Output stability and stabilization of Boolean control networks

被引：1
|
作者：
Li Z.-Q. [1 ]
Xiao H.-M. [2 ]
机构：
[1] School of Mathematics and Information Science, Henan University of Economics and Law, Zhengzhou, 450046, Henan
[2] School of Computer and Information Engineering, Henan University of Economics and Law, Zhengzhou, 450046, Henan
来源：
Li, Zhi-Qiang (lizhiqiang@amss.ac.cn) | 2017年 / South China University of Technology卷 / 34期
基金：
中国国家自然科学基金;
关键词：
Boolean control network; Output stability; Output stabilization; Semi-tensor product of matrices;
D O I：
10.7641/CTA.2017.60938
中图分类号：
学科分类号：
摘要：
Semi-tensor product of matrices is the main tool in converting logical variable to its vector form. Using semi-tensor product of matrices, the logical dynamical system is converted to discrete time affine linear system. Under framework of state space expression of Boolean network, the output stability and output stabilization are discussed in this paper. First, the definition of output stability of Boolean network is given, and the necessary and sufficient condition for output stability of Boolean network is obtained. Second, the output stabilization of Boolean control network is investigated and the different conditions for output stabilization are obtained. The output stability and stabilization discussed in this paper are generalizations of the known state stability and stabilization. © 2017, Editorial Department of Control Theory & Applications South China University of Technology. All right reserved.
引用
收藏
页码：1201 / 1207
页数：6
相关论文
共 27 条
  • [1] Yamada S., Shiono S., Joo A., Et al., Control mechanism of JAK/ STAT signal transduction pathway, FEBS Letters, 534, 1-3, pp. 190-196, (2003)
  • [2] Mestl T., Plahte E., Omholt S.W., A mathematical framework for describing and analysing gene regulatory networks, Journal of Theoretical Biology, 176, 2, pp. 291-300, (1995)
  • [3] Liang J., Lam J., Wang Z., State estimation for Markov-type genetic regulatory networks with delays and uncertain mode transition rates, Physics Letters A, 373, 47, pp. 4328-4337, (2009)
  • [4] Shmulevich I., Dougherty R., Kim S., Et al., Probabilistic Boolean neworks: A rule-based uncertainty model for gene regulatory networks, Bioinformatics, 18, 2, pp. 261-274, (2002)
  • [5] Kauffman S.A., Metabolic stability and epigenesis in randomly constructed genetic nets, Journal of Theoretical Biology, 22, 3, pp. 437-467, (1969)
  • [6] Kauffman S.A., The Origins of Order: Self-Organization and Selection in Evolution, (1993)
  • [7] Hopfensitz M., Ssel C., Maucheran M., Et al., Attractors in Boolean networks: a tutorial, Computational Statistics, 28, 1, pp. 19-36, (2013)
  • [8] Datta A., Pal R., Choudhary A., Control approaches for probabilistic gene regulatory networks, IEEE Signal Processing Magazine, 24, 1, pp. 54-63, (2007)
  • [9] Shmulevich I., Dougherty E., Zhang W., Gene perturbation and intervention in probabilistic Boolean networks, Bioinformatics, 18, 10, pp. 1319-1331, (2002)
  • [10] Shmulevich I., Dougherty E.R., Zhang W., Control of stationary behavior in probabilistic Boolean networks by means of structural intervention, Systematic Biology, 10, 2, pp. 431-446, (2002)
123