Abstract
In this study, the output tracking of delayed logical control networks (DLCNs) with state and control constraints is further investigated. Compared with other delays, state-dependent delay updates its value depending on the current state values and a pseudo-logical function. Multiple constraints mean that state values are constrained in a nonempty set and the design of the controller is conditioned. Using the semi-tensor product of matrices, dynamical equations of DLCNs are converted into an algebraic description, and an equivalent augmented system is constructed. Based on the augmented system, the output tracking problem is transformed into a set stabilization problem. A deformation of the state transition matrix is computed, and a necessary and sufficient condition is derived for the output tracking of a DLCN with multi-constraint. This condition is easily verified by mathematical software. In addition, the admissible state-feedback controller is designed to enable the outputs of the DLCN to track the reference signal. Finally, theoretical results are illustrated by an example.
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References
Akutsu T, Hayashida M, Ching WK, et al., 2007. Control of Boolean networks: hardness results and algorithms for tree structured networks. J Theor Biol, 244(4):670–679. https://doi.org/10.1016/j.jtbi.2006.09.023
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
Bof N, Fornasini E, Valcher ME, 2015. Output feedback stabilization of Boolean control networks. Automation, 57:21–28. https://doi.org/10.1016/j.automatica.2015.03.032
Chaouiya C, Naldi A, Thieffry D, 2012. Logical modelling of gene regulatory networks with GINsim. In: van Helden J, Toussaint A, Thieffry D (Eds.), Bacterial Molecular Networks. Springer, New York, p.463–479. https://doi.org/10.1007/978-1-61779-361-5_23
Cheng D, Qi H, Zhao Y, 2012. An Introduction to Semi-tensor Product of Matrices and its Applications. World Scientific, Singapore.
Chueh TH, Lu HHS, 2012. Inference of biological pathway from gene expression profiles by time delay Boolean networks. PLoS ONE, 7(8):e42095. https://doi.org/10.1371/journal.pone.0042095
Fan HB, Feng JE, Meng M, et al., 2018. General decomposition of fuzzy relations: semi-tensor product approach. Fuzzy Set Syst, p.1–16. 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
Fornasini E, Valcher ME, 2014. Optimal control of Boolean control networks. IEEE Trans Autom Contr, 59(5):1258–1270. https://doi.org/10.1109/TAC.2013.2294821
Guo YQ, Zhou RP, Wu YH, et al., 2019. Stability and set stability in distribution of probabilistic Boolean networks. IEEE Trans Autom Contr, 64(2):736–742. https://doi.org/10.1109/TAC.2018.2833170
Haider S, Pal R, 2012. Boolean network inference from time series data incorporating prior biological knowledge. BMC Genom, 13:S9. https://doi.org/10.1186/1471-2164-13-S6-S9
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
Laschov D, Margaliot M, 2012. Controllability of Boolean control networks via the Perro—Frobenius theory. Automation, 48(6):1218–1223. https://doi.org/10.1016/j.automatica.2012.03.022
Laschov D, Margaliot M, 2013. Minimum-time control of Boolean networks. SIAM J Contr Optim, 51(4):2869–2892. https://doi.org/10.1137/110844660
Li BW, Lou JG, Liu Y, et al., 2019. Robust invariant set analysis of Boolean networks. Complexity, 2019:2731395. https://doi.org/10.1155/2019/2731395
Li FF, 2018. Stability of Boolean networks with delays using pinning control. IEEE Trans Contr Netw Syst, 5(1):179–185. https://doi.org/10.1109/TCNS.2016.2585861
Li H, Zheng Y, Alsaadi F, 2019a. Algebraic formulation and topological structure of Boolean networks with state-dependent delay. J Comput Appl Math, 350:87–97. https://doi.org/10.1016/j.cam.2018.10.003
Li H, Xu X, Ding X, 2019b. Finite-time stability analysis of stochastic switched Boolean networks with impulsive effect. Appl Math Comput, 347:557–565. https://doi.org/10.1016/j.amc.2018.11.018
Li HT, Wang YZ, Xie LH, 2015. Output tracking control of Boolean control networks via state feedback: constant reference signal case. Automatica, 59:54–59. https://doi.org/10.1016/j.automatica.2015.06.004
Li XD, Li HT, Zhao GD, 2019. Function perturbation impact on feedback stabilization of Boolean control networks. IEEE Trans Neur Netw Learn Syst, 30(8):2548–2554. https://doi.org/10.1109/TNNLS.2018.2881168
Li YY, Li BW, Liu Y, et al., 2018. Set stability and set stabilization of switched Boolean networks with state-based switching. IEEE Access, 6:35624–35630. https://doi.org/10.1109/ACCESS.2018.2851391
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
Li ZQ, Cheng DZ, 2010. Algebraic approach to dynamics of multivalued networks. Int J Bifurc Chaos, 20(3):561–582. https://doi.org/10.1142/S0218127410025892
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., 2018a. 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., 2018b. 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
Meng M, Lam J, Feng JE, et al., 2019. Stability and stabilization of Boolean networks with stochastic delays. IEEE Trans Autom Contr, 64(2):790–796. https://doi.org/10.1109/TAC.2018.2835366
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. 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
Veliz-Cuba A, Stigler B, 2011. Boolean models can explain bistability in the lac operon. J Comput Biol, 18(6):783–794. https://doi.org/10.1089/cmb.2011.0031
Wang B, Feng JE, Meng M, 2019. Model matching of switched asynchronous sequential machines via matrix approach. Int J Contr, 92(10):2430–2440. https://doi.org/10.1080/00207179.2018.1441552
Wu YH, Sun XM, Zhao XD, et al., 2019. Optimal control of Boolean control networks with average cost: a policy iteration approach. Automatica, 100:378–387. https://doi.org/10.1016/j.automatica.2018.11.036
Yu YY, Feng JE, Pan JF, 2019a. Block decoupling of Boolean control networks. IEEE Trans Autom Contr, 64(8):3129–3140. https://doi.org/10.1109/TAC.2018.2880411
Yu YY, Wang B, Feng JE, 2019b. Input observability of Boolean control networks. Neurocomputing, 333:22–28. https://doi.org/10.1016/j.neucom.2018.12.014
Zhong J, Ho DWC, Lu JQ, et al., 2019. Pinning controllers for activation output tracking of Boolean network under one-bit perturbation. IEEE Trans Cybern, 49(9):3398–3408. https://doi.org/10.1109/TCYB.2018.2842819
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, 2018:9259348. https://doi.org/10.1155/2018/9259348
Zhu SY, Lu JQ, Liu Y, 2019a. Asymptotical stability of probabilistic Boolean networks with state delays. IEEE Trans Autom Contr, in press. https://doi.org/10.1109/TAC.2019.2934532
Zhu SY, Lu JQ, Liu Y, et al., 2019b. Output tracking of probabilistic Boolean networks by output feedback control. Inform Sci, 483:96–105. https://doi.org/10.1016/j.ins.2018.12.087
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Ya-ting ZHENG drafted the manuscript. Jun-e FENG revised and finalized the manuscript.
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Ya-ting ZHENG and Jun-e FENG declare that they have no conflict of interest.
Project supported by the National Natural Science Foundation of China (Nos. 61773371 and 61877036) and the Natural Science Foundation of Shandong Province, China (No. ZR2019MF002)
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Zheng, Yt., Feng, Je. Output tracking of delayed logical control networks with multi-constraint. Front Inform Technol Electron Eng 21, 316–323 (2020). https://doi.org/10.1631/FITEE.1900376
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DOI: https://doi.org/10.1631/FITEE.1900376
Key words
- Logical control networks
- Multi-constraint
- Output tracking
- Stabilization
- State-dependent delay
- Semi-tensor product