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.
Similar content being viewed by others
References
Aracena J, 2008. Maximum number of fixed points in regulatory Boolean networks. Bull Math Biol, 70(5):1398–1409. https://doi.org/10.1007/s11538-008-9304-7
Ay F, Xu F, Kahveci T, 2009. Scalable steady state analysis of Boolean biological regulatory networks. PLoS ONE, 4(12):e7992. https://doi.org/10.1371/journal.pone.0007992
Bang-Jensen J, Gutin G, 2008. Digraphs: Theory, Algorithms and Applications. Springer New York, USA.
Bof N, Fornasini E, Valcher ME, 2015. Output feedback stabilization of Boolean control networks. Automatica, 57:21–28. https://doi.org/10.1016/j.automatica.2015.03.032
Campbell C, Albert R, 2014. Stabilization of perturbed Boolean network attractors through compensatory interactions. BMC Syst Biol, 8, Article 53. https://doi.org/10.1186/1752-0509-8-53
Cheng DZ, Liu T, 2016. A survey on logical control systems. Unman Syst, 4(1):97–116. https://doi.org/10.1142/S2301385016400100
Cheng DZ, Qi HS, Li ZQ, 2010. Analysis and Control of Boolean Networks: a Semi-tensor Product Approach. Springer London, UK.
Cheng DZ, Qi HS, Li ZQ, et al., 2011. Stability and stabilization of Boolean networks. Int J Robust Nonlin Contr, 21(2):134–156. https://doi.org/10.1002/rnc.1581
Fan HB, Feng JE, Meng M, et al., 2018 General decomposition of fuzzy relations: semi-tensor product approach. Fuzzy Sets Syst, in press, https://doi.org/10.1016/j.fss.2018.12.012
Fornasini E, Valcher ME, 2013. Observability, reconstructibility and state observers of Boolean control networks. IEEE Trans Autom Contr, 58(6):1390–1401. https://doi.org/10.1109/TAC.2012.2231592
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. https://doi.org/10.1016/j.automatica.2015.08.006
Kauffman S, 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
Kauffman S, Peterson C, Samuelsson B, et al., 2003. Random Boolean network models and the yeast transcriptional network. PNAS, 100(25):14796–14799. https://doi.org/10.1073/pnas.2036429100
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, 2012. Controllability of Boolean control networks via the Perron-Frobenius theory. Automatica, 48(6):1218–1223. https://doi.org/10.1016/j.automatica.2012.03.022
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, Article 2731395. https://doi.org/10.1155/2019/2731395
Li FF, 2015. Pinning control design for the stabilization of Boolean networks. IEEE Trans Neur Netw Learn Syst, 27(7):1585–1590. https://doi.org/10.1109/TNNLS.2015.2449274
Li FF, 2016. Pinning control design for the synchronization of two coupled Boolean networks. IEEE Trans Circ Syst II, 63(3):309–313. https://doi.org/10.1109/TCSII.2015.2482658
Li HT, Wang YZ, 2013. Output feedback stabilization control design for Boolean control networks. Automatica, 49(12):3641–3645. https://doi.org/10.1016/j.automatica.2013.09.023
Li HT, Wang YZ, 2017. Further results on feedback stabilization control design of Boolean control networks. Automatica, 83:303–308. https://doi.org/10.1016/j.automatica.2017.06.043
Li R, Yang M, Chu TG, 2013. State feedback stabilization for Boolean control networks. IEEE Trans Autom Contr, 58(7):1853–1857. https://doi.org/10.1109/TAC.2013.2238092
Li XD, Ho DWC, Cao JD, 2019. Finite-time stability and settling-time estimation of nonlinear impulsive systems. Automatica, 99:361–368. https://doi.org/10.1016/j.automatica.2018.10.024
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. https://doi.org/10.1155/2018/1737685
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
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, Li ML, Liu Y, et al., 2018a. Nonsingularity of Grainlike cascade FSRs via semi-tensor product. Sci China Inform Sci, 61:010204. https://doi.org/10.1007/s11432-017-9269-6
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. https://doi.org/10.1137/18M1169308
Lu JQ, Li ML, Huang TW, et al., 2018c. The transformation between the Galois NLFSRs and the Fibonacci NLF-SRs via semi-tensor product of matrices. Automatica, 96:393–397. https://doi.org/10.1016/j.automatica.2018.07.011
Mao Y, Wang L, Liu Y, et al., 2018. Stabilization of evolutionary networked games with length-r information. Appl Math Comput, 337:442–451. https://doi.org/10.1016/j.amc.2018.05.027
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. https://doi.org/10.1109/TNNLS.2017.2737649
Mori F, Mochizuki A, 2017. Expected number of fixed points in Boolean networks with arbitrary topology. Phys Rev Lett, 119:028301. https://doi.org/10.1103/PhysRevLett.119.028301
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. https://doi.org/10.1186/s12918-016-0332-x
Pan J, Feng J, Meng M, 2019. Steady-state analysis of probabilistic Boolean networks. J Franklin Inst, 356(5):2994–3009. https://doi.org/10.1016/j.jfranklin.2019.01.039
Paulevé L, Richard A, 2012. Static analysis of Boolean networks based on interaction graphs: a survey. Electron Notes Theor Comput Sci, 284:93–104. https://doi.org/10.1016/j.entcs.2012.05.017
Robert F, 1986. Discrete Iterations: a Metric Study. Springer New York, USA.
Saadatpour A, Albert I, Albert R, 2010. Attractor analysis of asynchronous Boolean models of signal transduction networks. J Theor Biol, 266(4):641–656. https://doi.org/10.1016/j.jtbi.2010.07.022
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. https://doi.org/10.1371/journal.pcbi.1002267
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
Wang B, Feng J, 2019. On detectability of probabilistic Boolean networks. Inform Sci, 483:383–395. https://doi.org/10.1016/j.ins.2019.01.055
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. https://doi.org/10.1109/TNNLS.2017.2661863
Xiao YF, Dougherty ER, 2007. The impact of function perturbations in Boolean networks. Bioinformatics, 23(10):1265–1273. https://doi.org/10.1093/bioinformatics/btm093
Yang M, Li R, Chu TG, 2013. Controller design for disturbance decoupling of Boolean control networks. Automatica, 49(1):273–277. https://doi.org/10.1016/j.automatica.2012.10.010
Yu Y, Feng J, Pan J, et al., 2019. Block decoupling of Boolean control networks. IEEE Trans Autom Contr, 64(8):3129–3140. https://doi.org/10.1109/TAC.2018.2880411
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. https://doi.org/10.1109/TAC.2015.2501365
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. https://doi.org/10.1109/TNNLS.2015.2442593
Zhu QX, Lin W, 2019. Stabilizing Boolean networks by optimal event-triggered feedback control. Syst Contr Lett, 126:40–47. https://doi.org/10.1016/j.sysconle.2019.03.002
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. https://doi.org/10.1137/16M1070281
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. 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, Article 9259348. https://doi.org/10.1155/2018/9259348
Author information
Authors and Affiliations
Corresponding author
Additional information
Compliance with ethics guidelines
Jie ZHONG, Bo-wen LI, Yang LIU, and Wei-hua GUI declare that they have no conflict of interest.
Project supported by the National Natural Science Foundation of China (Nos. 61903339, 61321003, and 11671361) and the Zhejiang Provincial Natural Science Foundation of China (No. LD19A010001)
Rights and permissions
About this article
Cite this article
Zhong, J., Li, Bw., Liu, Y. et al. Output feedback stabilizer design of Boolean networks based on network structure. Front Inform Technol Electron Eng 21, 247–259 (2020). https://doi.org/10.1631/FITEE.1900229
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1631/FITEE.1900229