State feedback stabilization for boolean control networks

IEEE Transactions on Automatic Control

Volumn 58, Issue 7, 2013, Pages 1853-1857

  Li, Rui ^a   Yang, Meng ^a   Chu, Tianguang ^a  

^a PEKING UNIVERSITY   (China)

Author keywords

Algebraic representation; Boolean control networks; semi tensor product; state feedback stabilization; systems biology

Indexed keywords

ALGEBRAIC REPRESENTATIONS; BOOLEAN CONTROL NETWORKS; SEMI-TENSOR PRODUCT; STATE-FEEDBACK STABILIZATION; SYSTEMS BIOLOGY;

FEEDBACK CONTROL; NONLINEAR CONTROL SYSTEMS; STABILIZATION; STATE FEEDBACK;

BOOLEAN ALGEBRA;

EID: 84879897724     PISSN: 00189286     EISSN: None     Source Type: Journal    
DOI: 10.1109/TAC.2013.2238092     Document Type: Article

References (35)

1. S. A. Kauffman, "Metabolic stability and epigenesis in randomly constructed genetic nets," J. Theor. Biol., vol. 22, no. 3, pp. 437-467, Mar. 1969.
2. S. Huang and D. E. Ingber, "Shape-dependent control of cell growth, differentiation, and apoptosis: Switching between attractors in cell regulatory networks," Exp. Cell Res., vol. 261, no. 1, pp. 91-103, Nov. 2000.
3. S. A. Kauffman andE.D.Weinberger, "The NK model of rugged fitness landscapes and its application to maturation of the immune response," J. Theor. Biol., vol. 141, no. 2, pp. 211-245, Nov. 1989. (Pubitemid 20036173)
4. M. D. Stern, "Emergence of homeostasis and 'noise imprinting' in an evolution model," Proc. Nat. Acad. Sci. USA, vol. 96, no. 19, pp. 10 746-10 751, Sep. 1999. (Pubitemid 29442215)
5. S. Bornholdt and K. Sneppen, "Robustness as an evolutionary principle," Proc. Roy. Soc. Lond. B, vol. 267, no. 1459, pp. 2281-2286, Nov. 2000.
6. L. Wang, E. E. Pichler, and J. Ross, "Oscillations and chaos in neural networks: An exactly solvable model," Proc. Nat. Acad. Sci. USA, vol. 87, no. 23, pp. 9467-9471, Dec. 1990. (Pubitemid 120030648)
7. R. Albert and H. G. Othmer, "The topology of the regulatory interactions predicts the expression pattern of the segment polarity genes in Drosophila melanogaster," J. Theor. Biol., vol. 223, no. 1, pp. 1-18, Jul. 2003. (Pubitemid 36627542)
8. M. Chaves, R. Albert, and E. D. Sontag, "Robustness and fragility of Boolean models for genetic regulatory networks," J. Theor. Biol., vol. 235, no. 3, pp. 431-449, Aug. 2005. (Pubitemid 40693191)
9. T. Akutsu, M. Hayashida, W.-K. Ching, and M. K. Ng, "Control of Boolean networks: Hardness results and algorithms for tree structured networks," J. Theor. Biol., vol. 244, no. 4, pp. 670-679, Feb. 2007. (Pubitemid 46148979)
10. C. J. Langmead and S. K. Jha, "Symbolic approaches for finding control strategies in Boolean networks," J. Bioinform. Comput. Biol., vol. 7, no. 2, pp. 323-338, Apr. 2009.
11. D. Cheng and H. Qi, "Controllability and observability of Boolean control networks," Automatica, vol. 45, no. 7, pp. 1659-1667, Jul. 2009.
12. K. Kobayashi, J.-I. Imura, and K. Hiraishi, "Polynomial-time algorithm for controllability test of a class of Boolean biological networks," EURASIP J. Bioinform. Syst. Biol., vol. 2010, p. 210685, Jul. 2010.
13. F. Li and J. Sun, "Controllability of Boolean control networks with time delays in states," Automatica, vol. 47, no. 3, pp. 603-607, Mar. 2011.
14. D. Laschov and M. Margaliot, "Controllability of Boolean control networks via the Perron-Frobenius theory," Automatica, vol. 48, no. 6, pp. 1218-1223, Jun. 2012.
15. D. Cheng, Z. Li, and H. Qi, "Realization of Boolean control networks," Automatica, vol. 46, no. 1, pp. 62-69, Jan. 2010.
16. D. Laschov and M. Margaliot, "A maximum principle for single-input Boolean control networks," IEEE Trans. Autom. Control, vol. 56, no. 4, pp. 913-917, Apr. 2011.
17. D. Cheng, "Disturbance decoupling of Boolean control networks," IEEE Trans. Autom. Control, vol. 56, no. 1, pp. 2-10, Jan. 2011.
18. M. Yang, R. Li, and T. Chu, "Controller design for disturbance decoupling of Boolean control networks," Automatica, vol. 49, no. 1, pp. 273-277, Jan. 2013.
19. E. Fornasini and M. E. Valcher, "Observability and reconstructibility of Boolean control networks," in Proc. 51st IEEE Conf. Decision Control, Maui, HI, 2012, to be published.
20. A. Datta, A. Choudhary, M. L. Bittner, and E. R. Dougherty, "External control inMarkovian genetic regulatory networks," Mach. Learn., vol. 52, no. 1-2, pp. 169-191, Jul. 2003.
21. A. Datta, A. Choudhary, M. L. Bittner, and E. R. Dougherty, "External control inMarkovian genetic regulatory networks: The imperfect information case," Bioinformatics, vol. 20, no. 6, pp. 924-930, Apr. 2004. (Pubitemid 38559734)
22. M. Tan, R. Alhajj, and F. Polat, "Automated large-scale control of gene regulatory networks," IEEE Trans. Syst.,Man, Cybern. B, Cybern., vol. 40, no. 2, pp. 286-297, Apr. 2010.
23. F. Li and J. Sun, "Controllability of probabilistic Boolean control networks," Automatica, vol. 47, no. 12, pp. 2765-2771, Dec. 2011.
24. R. Pal, A. Datta, M. L. Bittner, and E. R. Dougherty, "Intervention in context-sensitive probabilistic Boolean networks," Bioinformatics, vol. 21, no. 7, pp. 1211-1218, Apr. 2005. (Pubitemid 40467947)
25. R. Pal, A. Datta, and E. R. Dougherty, "Optimal infinite-horizon control for probabilistic Boolean networks," IEEE Trans. Signal Process., vol. 54, no. 6, pp. 2375-2387, Jun. 2006. (Pubitemid 43805580)
26. B. Faryabi, G. Vahedi, J.-F. Chamberland, A. Datta, and E. R. Dougherty, "Intervention in context-sensitive probabilistic Boolean networks revisited," EURASIP J. Bioinform. Syst. Biol., vol. 2009, p. 360864, Feb. 2009.
27. S. Z. Denic, B. Vasic, C. D. Charalambous, and R. Palanivelu, "Robust control of uncertain context-sensitive probabilistic Boolean networks," IET Syst. Biol., vol. 3, no. 4, pp. 279-295, 2009.
28. K. Kobayashi and K. Hiraishi, "An integer programming approach to optimal control problems in context-sensitive probabilistic Boolean networks," Automatica, vol. 47, no. 6, pp. 1260-1264, Jun. 2011.
29. D. Cheng, H. Qi, Z. Li, and J. B. Liu, "Stability and stabilization of Boolean networks," Int. J. Robust Nonlinear Control, vol. 21, no. 2, pp. 134-156, Jan. 2011.
30. F. Li and J. Sun, "Stability and stabilization of Boolean networks with impulsive effects," Syst. Control Lett., vol. 61, no. 1, pp. 1-5, Jan. 2012.
31. H. Li, Y. Wang, and Z. Liu, "Simultaneous stabilization of Boolean control networks via semi-tensor product method," in Proc. 30th Chinese Control Conf., Yantai, China, 2011, pp. 6386-6391.
32. D. Cheng and H. Qi, "A linear representation of dynamics of Boolean networks," IEEE Trans. Autom. Control, vol. 55, no. 10, pp. 2251-2258, Oct. 2010.
33. D. Cheng, H. Qi, and Z. Li, Analysis and Control of Boolean Networks: A Semi-Tensor Product Approach. London, U.K.: Springer-Verlag, 2011.
34. A. Veliz-Cuba and B. Stigler, "Boolean models can explain bistability in the lac operon," J. Comput. Biol., vol. 18, no. 6, pp. 783-794, Jun. 2011.
35. Y.-K. Kwon and K.-H. Cho, "Analysis of feedback loops and robustness in network evolution based on Boolean models," BMC Bioinformatics, vol. 8, p. 430, Nov. 2007.