CLC number: TP13
On-line Access: 2024-08-27
Received: 2023-10-17
Revision Accepted: 2024-05-08
Crosschecked: 2019-12-11
Cited: 0
Clicked: 5787
Citations: Bibtex RefMan EndNote GB/T7714
Nan Jiang, Chi Huang, Yao Chen, Jürgen Kurths. Bisimulation-based stabilization of probabilistic Boolean control networks with state feedback control[J]. Frontiers of Information Technology & Electronic Engineering, 2020, 21(2): 268-280.
@article{title="Bisimulation-based stabilization of probabilistic Boolean control networks with state feedback control",
author="Nan Jiang, Chi Huang, Yao Chen, Jürgen Kurths",
journal="Frontiers of Information Technology & Electronic Engineering",
volume="21",
number="2",
pages="268-280",
year="2020",
publisher="Zhejiang University Press & Springer",
doi="10.1631/FITEE.1900447"
}
%0 Journal Article
%T Bisimulation-based stabilization of probabilistic Boolean control networks with state feedback control
%A Nan Jiang
%A Chi Huang
%A Yao Chen
%A Jürgen Kurths
%J Frontiers of Information Technology & Electronic Engineering
%V 21
%N 2
%P 268-280
%@ 2095-9184
%D 2020
%I Zhejiang University Press & Springer
%DOI 10.1631/FITEE.1900447
TY - JOUR
T1 - Bisimulation-based stabilization of probabilistic Boolean control networks with state feedback control
A1 - Nan Jiang
A1 - Chi Huang
A1 - Yao Chen
A1 - Jürgen Kurths
J0 - Frontiers of Information Technology & Electronic Engineering
VL - 21
IS - 2
SP - 268
EP - 280
%@ 2095-9184
Y1 - 2020
PB - Zhejiang University Press & Springer
ER -
DOI - 10.1631/FITEE.1900447
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.
[1]Bof N, Fornasini E, Valcher ME, 2015. Output feedback stabilization of Boolean control networks. Automatica, 57:21-28.
[2]Chen H, Liang J, Wang Z, 2016. Pinning controllability of autonomous Boolean control networks. Sci China Inform Sci, 59(7):070107.
[3]Cheng D, 2009. Input-state approach to Boolean networks. IEEE Trans Neur Netw, 20(3):512-521.
[4]Cheng D, Qi H, 2009. Controllability and observability of Boolean control networks. Automatica, 45(7):1659-1667.
[5]Cheng D, Li Z, Qi H, 2010a. Realization of Boolean control networks. Automatica, 46(1):62-69.
[6]Cheng D, Qi H, Li Z, 2010b. Analysis and Control of Boolean Networks. Springer, London, UK.
[7]Cheng D, Qi H, Li Z, et al., 2011. Stability and stabilization of Boolean networks. Int J Robust Nonl Contr, 21(2):134-156.
[8]Ching WK, Zhang SQ, Jiao Y, et al., 2009. Optimal control policy for probabilistic Boolean networks with hard constraints. IET Syst Biol, 3(2):90-99.
[9]Fornasini E, Valcher ME, 2012. Observability, reconstructibility and state observers of Boolean control networks. IEEE Trans Autom Contr, 58(6):1390-1401.
[10]Fornasini E, Valcher ME, 2014. Optimal control of Boolean control networks. IEEE Trans Autom Contr, 59(5):1258-1270.
[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]Huang C, Wang W, Cao JD, et al., 2018. {Synchronization-based passivity of partially coupled neural networks with event-triggered communication}. Neurocomputing, 319:134-143.
[13]Huang C, Lu JQ, Ho WCD, et al., 2020. {Stabilization of probabilistic Boolean networks via pinning control strategy}. Inform Sci, 510:205-217.
[14]Kauffman SA, 1969. Metabolic stability and epigenesis in randomly constructed genetic nets. J Theor Biol, 22(3):437-467.
[15]Laschov D, Margaliot M, 2012. Controllability of Boolean control networks via the Perron-Frobenius theory. Automatica, 48(6):1218-1223.
[16]Li BW, Lou JG, Liu Y, et al., 2019. Robust invariant set analysis of Boolean networks. Complexity, 2019:2731395.
[17]Li FF, 2016. Pinning control design for the stabilization of Boolean networks. IEEE Trans Neur Netw Learn Syst, 27(7):1585-1590.
[18]Li FF, Xie LH, 2019. Set stabilization of probabilistic Boolean networks using pinning control. IEEE Trans Neur Netw Learn Syst, 30(8):2555-2561.
[19]Li FF, Yu ZX, 2016. Anti-synchronization of two coupled Boolean networks. J Franklin Inst, 353(18):5013-5024.
[20]Li HT, Wang YZ, 2016. Minimum-time state feedback stabilization of constrained Boolean control networks. Asian J Contr, 18(5):1688-1697.
[21]Li R, Yang M, Chu TG, 2014a. State feedback stabilization for probabilistic Boolean networks. Automatica, 50(4):1272-1278.
[22]Li R, Yang M, Chu TG, 2014b. State feedback stabilization for probabilistic Boolean networks. Automatica, 50(4):1272-1278.
[23]Li R, Chu TG, Wang XY, 2018. Bisimulations of Boolean control networks. SIAM J Contr Optim, 56(1):388-416.
[24]Li YY, Li BW, Liu Y, et al., 2018. Set stability and stabilization of switched Boolean networks with state-based switching. IEEE Access, 6:35624-35630.
[25]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.
[26]Liang JH, Han J, 2012. Stochastic Boolean networks: an efficient approach to modeling gene regulatory networks. BMC Syst Biol, 6(1):113.
[27]Liang JL, Chen HW, Liu Y, 2017. On algorithms for state feedback stabilization of Boolean control networks. Automatica, 84:10-16.
[28]Liu RJ, Qian CJ, Liu SQ, et al., 2016. State feedback control design for Boolean networks. BMC Syst Biol, 10(3):70.
[29]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.
[30]Lu J, Zhong J, Huang C, et al., 2016. On pinning controllability of Boolean control networks. IEEE Trans Autom Contr, 61(6):1658-1663.
[31]Lu J, Li M, Huang T, et al., 2018a. The transformation between the Galois NLFSRs and the Fibonacci NLFSRs via semi-tensor product of matrices. Automatica, 96:393-397.
[32]Lu J, Sun L, Liu Y, et al., 2018b. Stabilization of Boolean control networks under aperiodic sampled-data control. SIAM J Contr Optim, 56(6):4385-4404.
[33]Ma Z, Wang ZJ, McKeown MJ, 2008. {Probabilistic Boolean network analysis of brain connectivity in Parkinson’s disease}. IEEE J Sel Top Signal Process, 2(6):975-985.
[34]Shmulevich I, Dougherty ER, Kim S, et al., 2002. Probabilistic Boolean networks: a rule-based uncertainty model for gene regulatory networks. Bioinformatics, 18(2):261-274.
[35]Sun LJ, Lu JQ, Ching WK, 2020. Switching-based stabilization of aperiodic sampled-data Boolean control networks with all subsystems unstable. Front Inform Technol Electron Eng, 21(2):260-267.
[36]Tong LY, Liu Y, Li YY, et al., 2018a. Robust control invariance of probabilistic Boolean control networks via event-triggered control. IEEE Access, 6:37767-37774.
[37]Tong LY, Liu Y, Lou JG, et al., 2018b. Static output feedback set stabilization for context-sensitive probabilistic Boolean control networks. Appl Math Comput, 332:263-275.
[38]Veliz-Cuba A, Stigler B, 2011. Boolean models can explain bistability in the lac operon. J Comput Biol, 18(6):783-794.
[39]Wang LP, Pichler EE, Ross J, 1990. Oscillations and chaos in neural networks: an exactly solvable model. PANS, 87(23):9467-9471.
[40]Xiong WJ, Ho WCD, Xu L, 2019. Multi-layered sampled-data iterative learning tracking for discrete systems with cooperative-antagonistic interactions. IEEE Trans Cybern, online.
[41]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.
[42]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.
[43]Zhu SY, Lou J, Liu Y, et al., 2018. Event-triggered control for the stabilization of probabilistic Boolean control networks. Complexity, 2018:9259348.
[44]Zhu SY, Lu JG, Liu Y, 2019. Asymptotical stability of probabilistic Boolean networks with state delays. IEEE Trans Autom Contr, online.
Open peer comments: Debate/Discuss/Question/Opinion
<1>