Full Text:   <1720>

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CLC number: O231

On-line Access: 2020-03-04

Received: 2019-07-29

Revision Accepted: 2019-09-21

Crosschecked: 2019-12-19

Cited: 0

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Citations:  Bibtex RefMan EndNote GB/T7714


Ya-ting Zhang


Jun-e Feng


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Frontiers of Information Technology & Electronic Engineering  2020 Vol.21 No.2 P.316-323


Output tracking of delayed logical control networks with multi-constraint

Author(s):  Ya-ting Zhang, Jun-e Feng

Affiliation(s):  School of Mathematics, Shandong University, Jinan 250100, China

Corresponding email(s):   fengjune@sdu.edu.cn

Key Words:  Logical control networks, Multi-constraint, Output tracking, Stabilization, State-dependent delay, Semi-tensor product

Ya-ting Zhang, Jun-e Feng. Output tracking of delayed logical control networks with multi-constraint[J]. Frontiers of Information Technology & Electronic Engineering, 2020, 21(2): 316-323.

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T1 - Output tracking of delayed logical control networks with multi-constraint
A1 - Ya-ting Zhang
A1 - Jun-e Feng
J0 - Frontiers of Information Technology & Electronic Engineering
VL - 21
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PB - Zhejiang University Press & Springer
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DOI - 10.1631/FITEE.1900376

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.





Darkslateblue:Affiliate; Royal Blue:Author; Turquoise:Article


[1]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.

[2]Ay F, Xu F, Kahveci T, 2009. Scalable steady state analysis of Boolean biological regulatory networks. PLoS ONE, 4(12):e7992.

[3]Bof N, Fornasini E, Valcher ME, 2015. Output feedback stabilization of Boolean control networks. Automatica, 57:21-28.

[4]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.

[5]Cheng D, Qi H, Zhao Y, 2012. An Introduction to Semi-tensor Product of Matrices and its Applications. World Scientific, Singapore.

[6]Chueh TH, Lu HHS, 2012. Inference of biological pathway from gene expression profiles by time delay Boolean networks. PLoS ONE, 7(8):e42095.

[7]Fan HB, Feng JE, Meng M, et al., 2018. General decomposition of fuzzy relations: semi-tensor product approach. Fuzzy Set Syst, p.1-16.

[8]Fornasini E, Valcher ME, 2013. Observability, reconstructibility and state observers of Boolean control networks. IEEE Trans Autom Contr, 58(6):1390-1401.

[9]Fornasini E, Valcher ME, 2014. Optimal control of Boolean control networks. IEEE Trans Autom Contr, 59(5):1258-1270.

[10]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.

[11]Haider S, Pal R, 2012. Boolean network inference from time series data incorporating prior biological knowledge. BMC Genom, 13:S9.

[12]Kauffman S, 1969. Metabolic stability and epigenesis in randomly constructed genetic nets. J Theor Biol, 22(3):437-467.

[13]Laschov D, Margaliot M, 2012. Controllability of {Boolean} control networks via the Perro–Frobenius theory. Automatica, 48(6):1218-1223.

[14]Laschov D, Margaliot M, 2013. Minimum-time control of Boolean networks. SIAM J Contr Optim, 51(4):2869-2892.

[15]Li BW, Lou JG, Liu Y, et al., 2019. Robust invariant set analysis of Boolean networks. Complexity, 2019:2731395.

[16]Li FF, 2018. Stability of Boolean networks with delays using pinning control. IEEE Trans Contr Netw Syst, 5(1):179-185.

[17]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.

[18]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.

[19]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.

[20]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.

[21]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.

[22]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.

[23]Li ZQ, Cheng DZ, 2010. Algebraic approach to dynamics of multivalued networks. Int J Bifurc Chaos, 20(3):561-582.

[24]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.

[25]Lu JQ, Zhong J, Ho DWC, et al., 2016. On controllability of delayed Boolean control networks. SIAM J Contr Optim, 54(2):475-494.

[26]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.

[27]Lu JQ, Li ML, Huang TW, et al., 2018b. The transformation between the Galois NLFSRs and the Fibonacci NLFSRs via semi-tensor product of matrices. Automatica, 96:393-397.

[28]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.

[29]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.

[30]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.

[31]Veliz-Cuba A, Stigler B, 2011. Boolean models can explain bistability in the lac operon. J Comput Biol, 18(6):783-794.

[32]Wang B, Feng JE, Meng M, 2019. Model matching of switched asynchronous sequential machines via matrix approach. Int J Contr, 92(10):2430-2440.

[33]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.

[34]Yu YY, Feng JE, Pan JF, 2019a. Block decoupling of Boolean control networks. IEEE Trans Autom Contr, 64(8):3129-3140.

[35]Yu YY, Wang B, Feng JE, 2019b. Input observability of Boolean control networks. Neurocomputing, 333:22-28.

[36]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.

[37]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.

[38]Zhu SY, Lou JG, Liu Y, et al., 2018. Event-triggered control for the stabilization of probabilistic Boolean control networks. Complexity, 2018:9259348.

[39]Zhu SY, Lu JQ, Liu Y, 2019a. Asymptotical stability of probabilistic {Boolean} networks with state delays. IEEE Trans Autom Contr, in press.

[40]Zhu SY, Lu JQ, Liu Y, et al., 2019b. Output tracking of probabilistic {Boolean} networks by output feedback control. Inform Sci, 483:96-105.

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