© The Institution of Engineering and Technology
In this research the output tracking problems with respect to a constant and a periodic output signal for switched Boolean networks (BNs) are studied. Based on the semi-tensor product of matrices, an algebraic expression of switched BNs is obtained. Then, some conditions are presented to ensure output tracking issues with respect to a constant and a periodic output signal, respectively. Further, a new design of switching-signal-triggered pinning controllers is proposed to achieve output tracking. Finally, the discussion of an apoptosis network shows that the theoretic results are effective in designing the switching-signal-triggered pinning controllers to achieve output tracking.
References
-
-
1)
-
8. Cheng, D., Qi, H., Li, Z.: ‘Analysis and control of boolean networks: a semi-tensor product approach’ (Springer-Verlag, New York, USA, 2011).
-
2)
-
21. Liu, Y., Chen, H., Lu, J., et al: ‘Controllability of probabilistic Boolean control networks based on transition probability matrices’, Automatica, 2015, 52, pp. 340–345.
-
3)
-
7. Farrow, C., Heidel, J., Maloney, J., et al: ‘Scalar equations for synchronous Boolean networks with biological applications’, IEEE Trans. Neural Netw., 2004, 15, (2), pp. 348–354.
-
4)
-
17. Lu, J., Zhong, J., Ho, D.W.C., et al: ‘On controllability of delayed boolean control networks’, SIAM J. Control Optim., 2016, 54, pp. 475–494.
-
5)
-
25. Liu, Z., Wang, Y., Cheng, D.: ‘Nonsingularity of feedback shift registers’, Automatica, 2015, 55, pp. 247–253.
-
6)
-
14. Bof, N., Fornasini, E., Valcher, M.E.: ‘Output feedback stabilization of Boolean control networks’, Automatica, 2015, 57, pp. 21–28.
-
7)
-
38. Xu, W., Chen, G., Ho, D.W.C.: ‘A layered event-triggered consensus scheme’, IEEE Trans. Cybern., 2016, , in press.
-
8)
-
23. Cheng, D., Xu, T., Qi, H.: ‘Evolutionarily stable strategy of networked evolutionary games’, IEEE Trans. Neural Netw. Learn Syst., 2014, 25, (7), pp. 1335–1345.
-
9)
-
20. Liu, Y., Lu, J., Wu, B.: ‘Some necessary and sufficient conditions for the output controllability of temporal Boolean control networks’, ESAIM Control Optim. Calc. Var., 2014, 20, (1), pp. 158–173.
-
10)
-
34. Li, H., Wang, Y.: ‘Controllability analysis and control design for switched Boolean networks with state and input constraints’, SIAM J. Control Optim., 2015, 53, (5), pp. 2955–2979.
-
11)
-
32. Fornasini, E., Valcher, M.E.: ‘Observability, reconstructibility and state observers of Boolean control networks’, IEEE Trans. Autom. Control, 2013, 58, (6), pp. 1390–1401.
-
12)
-
11. Laschov, D., Margaliot, M., Even, G.: ‘Observability of Boolean networks: a graphtheoretic approach’, Automatica, 2013, 49, (8), pp. 2351–2362.
-
13)
-
42. Niu, B., Zhao, X., Zhang, L., et al: ‘p-times differentiable unbounded functions for robust control of uncertain switched nonlinear systems with tracking constraints’, Int. J. Robust Nonlin. Control, 2015, 25, (16), pp. 2965–2983.
-
14)
-
29. Huang, S., Ingber, D.E.: ‘Shape-dependent control of cell growth, differentiation, and apoptosis: switching between attractors in cell regulatory networks’, Exp. Cell Res., 2000, 261, (1), pp. 91–103.
-
15)
-
39. Xu, W., Ho, D.W.C.: ‘Clustered event-triggered consensus analysis: an impulsive framework’, IEEE Trans. Ind. Electron., 2016, 63, (11), pp. 7133–7143.
-
16)
-
19. Zhong, J., Lu, J., Huang, T., et al: ‘Controllability and synchronization analysis of identical-hierarchy mixed-valued logical control networks’, IEEE Trans. Cybern., 2016, , in press.
-
17)
-
43. Niu, B., Zhao, J.: ‘Tracking control for output-constrained nonlinear switched systems with a barrier Lyapunov function’, Int. J. Syst. Sci., 2013, 44, pp. 978–985.
-
18)
-
24. Zhong, J., Lin, D.: ‘Driven stability of nonlinear feedback shift registers with inputs’, IEEE Trans. Commun., 2016, 64, (6), pp. 2274–2284.
-
19)
-
49. Chaves, M.: ‘Methods for qualitative analysis of genetic networks’. 2009 European Control Conf. (ECC), 2009, pp. 671–676.
-
20)
-
30. Xu, W., Ho, D.W.C., Li, L., et al: ‘Event-triggered schemes on leader-following consensus of general linear multiagent systems under different topologies’, IEEE Trans. Cybern., 2017, 47, (1), pp. 212–223.
-
21)
-
5. Kauffman, S.A.: ‘Metabolic stability and epigenesis in randomly constructed genetic nets’, J. Theor. Biol., 1969, 22, (3), pp. 437–467.
-
22)
-
48. Li, H., Wang, Y., Liu, Z.: ‘Stability analysis for switched Boolean networks under arbitrary switching signals’, IEEE Trans. Autom. Control, 2014, 59, (7), pp. 1978–1982.
-
23)
-
47. Li, F.: ‘Pinning control design for the stabilization of Boolean networks’, IEEE Trans. Neural Netw. Learn Syst, 2015, 27, (7), pp. 1585–1590.
-
24)
-
4. Liang, J., Lam, J., Wang, Z.: ‘State estimation for Markov-type genetic regulatory networks with delays and uncertain mode transition rates’, Phys. Lett. A, 2009, 373, (47), pp. 4328–4337.
-
25)
-
40. Padfield, D., Rittscher, J., Roysam, B.: ‘Coupled minimum-cost flow cell tracking for high-throughput quantitative analysis’, Med. Image Anal., 2011, 15, (4), pp. 650–668.
-
26)
-
33. Chen, H., Liang, J., Huang, T., et al: ‘Synchronization of arbitrarily switched Boolean networks’, IEEE Trans. Neural Netw. Learn Syst., 2017, 28, (3), pp. 612–619.
-
27)
-
37. Meijering, E., Dzyubachyk, O., Smal, I., et al: ‘Tracking in cell and developmental biology’, Semin. Cell Dev. Biol., 2009, 20, (8), pp. 894–902.
-
28)
-
22. Li, H., Wang, Y.: ‘Boolean derivative calculation with application to fault detection of combinational circuits via the semi-tensor product method’, Automatica, 2012, 48, (4), pp. 688–693.
-
29)
-
15. Li, H., Xie, L., Wang, Y.: ‘On robust control invariance of Boolean control networks’, Automatica, 2016, 68, pp. 392–396.
-
30)
-
31. Xu, W., Cao, J., Yu, W., et al: ‘Leader-following consensus of non-linear multi-agent systems with jointly connected topology’, IET Control Theory Appl., 2014, 8, (6), pp. 432–440.
-
31)
-
28. Tian, T.H., Burrage, K.: ‘Bistability and switching in the lysis/lysogeny genetic regulatory network of bacteriophage λ’, J. Theor. Biol., 2004, 227, (2), pp. 229–237.
-
32)
-
26. Han, X., Chen, Z., Liu, Z., et al: ‘Calculation of siphons and minimal siphons in petri nets based on semi-tensor product of matrices’, IEEE Trans. Syst. Man Cybern. Syst., 2017, 47, pp. 531–536.
-
33)
-
1. DeRisi, J.L., Iyer, V.R., Brown, P.O.: ‘Exploring the metabolic and genetic control of gene expression on a genomic scale’, Adv. Colloid Interface Sci., 1997, 278, (5338), pp. 680–686.
-
34)
-
12. Laschov, D., Margaliot, M.: ‘Controllability of Boolean control networks via the Perron–Frobenius theory’, Automatica, 2012, 48, (6), pp. 1218–1223.
-
35)
-
46. Li, H., Wang, Y., Guo, P.: ‘State feedback based output tracking control of probabilistic Boolean networks’, Inf. Sci., 2016, 349, pp. 1–11.
-
36)
-
36. Chen, H., Sun, J.: ‘Output controllability and optimal output control of state-dependent switched Boolean control networks’, Automatica, 2016, 50, (7), pp. 1929–1934.
-
37)
-
18. Zhong, J., Lu, J., Liu, Y., et al: ‘Synchronization in an array of output-coupled Boolean networks with time delay’, IEEE Trans. Neural Netw. Learn Syst., 2014, 25, (12), pp. 2288–2294.
-
38)
-
13. Zou, Y., Zhu, J.: ‘Cycles of periodically time-variant Boolean networks’, Automatica, 2015, 51, pp. 175–179.
-
39)
-
9. Cheng, D., Qi, H.: ‘A linear representation of dynamics of Boolean networks’, IEEE Trans. Autom. Control, 2010, 55, (10), pp. 2251–2258.
-
40)
-
35. Zhang, K., Zhang, L., Xie, L.: ‘Finite automata approach to observability of switched Boolean control networks’, Nonlinear Anal.: Hybrid Syst., 2016, 19, pp. 186–197.
-
41)
-
44. Li, H., Wang, Y., Xie, L.: ‘Output tracking control of Boolean control networks via state feedback: Constant reference signal case’, Automatica, 2015, 59, pp. 54–59.
-
42)
-
16. Lu, J., Zhong, J., Huang, C., et al: ‘On pinning controllability of Boolean control networks’, IEEE Trans. Autom. Control, 2016, 61, pp. 1658–1663.
-
43)
-
45. Li, H., Wang, Y.: ‘Output tracking of switched Boolean networks under open-loop/closed-loop switching signals’, Nonlinear Anal.: Hybrid Syst., 2016, 22, pp. 137–146.
-
44)
-
10. Cheng, D., Qi, H.: ‘Controllability and observability of Boolean control networks’, Automatica, 2009, 45, (7), pp. 1659–1667.
-
45)
-
41. Niu, B., Zhao, J.: ‘Barrier Lyapunov functions for the output tracking control of constrained nonlinear switched systems’, Syst. Control Lett., 2013, 62, (10), pp. 963–971.
-
46)
-
3. Julius, A.A., Halász, Á., Sakar, M.S., et al: ‘Stochastic modeling and control of biological systems: the lactose regulation system of Escherichia coli’, IEEE Trans. Autom. Control, 2008, 53, pp. 51–65.
-
47)
-
27. Gardner, T.S., Cantor, C.R., Collins, J.J.: ‘Construction of a genetic toggle switch in Escherichia coli’, Nature, 2013, 403, (6767), pp. 339–342.
-
48)
-
6. Heidel, J., Maloney, J., Farrow, C., et al: ‘Finding cycles in synchronous Boolean networks with applications to biochemical systems’, Int. J. Bifurcation Chaos, 2003, 13, (03), pp. 535–552.
-
49)
-
2. Botstein, D., Fink, G.R.: ‘Yeast: an experimental organism for modern biology’, Adv. Colloid Interface Sci., 1988, 240, (4858), pp. 1439–1443.
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