN Habib M.. Complete synchronization of coupled Boolean networks with arbitrary finite delays[J]. Frontiers of Information Technology & Electronic Engineering, 2020, 21(2): 281-293.
DOI：

LIU Jie, LI Lulu, FARDOUN Habib M.. Complete synchronization of coupled Boolean networks with arbitrary finite delays[J]. Frontiers of Information Technology & Electronic Engineering, 2020, 21(2): 281-293. DOI： 10.1631/FITEE.1900438.

摘要

研究耦合延迟布尔网络完全同步性问题。文中所讨论的耦合延迟布尔网络模型中，状态延迟和输出延迟可能不相等，并且每个布尔网络中的状态延迟也可能不相等。基于矩阵半张量积获得耦合延迟布尔网络达到完全同步的充要条件。提供解决耦合延迟布尔网络完全同步性的有效算法。最后，通过数值算例说明该算法的有效性。

Abstract

In this study

the complete synchronization problem of coupled delayed Boolean networks (CDBNs) is investigated. The state delays and output delays may not be equal

and the state delay in each Boolean network may be different in the proposed CDBN model. Based on the semi-tensor product of matrices

a necessary and sufficient condition for the complete synchronization of CDBNs is obtained. Then

an efficient algorithm for solving the synchronization of CDBNs is provided. Finally

numerical examples are presented to demonstrate the effectiveness of our algorithm.

关键词

Keywords

references

DZ Cheng , , , HS Qi . . A linear representation of dynamics of Boolean networks . . IEEE Trans Autom Contr , , 2010 . . 55 ( ( 10 ): ): 2251 - - 2258 . . DOI: 10.1109/TAC.2010.2043294 http://doi.org/10.1109/TAC.2010.2043294 . .

DZ Cheng , , , HS Qi , , , ZQ Li . . Analysis and Control of Boolean Networks: a Semi-tensor Product Approach . . Springer-Verlag, London. , , 2011 . . .

E Fornasini , , , ME Valcher . . Fault detection analysis of Boolean control networks . . IEEE Trans Autom Contr , , 2015 . . 60 ( ( 10 ): ): 2734 - - 2739 . . DOI: 10.1109/TAC.2015.2396646 http://doi.org/10.1109/TAC.2015.2396646 . .

YQ Guo , , , P Wang , , , WH Gui , , , 等 . . Set stability and set stabilization of Boolean control networks based on invariant subsets . . Automatica , , 2015 . . 61 106 - - 112 . . DOI: 10.1016/j.automatica.2015.08.006 http://doi.org/10.1016/j.automatica.2015.08.006 . .

J Heidel , , , J Maloney , , , C Farrow , , , 等 . . Finding cycles in synchronous Boolean networks with applications to biochemical systems . . Int J Bifurc Chaos , , 2003 . . 13 ( ( 3 ): ): 535 - - 552 . . DOI: 10.1142/S0218127403006765 http://doi.org/10.1142/S0218127403006765 . .

C Huang , , , JQ Lu , , , DWC Ho , , , 等 . . Stabilization of probabilistic Boolean networks via pinning control strategy . . Inform Sci , , 2020 . . 510 205 - - 217 . . DOI: 10.1016/j.ins.2019.09.029 http://doi.org/10.1016/j.ins.2019.09.029 . .

SA Kauffman . . Metabolic stability and epigenesis in randomly constructed genetic nets . . J Theor Biol , , 1969 . . 22 ( ( 3 ): ): 437 - - 467 . . DOI: 10.1016/0022-5193(69)90015-0 http://doi.org/10.1016/0022-5193(69)90015-0 . .

K Kobayashi , , , K Hiraishi . . Design of probabilistic Boolean networks based on network structure and steady-state probabilities . . IEEE Trans Neur Netw Learn Syst , , 2017 . . 28 ( ( 8 ): ): 1966 - - 1971 . . DOI: 10.1109/TNNLS.2016.2572063 http://doi.org/10.1109/TNNLS.2016.2572063 . .

D Laschov , , , M Margaliot , , , G Even . . Observability of Boolean networks: a graph-theoretic approach . . Automatica , , 2013 . . 49 ( ( 8 ): ): 2351 - - 2362 . . DOI: 10.1016/j.automatica.2013.04.038 http://doi.org/10.1016/j.automatica.2013.04.038 . .

BW Li , , , JQ Lu , , , J Zhong , , , 等 . . Fast-time stability of temporal Boolean networks . . IEEE Trans Neur Netw Learn Syst , , 2019a . . 30 ( ( 8 ): ): 2285 - - 2294 . . DOI: 10.1109/TNNLS.2018.2881459 http://doi.org/10.1109/TNNLS.2018.2881459 . .

BW Li , , , JQ Lu , , , Y Liu , , , 等 . . The outputs robustness of Boolean control networks via pinning control . . IEEE Trans Contr Netw Syst, in press , , 2019b . . DOI: 10.1109/TCNS.2019.2913543 http://doi.org/10.1109/TCNS.2019.2913543 . .

BW Li , , , JG Lou , , , Y Liu , , , 等 . . Robust invariant set analysis of Boolean networks . . Complexity , , 2019c . . 2019 2731395 DOI: 10.1155/2019/2731395 http://doi.org/10.1155/2019/2731395 . .

R Li , , , TG Chu . . Complete synchronization of Boolean networks . . IEEE Trans Neur Netw Learn Syst , , 2012 . . 23 ( ( 5 ): ): 840 - - 846 . . DOI: 10.1109/TNNLS.2012.2190094 http://doi.org/10.1109/TNNLS.2012.2190094 . .

YY Li . . Impulsive synchronization of stochastic neural networks via controlling partial states . . Neur Process Lett , , 2017 . . 46 ( ( 1 ): ): 59 - - 69 . . DOI: 10.1007/s11063-016-9568-0 http://doi.org/10.1007/s11063-016-9568-0 . .

YY Li , , , BW Li , , , Y Liu , , , 等 . . Set stability and stabilization of switched Boolean networks with state-based switching . . IEEE Access , , 2018a . . 6 35624 - - 35630 . . DOI: 10.1109/ACCESS.2018.2851391 http://doi.org/10.1109/ACCESS.2018.2851391 . .

YY Li , , , JG Lou , , , Z Wang , , , 等 . . Synchronization of dynamical networks with nonlinearly coupling function under hybrid pinning impulsive controllers . . J Franklin Inst , , 2018b . . 355 ( ( 14 ): ): 6520 - - 6530 . . DOI: 10.1016/j.jfranklin.2018.06.021 http://doi.org/10.1016/j.jfranklin.2018.06.021 . .

YY Li , , , RJ Liu , , , JG Lou , , , 等 . . Output tracking of Boolean control networks driven by constant reference signal . . IEEE Access , , 2019 . . 7 112572 - - 112577 . . DOI: 10.1109/ACCESS.2019.2934740 http://doi.org/10.1109/ACCESS.2019.2934740 . .

RJ Liu , , , JQ Lu , , , Y Liu , , , 等 . . Delayed feedback control for stabilization of Boolean control networks with state delay . . IEEE Trans Neur Netw Learn Syst , , 2018 . . 29 ( ( 7 ): ): 3283 - - 3288 . . DOI: 10.1109/TNNLS.2017.2659386 http://doi.org/10.1109/TNNLS.2017.2659386 . .

Y Liu , , , LJ Sun , , , JQ Lu , , , 等 . . Feedback controller design for the synchronization of Boolean control networks . . IEEE Trans Neur Netw Learn Syst , , 2016 . . 27 ( ( 9 ): ): 1991 - - 1996 . . DOI: 10.1109/TNNLS.2015.2461012 http://doi.org/10.1109/TNNLS.2015.2461012 . .

Y Liu , , , BW Li , , , JQ Lu , , , 等 . . Pinning control for the disturbance decoupling problem of Boolean networks . . IEEE Trans Autom Contr , , 2017 . . 62 ( ( 12 ): ): 6595 - - 6601 . . DOI: 10.1109/TAC.2017.2715181 http://doi.org/10.1109/TAC.2017.2715181 . .

JQ Lu , , , J Zhong , , , DWC Ho , , , 等 . . On controllability of delayed Boolean control networks . . SIAM J Contr Optim , , 2016 . . 54 ( ( 2 ): ): 475 - - 494 . . DOI: 10.1137/140991820 http://doi.org/10.1137/140991820 . .

JQ Lu , , , LJ Sun , , , Y Liu , , , 等 . . Stabilization of Boolean control networks under aperiodic sampled-data control . . SIAM J Contr Optim , , 2018 . . 56 ( ( 6 ): ): 4385 - - 4404 . . DOI: 10.1137/18M1169308 http://doi.org/10.1137/18M1169308 . .

M Meng , , , J Lam , , , JE Feng , , , 等 . . Stability and guaranteed cost analysis of time-triggered Boolean networks . . IEEE Trans Neur Netw Learn Syst , , 2018 . . 29 ( ( 8 ): ): 3893 - - 3899 . . DOI: 10.1109/TNNLS.2017.2737649 http://doi.org/10.1109/TNNLS.2017.2737649 . .

KA Richardson . . Simplifying Boolean networks . . Adv Compl Syst , , 2005 . . 8 ( ( 4 ): ): 365 - - 381 . . DOI: 10.1142/S0219525905000518 http://doi.org/10.1142/S0219525905000518 . .

I Shmulevich , , , H Lähdesmäki , , , ER Dougherty , , , 等 . . The role of certain post classes in Boolean network models of genetic networks . . PNAS , , 2003 . . 100 ( ( 19 ): ): 10734 - - 10739 . . DOI: 10.1073/pnas.1534782100 http://doi.org/10.1073/pnas.1534782100 . .

LJ Sun , , , JQ Lu , , , W Ching . . Switching-based stabilization of aperiodic sampled-data Boolean control networks with all subsystems unstable . . Front Inform Technol Electron Eng , , 2020 . . 21 ( ( 2 ): ): 260 - - 267 . . DOI: 10.1631/FITEE.1900312 http://doi.org/10.1631/FITEE.1900312 . .

LY Tong , , , Y Liu , , , YY Li , , , 等 . . Robust control invariance of probabilistic Boolean control networks via event-triggered control . . IEEE Access , , 2018 . . 6 37767 - - 37774 . . DOI: 10.1109/ACCESS.2018.2828128 http://doi.org/10.1109/ACCESS.2018.2828128 . .

YH Wu , , , TL Shen . . A finite convergence criterion for the discounted optimal control of stochastic logical networks . . IEEE Trans Autom Contr , , 2018 . . 63 ( ( 1 ): ): 262 - - 268 . . DOI: 10.1109/TAC.2017.2720730 http://doi.org/10.1109/TAC.2017.2720730 . .

JJ Yang , , , JQ Lu , , , LL Li , , , 等 . . Event-triggered control for the synchronization of Boolean control networks . . Nonl Dynam , , 2019 . . 96 ( ( 2 ): ): 1335 - - 1344 . . DOI: 10.1007/s11071-019-04857-2 http://doi.org/10.1007/s11071-019-04857-2 . .

JJ Yang , , , JQ Lu , , , JG Lou , , , 等 . . Synchronization of drive-response Boolean control networks with impulsive disturbances . . Appl Math Comput , , 2020 . . 364 124679 DOI: 10.1016/j.amc.2019.124679 http://doi.org/10.1016/j.amc.2019.124679 . .

J Zhong , , , JQ Lu , , , Y Liu , , , 等 . . Synchronization in an array of output-coupled Boolean networks with time delay . . IEEE Trans Neur Netw Learn Syst , , 2014 . . 25 ( ( 12 ): ): 2288 - - 2294 . . DOI: 10.1109/TNNLS.2014.2305722 http://doi.org/10.1109/TNNLS.2014.2305722 . .

J Zhong , , , JQ Lu , , , TW Huang , , , 等 . . Controllability and synchronization analysis of identical-hierarchy mixed-valued logical control networks . . IEEE Trans Cybern , , 2017 . . 47 ( ( 11 ): ): 3482 - - 3493 . . DOI: 10.1109/TCYB.2016.2560240 http://doi.org/10.1109/TCYB.2016.2560240 . .

J Zhong , , , Y Liu , , , K Kou , , , 等 . . On the ensemble controllability of Boolean control networks using STP method . . Appl Math Comput , , 2019 . . 358 51 - - 62 . . DOI: 10.1016/j.amc.2019.03.059 http://doi.org/10.1016/j.amc.2019.03.059 . .

J Zhong , , , BW Li , , , Y Liu , , , 等 . . Output feedback stabilizer design of Boolean networks based on network structure . . Front Inform Technol Electron Eng , , 2020 . . 21 ( ( 2 ): ): 247 - - 259 . . DOI: 10.1631/FITEE.1900229 http://doi.org/10.1631/FITEE.1900229 . .

QX Zhu , , , Y Liu , , , JQ Lu , , , 等 . . On the optimal control of Boolean control networks . . SIAM J Contr Optim , , 2018 . . 56 ( ( 2 ): ): 1321 - - 1341 . . DOI: 10.1137/16M1070281 http://doi.org/10.1137/16M1070281 . .

QX Zhu , , , Y Liu , , , JQ Lu , , , 等 . . Further results on the controllability of Boolean control networks . . IEEE Trans Autom Contr , , 2019 . . 64 ( ( 1 ): ): 440 - - 442 . . DOI: 10.1109/TAC.2018.2830642 http://doi.org/10.1109/TAC.2018.2830642 . .

SY Zhu , , , JG Lou , , , Y Liu , , , 等 . . Event-triggered control for the stabilization of probabilistic Boolean control networks . . Complexity , , 2018 . . 2018 9259348 DOI: 10.1155/2018/9259348 http://doi.org/10.1155/2018/9259348 . .

SY Zhu , , , JQ Lu , , , Y Liu . . Asymptotical stability of probabilistic Boolean networks with state delays . . IEEE Trans Autom Contr, in press , , 2019 . . DOI: 10.1109/TAC.2019.2934532 http://doi.org/10.1109/TAC.2019.2934532 . .

YL Zou , , , JD Zhu . . System decomposition with respect to inputs for Boolean control networks . . Automatica , , 2014 . . 50 ( ( 4 ): ): 1304 - - 1309 . . DOI: 10.1016/j.automatica.2014.02.039 http://doi.org/10.1016/j.automatica.2014.02.039 . .

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