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Observability for Markovian Jump Boolean Network with Random Delay Effect in States

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Abstract

This article investigates the observability for Markovian jump Boolean network with random delay effect (MJBNRDE) in states which including two mutually independent Markov chains. First, the observability of MJBNRDE is converted into set reachability of the interconnected MJBNRDE by semi-tensor product and a parallel extension technique. Then, we define an indicator matrix and invariant subset to convert the observability of MJBNRDE into stability of the reduced dynamical system. A necessary and sufficient criterion is provided to determine whether a MJBNRDE is asymptotically observable in distribution. Finally, two numerical examples are employed to illustrate the efficiency of theoretical results.

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References

  1. Kauffman, S.A.: Metabolic stability and epigenesis in randomly constructed genetic nets. J. Theor. Biol. 22, 437–467 (1968)

    Article  Google Scholar 

  2. Cheng, D., Qi, H.: Semi-tensor Product of Matrices-Theory and Applications. Science Press, Beijing (2007)

    Google Scholar 

  3. Wang, Y., Yang, Y., Liu, Y., et al.: Fault detection and pinning control of Boolean networks. Appl. Math. Comput. 429, 127232 (2022)

    MATH  Google Scholar 

  4. Li, L., Zhang, A., Lu, J.: Robust set stability of probabilistic Boolean networks under general stochastic function perturbation. Inf. Sci. 582, 833–849 (2022)

    Article  Google Scholar 

  5. Yang, M., Li, R., Chu, T.: Controller design for disturbance decoupling of Boolean control networks. Automatica 49, 273–277 (2013)

    Article  MATH  Google Scholar 

  6. Li, H., Wang, Y., Xie, L., et al.: Disturbance decoupling control design for switched Boolean control networks. Syst. Control Lett. 72, 1–6 (2014)

    Article  MATH  Google Scholar 

  7. Zhang, Z., Leifeld, T., Zhang, P.: Unknown input decoupling and estimation in observer design for Boolean control networks. IFAC-PapersOnLine 50, 2917–2922 (2017)

    Article  Google Scholar 

  8. Zhang, Z., Leifeld, T., Zhang, P.: Reconstructibility analysis and observer design for Boolean control networks. IEEE Trans. Control Netw. Syst. 7, 516–528 (2020)

    Article  MATH  Google Scholar 

  9. Zhang, Z., Zhang, P., Leifeld, T.: Reduced-order observer design for fault diagnosis of Boolean control networks. Automatica 146, 110618 (2022)

    Article  MATH  Google Scholar 

  10. Yang, X., Li, H.: On state feedback asymptotical stabilization of probabilistic Boolean control networks. Syst. Control Lett. 160, 105107 (2022)

    Article  MATH  Google Scholar 

  11. Shmulevich, I., Dougherty, E.R., Zhang, W.: From Boolean to probabilistic Boolean networks as models of genetic regulatory networks. Proc. IEEE 90, 1778–1792 (2002)

    Article  Google Scholar 

  12. Liu, Y., Chen, H., Lu, J., et al.: Controllability of probabilistic Boolean control networks based on transition probability matrices. Automatica 52, 340–345 (2015)

    Article  MATH  Google Scholar 

  13. Liu, F., Cui, Y., Wang, J., et al.: Observability of probabilistic Boolean multiplex networks. Asian J. Control 23, 1583–1590 (2021)

    Article  Google Scholar 

  14. Huang, C., Lu, J., Ho, W.C., et al.: Stabilization of probabilistic Boolean networks via pinning control strategy. Inf. Sci. 510, 205–217 (2020)

    Article  MATH  Google Scholar 

  15. Liu, Q., Guo, X., Zhou, T.: Optimal control for probabilistic Boolean networks. IET Syst. Biol. 4, 99–107 (2010)

    Article  Google Scholar 

  16. Pal, R., Datta, A., Dougherty, E.R.: Optimal infinite-horizon control for probabilistic Boolean networks. IEEE Trans. Signal Process. 54, 2375–2387 (2006)

    Article  MATH  Google Scholar 

  17. Guo, Y.: Observability of Boolean control networks using parallel extension and set reachability. IEEE Trans. Neural Netw. Learn. Syst. 29, 6402–6408 (2018)

    Article  Google Scholar 

  18. Zhou, R., Guo, Y., Gui, W.: Set reachability and observability of probabilistic Boolean networks. Automatica 106, 230–241 (2019)

    Article  MATH  Google Scholar 

  19. Ding, X., Li, H., Wang, S.: Set stability and synchronization of logical networks with probabilistic time delays. J. Franklin Inst. 355, 7735–7748 (2018)

    Article  MATH  Google Scholar 

  20. Zhu, S., Lu, J., Liu, Y.: Asymptotical stability of probabilistic Boolean networks with state delays. IEEE Trans. Autom. Control 65, 1779–1784 (2020)

    Article  MATH  Google Scholar 

  21. Datta, A., Choudhary, A., Bittner, M.L., et al.: External control in Markovian genetic regulatory networks. Mach. Learn. 52, 169–191 (2003)

    Article  MATH  Google Scholar 

  22. Meng, M., Xiao, G., Zhai, C., et al.: Controllability of Markovian jump Boolean control networks. Automatica 106, 70–76 (2019)

    Article  MATH  Google Scholar 

  23. Possieri, C., Teel, A.R.: Asymptotic stability in probability for stochastic Boolean networks. Automatica 83, 1–9 (2017)

    Article  MATH  Google Scholar 

  24. Zhang, Q., Feng, J., Yan, Y.: Finite-time pinning stabilization of Markovian jump Boolean networks. J. Franklin Inst. 357, 7020–7036 (2020)

    Article  MATH  Google Scholar 

  25. Zhu, S., Feng, J.: The set stabilization problem for Markovian jump Boolean control networks: An average optimal control approach. Appl. Math. Comput. 402, 126133 (2021)

    MATH  Google Scholar 

  26. Zhu, S., Lu, J., Lou, Y., et al.: Induced-equations-based stability analysis and stabilization of Markovian jump Boolean networks. IEEE Trans. Autom. Control 66, 4820–4827 (2021)

    Article  MATH  Google Scholar 

  27. Zhu, S., Lu, J., Lin, L., et al.: Minimum-time and minimum-triggering observability of stochastic Boolean networks. IEEE Trans. Autom. Control 67, 1558–1565 (2022)

    Article  MATH  Google Scholar 

  28. Laschov, D., Margaliot, M., Even, G.: Observability of Boolean networks: A graph-theoretic approach. Automatica 49, 2351–2362 (2013)

    Article  MATH  Google Scholar 

  29. Zhao, Y., Qi, H., Cheng, D.: Input-state incidence matrix of Boolean control networks and its applications. Syst. Control Lett. 59, 767–774 (2010)

    Article  MATH  Google Scholar 

  30. Cheng, D., Qi, H., Li, Z.: Analysis and Control of Boolean Networks. Springer, London (2011)

    Book  Google Scholar 

  31. Haddad, W.M., Chellaboina, V., Hui, Q.: Nonnegative and Compartmental Dynamical Systems. Princeton University Press, New Jersey (2010)

    Book  MATH  Google Scholar 

  32. Cheng, D., Li, C., He, F.: Observability of Boolean networks via set controllability approach. Syst. Control Lett. 115, 22–25 (2018)

    Article  MATH  Google Scholar 

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Acknowledgements

The authors are grateful to the referees for their careful reading of the manuscript and valuable comments. The authors thank the help from the editor too.

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Authors and Affiliations

  1. Department of Mathematics and Supercomputing Algorithm and Application Laboratory of Guizhou University and Gui’an Scientific Innovation Company, Guizhou University, Guiyang, 550025, Guizhou, People’s Republic of China

    Xudong Gui & JinRong Wang

  2. School of Mathematics, Renmin University of China, Beijing, 100872, People’s Republic of China

    Dong Shen

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  1. Xudong Gui
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  2. JinRong Wang
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  3. Dong Shen
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Correspondence to JinRong Wang.

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This work is partially supported by the National Natural Science Foundation of China (12161015), Guizhou Data Driven Modeling Learning and Optimization Innovation Team ([2020]5016), and Super Computing Algorithm and Application Laboratory of Guizhou University and Gui’an Scientific Innovation Company (K22-0116-003).

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Gui, X., Wang, J. & Shen, D. Observability for Markovian Jump Boolean Network with Random Delay Effect in States. Qual. Theory Dyn. Syst. 22, 21 (2023). https://doi.org/10.1007/s12346-022-00721-8

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