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SCIENCE CHINA Information Sciences, Volume 59, Issue 9: 092204(2016) https://doi.org/10.1007/s11432-015-5423-6

Controllability of probabilistic Boolean control networks with time-variant delays in states

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  • ReceivedFeb 9, 2016
  • AcceptedApr 6, 2016
  • PublishedAug 23, 2016

Abstract

This paper investigates the controllability of probabilistic Boolean control networks (PBCNs) with time-variant delays in states. By cutting the time sequence, we split the network into at most countably infinitely many subnetworks with no delays, where any one of the longest subnetworks is called a controllability constructed path (CCP). When the CCP is of infinite length, we prove that the network is controllable iff any CCP is controllable, and give an equivalent condition for the controllability of the network. When it is of finite length, we give a necessary condition and a sufficient condition for the controllability of the network, and show that the controllability of the network is not equivalent to the controllability of a CCP.


Acknowledgment

Acknowledgments

This work was partly supported by National Natural Science Foundation of China (Grant No. 61573288) and Program for New Century Excellent Talents in University of Ministry of Education of China.


References

[1] Kauffman S A. Metabolic stability and epigenesis in randomly constructed genetic nets. J Theor Biol, 1969, 22: 437-467 CrossRef Google Scholar

[2] Akutsu T, Hayashida M, Ching W, et al. Control of Boolean networks: hardness results and algorithms for tree structured networks. J Theor Biol, 2007, 244: 670-679 CrossRef Google Scholar

[3] Cheng D, Qi H. Controllability and observability of Boolean control networks. Automatica, 2009, 45: 1659-1667 CrossRef Google Scholar

[4] Li F, Sun J. Controllability of Boolean control networks with time delays in states. Automatica, 2011, 47: 603-607 CrossRef Google Scholar

[5] Cheng D, Zhao Y. Identification of Boolean control networks. Automatica, 2011, 47: 702-710 CrossRef Google Scholar

[6] Zhang L, Zhang K. Controllability and observability of Boolean control networks with time-variant delays in states. IEEE Trans Neural Netw Learn Syst, 2013, 24: 1478-1484 CrossRef Google Scholar

[7] Zhao Y, Cheng D. Controllability and stabilizability of probabilistic logical control networks. In: the 51st IEEE Conference on Decision and Control, Maui, 2012. 6729--6734. Google Scholar

[8] Zhao Y, Cheng D Z. On controllability and stabilizability of probabilistic Boolean control networks. Sci China Inf Sci, 2014, 57: 012202-1484 Google Scholar

[9] Chen H, Sun J. A new approach for global controllability of higher order Boolean control network. Neural Netw, 2013, 39: 12-17 CrossRef Google Scholar

[10] Chen H, Sun J. Output controllability and optimal output control of state-dependent switched Boolean control network. Automatica, 2014, 50: 1929-1934 CrossRef Google Scholar

[11] Li F, Sun J. Controllability of probabilistic Boolean control networks. Automatica, 2011, 47: 2765-2771 CrossRef Google Scholar

[12] Cheng D, Qi H, Li Z. Analysis and control of Boolean networks: a semi-tensor product approach. London: Springer, 2011. Google Scholar

[13] Shmulevich I, Dougherty E R, Kim S, et al. Probabilistic Boolean networks: a rule-based uncertainty model for gene regulatory networks. Bioinformatics, 2002, 2: 261-274 Google Scholar

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