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

• Autores: Xudong Gui, JinRong Wang, Dong Shen
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 22, Nº 1, 2023
• Idioma: inglés
• Enlaces
  • Texto completo
• Resumen

  • 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.

• Referencias bibliográficas
  • 1. Kauffman, S.A.: Metabolic stability and epigenesis in randomly constructed genetic nets. J. Theor. Biol. 22, 437–467 (1968)
  • 2. Cheng, D., Qi, H.: Semi-tensor Product of Matrices-Theory and Applications. Science Press, Beijing (2007)
  • 3. Wang, Y., Yang, Y., Liu, Y., et al.: Fault detection and pinning control of Boolean networks. Appl. Math. Comput. 429, 127232 (2022)
  • 4. Li, L., Zhang, A., Lu, J.: Robust set stability of probabilistic Boolean networks under general stochastic function perturbation. Inf....
  • 5. Yang, M., Li, R., Chu, T.: Controller design for disturbance decoupling of Boolean control networks. Automatica 49, 273–277 (2013)
  • 6. Li, H., Wang, Y., Xie, L., et al.: Disturbance decoupling control design for switched Boolean control networks. Syst. Control Lett. 72,...
  • 7. Zhang, Z., Leifeld, T., Zhang, P.: Unknown input decoupling and estimation in observer design for Boolean control networks. IFAC-PapersOnLine...
  • 8. Zhang, Z., Leifeld, T., Zhang, P.: Reconstructibility analysis and observer design for Boolean control networks. IEEE Trans. Control Netw....
  • 9. Zhang, Z., Zhang, P., Leifeld, T.: Reduced-order observer design for fault diagnosis of Boolean control networks. Automatica 146, 110618...
  • 10. Yang, X., Li, H.: On state feedback asymptotical stabilization of probabilistic Boolean control networks. Syst. Control Lett. 160, 105107...
  • 11. Shmulevich, I., Dougherty, E.R., Zhang, W.: From Boolean to probabilistic Boolean networks as models of genetic regulatory networks. Proc....
  • 12. Liu, Y., Chen, H., Lu, J., et al.: Controllability of probabilistic Boolean control networks based on transition probability matrices....
  • 13. Liu, F., Cui, Y., Wang, J., et al.: Observability of probabilistic Boolean multiplex networks. Asian J. Control 23, 1583–1590 (2021)
  • 14. Huang, C., Lu, J., Ho, W.C., et al.: Stabilization of probabilistic Boolean networks via pinning control strategy. Inf. Sci. 510, 205–217...
  • 15. Liu, Q., Guo, X., Zhou, T.: Optimal control for probabilistic Boolean networks. IET Syst. Biol. 4, 99–107 (2010)
  • 16. Pal, R., Datta, A., Dougherty, E.R.: Optimal infinite-horizon control for probabilistic Boolean networks. IEEE Trans. Signal Process....
  • 17. Guo, Y.: Observability of Boolean control networks using parallel extension and set reachability. IEEE Trans. Neural Netw. Learn. Syst....
  • 18. Zhou, R., Guo, Y., Gui, W.: Set reachability and observability of probabilistic Boolean networks. Automatica 106, 230–241 (2019)
  • 19. Ding, X., Li, H., Wang, S.: Set stability and synchronization of logical networks with probabilistic time delays. J. Franklin Inst. 355,...
  • 20. Zhu, S., Lu, J., Liu, Y.: Asymptotical stability of probabilistic Boolean networks with state delays. IEEE Trans. Autom. Control 65, 1779–1784...
  • 21. Datta, A., Choudhary, A., Bittner, M.L., et al.: External control in Markovian genetic regulatory networks. Mach. Learn. 52, 169–191 (2003)
  • 22. Meng, M., Xiao, G., Zhai, C., et al.: Controllability of Markovian jump Boolean control networks. Automatica 106, 70–76 (2019)
  • 23. Possieri, C., Teel, A.R.: Asymptotic stability in probability for stochastic Boolean networks. Automatica 83, 1–9 (2017)
  • 24. Zhang, Q., Feng, J., Yan, Y.: Finite-time pinning stabilization of Markovian jump Boolean networks. J. Franklin Inst. 357, 7020–7036 (2020)
  • 25. Zhu, S., Feng, J.: The set stabilization problem for Markovian jump Boolean control networks: An average optimal control approach. Appl....
  • 26. Zhu, S., Lu, J., Lou, Y., et al.: Induced-equations-based stability analysis and stabilization of Markovian jump Boolean networks. IEEE...
  • 27. Zhu, S., Lu, J., Lin, L., et al.: Minimum-time and minimum-triggering observability of stochastic Boolean networks. IEEE Trans. Autom....
  • 28. Laschov, D., Margaliot, M., Even, G.: Observability of Boolean networks: A graph-theoretic approach. Automatica 49, 2351–2362 (2013)
  • 29. Zhao, Y., Qi, H., Cheng, D.: Input-state incidence matrix of Boolean control networks and its applications. Syst. Control Lett. 59, 767–774...
  • 30. Cheng, D., Qi, H., Li, Z.: Analysis and Control of Boolean Networks. Springer, London (2011)
  • 31. Haddad, W.M., Chellaboina, V., Hui, Q.: Nonnegative and Compartmental Dynamical Systems. Princeton University Press, New Jersey (2010)
  • 32. Cheng, D., Li, C., He, F.: Observability of Boolean networks via set controllability approach. Syst. Control Lett. 115, 22–25 (2018)