Some necessary and sufficient conditions for the output controllability of temporal Boolean control networks

 Access to full text

1. [1] T. Akutsu, M. Hayashida, W. Ching and M. Ng, Control of Boolean networks: hardness results and algorithms for tree structured networks. J. Theor. Biol.244 (2007) 670–679. MR2306355
2. [2] J. Cao and F. Ren, Exponential stability of discrete-time genetic regulatory networks with delays. IEEE Transactions on Neural Networks19 (2008) 520–523. 
3. [3] J. Cao, K. Yuan and H. Li, Global asymptotical stability of recurrent neural networks with multiple discrete delays and distributed delays. IEEE Transactions on Neural Networks17 (2006) 1646–1651. 
4. [4] L. Chen and K. Aihara, Stability of genetic regulatory networks with time delay. IEEE Transactions on Circuits and Systems I: Fundamental Theory Appl. 49 (2002) 602–608. MR1909315
5. [5] H. Chen and J. Sun, A new approach for global controllability of higher order Boolean control network. Neural Networks39 (2013) 12–17. Zbl1327.93073
6. [6] D. Cheng, Semi-tensor product of matrices and its applicationsa survey. Proc. of ICCM3 (2007) 641–668. Zbl1059.15033
7. [7] D. Cheng, Input-state approach to Boolean networks. IEEE Transactions on Neural Networks20 (2009) 512–521. 
8. [8] D. Cheng and H. Qi, Controllability and observability of Boolean control networks. Automatica45 (2009) 1659–1667. Zbl1184.93014MR2879479
9. [9] D. Cheng and H. Qi, A linear representation of dynamics of Boolean networks. IEEE Transactions on Automatic Control55 (2010) 2251–2258. MR2742217
10. [10] D. Cheng, Z. Li and H. Qi, Realization of Boolean control networks. Automatica46 (2010) 62–69. Zbl1214.93031MR2578273
11. [11] D. Cheng, H. Qi and Z. Li, Analysis and Control of Boolean Networks: A Semi-tensor Product Approach. Springer Verlag (2011). Zbl1209.93001MR2761796
12. [12] C. Chi-Tsong, Linear System Theory and Design (1999). 
13. [13] D. Chyung, On the controllability of linear systems with delay in control. IEEE Transactions on Automatic Control15 (1970) 255–257. Zbl0418.93009MR274077
14. [14] C. Cotta, On the evolutionary inference of temporal Boolean networks. Lect. Notes Comput. Sci. (2003) 494–501. 
15. [15] C. Fogelberg and V. Palade, Machine learning and genetic regulatory networks: A review and a roadmap, Foundations of Computational, Intelligence 1 (2009) 3–34. 
16. [16] M. Ghil, I. Zaliapin and B. Coluzzi, Boolean delay equations: A simple way of looking at complex systems. Physica D Nonlinear Phenomena237 (2008) 2967–2986. Zbl1153.37315MR2514922
17. [17] S. Hansen and O. Imanuvilov, Exact controllability of a multilayer rao-nakra plate with clamped boundary conditions. ESAIM: COCV 17 (2011) 1101–1132. Zbl1238.93012MR2859867
18. [18] W. He and J. Cao, Exponential synchronization of hybrid coupled networks with delayed coupling. IEEE Transactions on Neural Networks21 (2010) 571–583. 
19. [19] S. Huang and D. Ingber, Shape-dependent control of cell growth, differentiation, and apoptosis: switching between attractors in cell regulatory networks. Experimental Cell Research261 (2000) 91–103. 
20. [20] T. Kailath, Linear systems, Vol. 1. Prentice-Hall Englewood Cliffs, NJ (1980). Zbl0454.93001MR569473
21. [21] S. Kauffman, Metabolic stability and epigenesis in randomly constructed genetic nets. J. Theor. Biol.22 (1969) 437–467. 
22. [22] S. Kauffman, The origins of order: Self organization and selection in evolution. Oxford University Press, USA (1993). 
23. [23] S. Kauffman, At home in the universe: The search for laws of self-organization and complexity. Oxford University Press, USA (1995). 
24. [24] O. Kavian and O. Traoré, Approximate controllability by birth control for a nonlinear population dynamics model. ESAIM: COCV 17 (2011) 1198–1213. Zbl1236.93022MR2859872
25. [25] K. Kobayashi, J. Imura and K. Hiraishi, Polynomial-time controllability analysis of Boolean networks. Amer. Control Confer. ACC’09. IEEE (2009) 1694–1699. 
26. [26] D. Laschov and M. Margaliot, A maximum principle for single-input Boolean control networks. IEEE Transactions on Automatic Control56 (2011) 913–917. MR2815405
27. [27] D. Laschov and M. Margaliot, Controllability of Boolean control networks via Perron-Frebenius theory. Automatica48 (2012) 1218–1223. Zbl1244.93026MR2917535
28. [28] D. Laschov and M. Margaliot, A pontryagin maximum principle for multi-input Boolean control networks, Recent Advances in Dynamics and Control of Neural Networks. In press. Zbl1276.49013
29. [29] X. Li, S. Rao and W. Jiang, et al., Discovery of time-delayed gene regulatory networks based on temporal gene expression profiling. BMC bioinformatics 7 (2006) 26. 
30. [30] F. Li and J. Sun, Controllability of Boolean control networks with time delays in states. Automatica47 (2011) 603–607. Zbl1220.93010MR2878317
31. [31] F. Li, and J. Sun, Controllability of higher order Boolean control networks. Appl. Math. Comput.219 (2012) 158–169. Zbl1311.92083MR2949582
32. [32] F. Li and J. Sun, Stability and stabilization of Boolean networks with impulsive effects. Systems Control Lett.61 (2012) 1–5. Zbl1250.93078MR2878678
33. [33] F. Li, J. Sun and Q. Wu, Observability of Boolean control networks with state time delays. IEEE Transactions on Neural Networks22 (2011) 948–954. 
34. [34] Y. Liu, H. Chen and B. Wu, Controllability of Boolean control networks with impulsive effects and forbidden states. Math. Meth. Appl. Sci. (2013). DOI: 10.1002/mma.2773. Zbl1282.93054MR3150957
35. [35] 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 Control56 (2011) 395–399. MR2761109
36. [36] J. Lu, D. Ho and J. Kurths, Consensus over directed static networks with arbitrary finite communication delays. Phys. Rev. E 80 (2009) 066121. 
37. [37] S. Lyu, Combining Boolean method with delay times for determining behaviors of biological networks, in Engrg. Medicine Biology Soc. EMBC 2009., IEEE (2009) 4884–4887. 
38. [38] A. Silvescu, V. Honavar, Temporal Boolean network models of genetic networks and their inference from gene expression time series. Complex Systems13 (2001) 61–78. Zbl1167.92335MR1853669
39. [39] G. Tenenbaum and M. Tucsnak, On the null-controllability of diffusion equations. ESAIM: COCV 17 (2011) 1088–1100. Zbl1236.93025MR2859866
40. [40] Z. Wang, J. Lam, G. Wei, K. Fraser and X. Liu, Filtering for nonlinear genetic regulatory networks with stochastic disturbances. IEEE Transactions on Automatic Control53 (2008) 2448–2457. MR2466606
41. [41] G. Xie, L. Wang, Output controllability of switched linear systems. IEEE International Symposium on Intelligent Control (2003) 134–139. 
42. [42] G. Xie, J. Yu and L. Wang, Necessary and sufficient conditions for controllability of switched impulsive control systems with time delay, in 45th IEEE Conference on Decision and Control (2006) 4093–4098. 
43. [43] W. Yu, J. Lu, G. Chen, Z. Duan and Q. Zhou, Estimating uncertain delayed genetic regulatory networks: an adaptive filtering approach. IEEE Transactions on Automatic Control54 (2009) 892–897. MR2514830
44. [44] Y. Zhao, H. Qi and D. Cheng, Input-state incidence matrix of Boolean control networks and its applications. Systems and Control Lett.59 (2010) 767–774. Zbl1217.93026MR2779787
45. [45] S. Zhao and J. Sun, Controllability and observability for a class of time-varying impulsive systems. Nonlinear Analysis: Real World Appl. 10 (2009) 1370–1380. Zbl1159.93315MR2502952
46. [46] S. Zhao and J. Sun, Controllability and observability for time-varying switched impulsive controlled systems. Internat. J. Robust Nonl. Control20 (2010) 1313–1325. Zbl1206.93019MR2680708
47. [47] S. Zhao and J. Sun, A geometric approach for reachability and observability of linear switched impulsive systems. Nonl. Anal. Theory, Methods Appl. 72 (2010) 4221–4229. Zbl1189.93021MR2606779