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.
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References
Cheng DZ, Qi HS, 2010. A linear representation of dynamics of Boolean networks. IEEE Trans Autom Contr, 55(10):2251–2258. https://doi.org/10.1109/TAC.2010.2043294
Cheng DZ, Qi HS, Li ZQ, 2011. Analysis and Control of Boolean Networks: a Semi-tensor Product Approach. Springer-Verlag, London.
Fornasini E, Valcher ME, 2015. Fault detection analysis of Boolean control networks. IEEE Trans Autom Contr, 60(10):2734–2739. https://doi.org/10.1109/TAC.2015.2396646
Guo YQ, Wang P, Gui WH, et al., 2015. Set stability and set stabilization of Boolean control networks based on invariant subsets. Automatica, 61:106–112. https://doi.org/10.1016/j.automatica.2015.08.006
Heidel J, Maloney J, Farrow C, et al., 2003. Finding cycles in synchronous Boolean networks with applications to biochemical systems. Int J Bifurc Chaos, 13(3):535–552. https://doi.org/10.1142/S0218127403006765
Huang C, Lu JQ, Ho DWC, et al., 2020. Stabilization of probabilistic Boolean networks via pinning control strategy. Inform Sci, 510:205–217. https://doi.org/10.1016/j.ins.2019.09.029
Kauffman SA, 1969. Metabolic stability and epigenesis in randomly constructed genetic nets. J Theor Biol, 22(3):437–467. https://doi.org/10.1016/0022-5193(69)90015-0
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. https://doi.org/10.1109/TNNLS.2016.2572063
Laschov D, Margaliot M, Even G, 2013. Observability of Boolean networks: a graph-theoretic approach. Automatica, 49(8):2351–2362. https://doi.org/10.1016/j.automatica.2013.04.038
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. https://doi.org/10.1109/TNNLS.2018.2881459
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. https://doi.org/10.1109/TCNS.2019.2913543
Li BW, Lou JG, Liu Y, et al., 2019c. Robust invariant set analysis of Boolean networks. Complexity, 2019:2731395. https://doi.org/10.1155/2019/2731395
Li R, Chu TG, 2012. Complete synchronization of Boolean networks. IEEE Trans Neur Netw Learn Syst, 23(5):840–846. https://doi.org/10.1109/TNNLS.2012.2190094
Li YY, 2017. Impulsive synchronization of stochastic neural networks via controlling partial states. Neur Process Lett, 46(1):59–69. https://doi.org/10.1007/s11063-016-9568-0
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. https://doi.org/10.1109/ACCESS.2018.2851391
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. https://doi.org/10.1016/j.jfranklin.2018.06.021
Li YY, Liu RJ, Lou JG, et al., 2019. Output tracking of Boolean control networks driven by constant reference signal. IEEE Access, 7:112572–112577. https://doi.org/10.1109/ACCESS.2019.2934740
Liu RJ, Lu JQ, Liu Y, et al., 2018. Delayed feedback control for stabilization of Boolean control networks with state delay. IEEE Trans Neur Netw Learn Syst, 29(7):3283–3288. https://doi.org/10.1109/TNNLS.2017.2659386
Liu Y, Sun LJ, Lu JQ, et al., 2016. Feedback controller design for the synchronization of Boolean control networks. IEEE Trans Neur Netw Learn Syst, 27(9):1991–1996. https://doi.org/10.1109/TNNLS.2015.2461012
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. https://doi.org/10.1109/TAC.2017.2715181
Lu JQ, Zhong J, Ho DWC, et al., 2016. On controllability of delayed Boolean control networks. SIAM J Contr Optim, 54(2):475–494. https://doi.org/10.1137/140991820
Lu JQ, Sun LJ, Liu Y, et al., 2018. Stabilization of Boolean control networks under aperiodic sampled-data control. SIAM J Contr Optim, 56(6):4385–4404. https://doi.org/10.1137/18M1169308
Meng M, Lam J, Feng JE, et al., 2018. Stability and guaranteed cost analysis of time-triggered Boolean networks. IEEE Trans Neur Netw Learn Syst, 29(8):3893–3899. https://doi.org/10.1109/TNNLS.2017.2737649
Richardson KA, 2005. Simplifying Boolean networks. Adv Compl Syst, 8(4):365–381. https://doi.org/10.1142/S0219525905000518
Shmulevich I, Lähdesmäki H, Dougherty ER, et al., 2003. The role of certain post classes in Boolean network models of genetic networks. PNAS, 100(19):10734–10739. https://doi.org/10.1073/pnas.1534782100
Sun LJ, Lu JQ, Ching W, 2020. Switching-based stabilization of aperiodic sampled-data Boolean control networks with all subsystems unstable. Front Inform Technol Electron Eng, 21(2):260–267. https://doi.org/10.1631/FITEE.1900312
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. https://doi.org/10.1109/ACCESS.2018.2828128
Wu YH, Shen TL, 2018. A finite convergence criterion for the discounted optimal control of stochastic logical networks. IEEE Trans Autom Contr, 63(1):262–268. https://doi.org/10.1109/TAC.2017.2720730
Yang JJ, Lu JQ, Li LL, et al., 2019. Event-triggered control for the synchronization of Boolean control networks. Nonl Dynam, 96(2):1335–1344. https://doi.org/10.1007/s11071-019-04857-2
Yang JJ, Lu JQ, Lou JG, et al., 2020. Synchronization of drive-response Boolean control networks with impulsive disturbances. Appl Math Comput, 364:124679. https://doi.org/10.1016/j.amc.2019.124679
Zhong J, Lu JQ, Liu Y, et al., 2014. Synchronization in an array of output-coupled Boolean networks with time delay. IEEE Trans Neur Netw Learn Syst, 25(12):2288–2294. https://doi.org/10.1109/TNNLS.2014.2305722
Zhong J, Lu JQ, Huang TW, et al., 2017. Controllability and synchronization analysis of identical-hierarchy mixed-valued logical control networks. IEEE Trans Cybern, 47(11):3482–3493. https://doi.org/10.1109/TCYB.2016.2560240
Zhong J, Liu Y, Kou K, et al., 2019. On the ensemble controllability of Boolean control networks using STP method. Appl Math Comput, 358:51–62. https://doi.org/10.1016/j.amc.2019.03.059
Zhong J, Li BW, Liu Y, et al., 2020. Output feedback stabilizer design of Boolean networks based on network structure. Front Inform Technol Electron Eng, 21(2):247–259. https://doi.org/10.1631/FITEE.1900229
Zhu QX, Liu Y, Lu JQ, et al., 2018. On the optimal control of Boolean control networks. SIAM J Contr Optim, 56(2):1321–1341. https://doi.org/10.1137/16M1070281
Zhu QX, Liu Y, Lu JQ, et al., 2019. Further results on the controllability of Boolean control networks. IEEE Trans Autom Contr, 64(1):440–442. https://doi.org/10.1109/TAC.2018.2830642
Zhu SY, Lou JG, Liu Y, et al., 2018. Event-triggered control for the stabilization of probabilistic Boolean control networks. Complexity, 2018:9259348. https://doi.org/10.1155/2018/9259348
Zhu SY, Lu JQ, Liu Y, 2019. Asymptotical stability of probabilistic Boolean networks with state delays. IEEE Trans Autom Contr, in press. https://doi.org/10.1109/TAC.2019.2934532
Zou YL, Zhu JD, 2014. System decomposition with respect to inputs for Boolean control networks. Automatica, 50(4):1304–1309. https://doi.org/10.1016/j.automatica.2014.02.039
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Jie LIU designed the research. Lulu LI and Jie LIU completed the mathematical proof. Jie LIU drafted the manuscript. Lulu LI helped organize the manuscript. Habib M. FARDOUN revised and finalized the manuscript.
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Jie LIU, Lulu LI, and Habib M. FARDOUN declare that they have no conflict of interest.
Project supported by the National Natural Science Foundation of China (No. 61503115), the Fundamental Research Funds for the Central Universities, China (No. JZ2017HGTB0188), and the National Innovative Program for College Students, China (No. 201810359056)
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Liu, J., Li, L. & Fardoun, H.M. Complete synchronization of coupled Boolean networks with arbitrary finite delays. Front Inform Technol Electron Eng 21, 281–293 (2020). https://doi.org/10.1631/FITEE.1900438
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DOI: https://doi.org/10.1631/FITEE.1900438