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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 631639, 9 pages
http://dx.doi.org/10.1155/2013/631639
Research Article

A Note on the Observability of Temporal Boolean Control Network

1College of Mathematics, Physics and Information Engineering, Zhejiang Normal University, Jinhua 321004, China
2Academic Affairs Division, Zhejiang Normal University, Jinhua 321004, China
3Department of Mathematics, Tongji University, Shanghai 200092, China

Received 2 December 2012; Accepted 24 February 2013

Academic Editor: Qi Luo

Copyright © 2013 Wenping Shi et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. S. A. Kauffman, “Metabolic stability and epigenesis in randomly constructed genetic nets,” Journal of Theoretical Biology, vol. 22, no. 3, pp. 437–467, 1969. View at Scopus
  2. S. Kauffman, The Origins of Order: Self-Organization and Selection in Evolution, Oxford University Press, New York, NY, USA, 1993.
  3. S. Kauffman, At Home in the Universe, Oxford University Press, New York, NY, USA, 1995.
  4. D. Cheng, “Semi-tensor product of matrices and its applications: a survey,” in Proceedings of the 4th International Congress of Chinese Mathematicians, pp. 641–668, Hangzhou, China, December 2007.
  5. S. Huang and D. E. Ingber, “Shape-dependent control of cell growth, differentiation, and apoptosis: Switching between attractors in cell regulatory networks,” Experimental Cell Research, vol. 261, no. 1, pp. 91–103, 2000. View at Publisher · View at Google Scholar · View at Scopus
  6. D. Cheng, “Input-state approach to Boolean networks,” IEEE Transactions on Neural Networks, vol. 20, no. 3, pp. 512–521, 2009. View at Publisher · View at Google Scholar · View at Scopus
  7. D. Cheng, Z. Li, and H. Qi, “Realization of Boolean control networks,” Automatica, vol. 46, no. 1, pp. 62–69, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. D. Cheng and H. Qi, “Controllability and observability of Boolean control networks,” Automatica, vol. 45, no. 7, pp. 1659–1667, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. D. Cheng and H. Qi, “A linear representation of dynamics of Boolean networks,” IEEE Transactions on Automatic Control, vol. 55, no. 10, pp. 2251–2258, 2010. View at Publisher · View at Google Scholar · View at MathSciNet
  10. D. Laschov and M. Margaliot, “Controllability of Boolean control networks via the Perron-Frobenius theory,” Automatica, vol. 48, no. 6, pp. 1218–1223, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. D. Laschov and M. Margaliot, “A maximum principle for single-input Boolean control networks,” IEEE Transactions on Automatic Control, vol. 56, no. 4, pp. 913–917, 2011. View at Publisher · View at Google Scholar · View at MathSciNet
  12. D. Laschov and M. Margaliot, “A pontryagin maximum principle for multi-input boolean control networks,” in Recent Advances in Dynamics and Control of Neural Networks, Cambridge Scientific Publishers, 2011.
  13. Z.-H. Guan, T.-H. Qian, and X. Yu, “Controllability and observability of linear time-varying impulsive systems,” IEEE Transactions on Circuits and Systems I, vol. 49, no. 8, pp. 1198–1208, 2002. View at Publisher · View at Google Scholar · View at MathSciNet
  14. Y. Liu and S. Zhao, “Controllability for a class of linear time-varying impulsive systems with time delay in control input,” IEEE Transactions on Automatic Control, vol. 56, no. 2, pp. 395–399, 2011. View at Publisher · View at Google Scholar · View at MathSciNet
  15. Y. Liu and S. Zhao, “Controllability analysis of linear time-varying systems with multiple time delays and impulsive effects,” Nonlinear Analysis: Real World Applications, vol. 13, no. 2, pp. 558–568, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  16. G. Xie and L. Wang, “Necessary and sufficient conditions for controllability and observability of switched impulsive control systems,” IEEE Transactions on Automatic Control, vol. 49, no. 6, pp. 960–966, 2004. View at Publisher · View at Google Scholar · View at MathSciNet
  17. S. Zhao and J. Sun, “Controllability and observability for time-varying switched impulsive controlled systems,” International Journal of Robust and Nonlinear Control, vol. 20, no. 12, pp. 1313–1325, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  18. S. Zhao and J. Sun, “A geometric approach for reachability and observability of linear switched impulsive systems,” Nonlinear Analysis, vol. 72, no. 11, pp. 4221–4229, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  19. F. Li, J. Sun, and Q. Wu, “Observability of boolean control networks with state time delays,” IEEE Transactions on Neural Networks, vol. 22, no. 6, pp. 948–954, 2011. View at Publisher · View at Google Scholar
  20. J. Lu, D. W. C. Ho, and J. Kurths, “Consensus over directed static networks with arbitrary finite communication delays,” Physical Review E, vol. 80, no. 6, Article ID 066121, 2009. View at Publisher · View at Google Scholar · View at Scopus
  21. J. Lu, D. W. C. Ho, and J. Cao, “Synchronization in an array of nonlinearly coupled chaotic neural networks with delay coupling,” International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, vol. 18, no. 10, pp. 3101–3111, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  22. S. Lyu, “Combining boolean method with delay times for determining behaviors of biological networks,” in Proceedings of the 31st Annual International Conference of the IEEE Engineering in Medicine and Biology Society, pp. 4884–4887, Minneapolis, Minn, USA, September 2009.
  23. C. Cotta, “On the evolutionary inference of temporal boolean networks,” in Computational Methods in Neural Modeling, vol. 2686 of Lecture Notes in Computer Science, pp. 494–501, 2003.
  24. C. Fogelberg and V. Palade, “Machine learning and genetic regulatory networks: a review and a roadmap,” in Foundations of Computational, Intelligence, vol. 201 of Studies in Computational Intelligence, pp. 3–34, 2009. View at Publisher · View at Google Scholar
  25. A. Silvescu and V. Honavar, “Temporal Boolean network models of genetic networks and their inference from gene expression time series,” Complex Systems, vol. 13, no. 1, pp. 61–78, 2001. View at Zentralblatt MATH · View at MathSciNet
  26. D. Cheng, H. Qi, and Z. Li, Analysis and Control of Boolean Networks: A Semi-Tensor Product Approach, Springer, New York, NY, USA, 2011. View at Publisher · View at Google Scholar · View at MathSciNet
  27. Y. Liu, J. Lu, and B. Wu, “Some necessary and sufficient conditions for the output controllability of temporal Boolean control networks,” ESAIM: Control, Optimization and Calculus of Variations. In press.
  28. Y. Liu, H. Chen, and B. Wu, “Controllability of Boolean control networks with impulsive effects and forbidden states,” Mathematical Methods in the Applied Sciences, 2013. View at Publisher · View at Google Scholar