Location via proxy:   [ UP ]  
[Report a bug]   [Manage cookies]                
Skip to main content
Springer Nature Link
Log in

Event-Triggered \(H_\infty \) State Estimation for Coupled and Switched Genetic Regulatory Networks

  • Published:
Circuits, Systems, and Signal Processing Aims and scope Submit manuscript

Abstract

This paper investigates the problem of event-triggered \(H_\infty \) state estimation for switched genetic regulatory networks with static coupling via a sojourn-probability-dependent approach. The measurements of the network are evaluated by the event-triggers which are only undertaken at the switching times. By employing a time-delay approach, the estimation can be achieved by determining the exponential mean-square stability of the switched system with time-varying delay and known sojourn probability, while the system prescribes an \(H_\infty \) performance level. A co-design approach for the event-triggered mechanism and the estimators is presented by means of a novel Lyapunov–Krasovskii functional combining with refined Jensen-based inequalities. Finally, a numerical example is given to demonstrate the effectiveness of the designed estimators.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7

Similar content being viewed by others

References

  1. A.D. Ames, P. Tabuada, S. Sastry, On the stability of zeno equilibria. Lecture notes in computer science. 3927, 34–48 (2006). Springer, Berlin

  2. J. Cao, F. Ren, Exponential stability of discrete-time genetic regulatory networks with delays. IEEE Trans. Neural Netw. 19(3), 520–523 (2008)

    Article  Google Scholar 

  3. J. Cao, R. Rakkiyappan, K. Maheswari, A. Chandrasekar, Exponential \(H_\infty \) filtering analysis for discrete-time switched neural networks with random delays using sojourn probabilities. Sci. China Technol. Sci. 59(3), 387–402 (2016)

    Article  Google Scholar 

  4. G. Chen, J. Zhou, Z. Liu, Global synchronization of coupled delayed neural networks and applications to chaotic CNN models. Int. J. Bifurcat. Chaos 14(7), 2229–2240 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  5. T. Dong, A.J. Wang, H.Y. Zhu, X.F. Liao, Event-triggered synchronization for reaction-diffusion complex networks via random sampling. Physica A Stat. Mech. Appl. 495, 454–462 (2018)

    Article  MathSciNet  Google Scholar 

  6. X. Ge, Q.-L. Han, Distributed event-triggered \(H_\infty \) filtering over sensor networks with communication delays. Inf. Sci. 291, 128–142 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  7. F. Hoppensteadt, E. Izhikevich, Pattern recognition via synchronization in phase-locked loop neural networks. IEEE Trans. Neural Netw. 11(3), 734–738 (2000)

    Article  Google Scholar 

  8. A. Hu, J. Cao, M. Hu, L. Guo, Event-triggered consensus of Markovian jumping multi-agent systems via stochastic sampling. IET Control Theory Appl. 9(13), 1964–1972 (2015)

    Article  MathSciNet  Google Scholar 

  9. Q. Li, B. Shen, Y. Liu, F.E. Alsaadi, Event-triggered \(H_\infty \) state estimation for discrete-time stochastic genetic regulatory networks with Markovian jumping parameters and time-varying delays. Neurocomputing 174, 912–920 (2016)

    Article  Google Scholar 

  10. J. Liang, J. Lam, Z. Wang, State estimation for Markov-type genetic regulatory networks with delays and uncertain mode transition rates. Phys. Lett. A 373, 4328–4337 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  11. Y. Liu, Z. Wang, Y. Yuan, F.E. Alsaadi, Partial-nodes-based state estimation for complex networks with unbounded distributed delays. IEEE Trans. Neural Netw. Learn. Syst. 29(8), 3906–3912 (2018)

    Article  MathSciNet  Google Scholar 

  12. Y. Liu, J.H. Park, B.-Z. Guo, F. Fang, F. Zhou, Event-triggered dissipative synchronization for Markovian jump neural networks with general transition probabilities. Inter. J. Robust Nonlinear Control 28(13), 3893–3908 (2018)

    Article  MATH  Google Scholar 

  13. K. Mathiyalagan, H. Su, P. Shi, R. Sakthivel, Exponential \(H_\infty \) filtering for discrete-time switched neural networks with random delays. IEEE Trans. Cybern. 45(4), 676–687 (2015)

    Article  Google Scholar 

  14. P. Park, J.W. Ko, C. Jeong, Reciprocally convex approach to stability of systems with time-varying delays. Automatica 47(1), 235–238 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  15. B. Qiao, X. Su, R. Jia, Y. Shi, M.S. Mahmoud, Event-triggered fault detection filtering for discrete-time Markovian jump systems. Signal Process. 152, 384–391 (2018)

    Article  Google Scholar 

  16. R. Rakkiyappan, R. Sasirekha, Y. Zhu, L. Zhang, \(H_\infty \) state estimator design for discrete-time switched neural networks with multiple missing measurements and sojourn probabilities. J. Frankl. Inst. 353(6), 1358–1385 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  17. R. Samidurai, R. Manivannan, C.K. Ahn, H.R. Karimi, New criteria for stability of generalized neural networks including Markov jump parameters and additive time delays. IEEE Trans. Syst. Man Cybern.-Syst. 48(4), 485–499 (2018)

    Article  Google Scholar 

  18. R. Saravanakumar, S. B. Stojanovic, D. D. Radosavljevic, C. Ki Ahn, H. R. Karimi, Finite-time passivity-based stability criteria for delayed discrete-time neural networks via new weighted summation inequalities. IEEE Trans. Neural Netw. Learn. Syst. 30(1), 58–71 (2019)

    Article  MathSciNet  Google Scholar 

  19. R. Sasirekha, R. Rakkiyappan, Extended dissipativity state estimation for switched discrete-time complex dynamical networks with multiple communication channels: A sojourn probability dependent approach. Neurocomputing 267, 55–68 (2017)

    Article  Google Scholar 

  20. A. Seuret, F. Gouaisbaut, E. Fridman, Stability of discrete-time systems with time-varying delays via a novel summation inequality. IEEE Trans. Autom. Control 60(10), 2740–2745 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  21. H. Shen, Y. Zhu, L. Zhang, J.H. Park, Extended dissipative state estimation for Markov jump neural networks with unreliable links. IEEE Trans. Neural Netw. Learn. Syst. 28(3), 346–358 (2017)

    Article  MathSciNet  Google Scholar 

  22. H. Song, L. Yu, W. Zhang, Networked \(H_\infty \) filtering for linear discrete-time systems. Inf. Sci. 181, 686–696 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  23. X.J. Su, X.X. Liu, P. Shi, Y.D. Song, Sliding mode control of hybrid switched systems via an event-triggered mechanism. Automatica 90, 294–303 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  24. X.G. Tan, J.D. Cao, X.D. Li, A. Alsaedi, Leader-following mean square consensus of stochastic multi-agent systems with input delay via event-triggered control. IET Control Theory Appl. 12(2), 299–309 (2018)

    Article  MathSciNet  Google Scholar 

  25. Y. Tan, D. Du, Q. Qi, State estimation for Markovian jump systems with an event-triggered communication scheme. Circuits Syst. Signal Process. 36, 2–24 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  26. E. Tian, W.K. Wong, D. Yue, T.-C. Yang, \(H_\infty \) filtering for discrete-time switched systems with known sojourn probabilities. IEEE Trans. Autom. Control 60(9), 2446–2451 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  27. X. Wan, Z. Wang, C. Ren, \(H_\infty \) state estimation for discrete time-delayed stochastic genetic regulatory networks with known sojourn probabilities, in Proceedings of the 23rd International Conference on Automation and Computing (ICAC), (2017), pp. 1–6

  28. A. Wang, T. Dong, X. Liao, Event-triggered synchronization strategy for complex dynamical networks with the Markovian switching topologies. Neural Netw. 74, 52–57 (2016)

    Article  MATH  Google Scholar 

  29. L.C. Wang, Z.D. Wang, T.W. Huang, G.L. Wei, An event-triggered approach to state estimation for a Class of complex networks with mixed time delays and nonlinearities. IEEE Trans. Cybern. 46(11), 2497–2508 (2016)

    Article  Google Scholar 

  30. J. Wang, M. Xing, Y. Sun, J. Li, J. Lu, Event-triggered dissipative state estimation for Markov jump neural networks with random uncertainties. J. Frankl. Inst. (2018). https://doi.org/10.1016/j.jfranklin.2018.01.021

  31. X. Wang, G. Yang, Event-based weighted residual generator design via non-PDC scheme for fault diagnosis in T–S fuzzy systems. J. Frankl. Inst. 355(6), 3145–3167 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  32. H. Wang, D. Zhang, R. Lu, Event-triggered \(H_\infty \) filter design for Markovian jump systems with quantization. Nonlinear Anal. Hybrid Syst. 28, 23–41 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  33. Z. Wang, Y. Xu, R.Q. Lu, H. Peng, Finite-time state estimation for coupled Markovian neural networks with sensor nonlinearities. IEEE Trans. Neural Netw. Learn. Syst. 28(3), 630–638 (2017)

    Article  MathSciNet  Google Scholar 

  34. J.Y. Wang, H.G. Zhang, Z.S. Wang, Z.W. Liu, Sampled-data synchronization of Markovian coupled neural networks with mode delays based on mode-dependent LKF. IEEE Trans. Neural Netw. Learn. Syst. 28(11), 2626–2637 (2017)

    Article  MathSciNet  Google Scholar 

  35. S.P. Wen, Z.G. Zeng, M.Z.Q. Chen, T.W. Huang, Synchronization of switched neural networks with communication delays via the event-triggered control. IEEE Trans. Neural Netw. Learn. Syst. 28(10), 2334–2343 (2017)

    Article  MathSciNet  Google Scholar 

  36. Z.-G. Wu, Z. Xu, P. Shi, M.Z.Q. Chen, H. Su, Nonfragile state estimation of quantized complex networks with switching topologies. IEEE Trans. Neural Netw. Learn. Syst. 29(10), 5111–5121 (2018)

    Article  MathSciNet  Google Scholar 

  37. X. Xiao, L. Zhou, G. Lu, Event-triggered \(H_\infty \) filtering of continuous-time switched linear systems. Signal Process. 141, 343–349 (2017)

    Article  Google Scholar 

  38. Y. Xu, R. Lu, P. Shi, J. Tao, S. Xie, Robust estimation for neural networks with randomly occurring distributed delays and Markovian jump coupling. IEEE Trans. Neural Netw. Learn. Syst. 29(4), 845–855 (2018)

    Article  MathSciNet  Google Scholar 

  39. H. Yan, H. Zhang, F. Yang, X. Zhan, C. Peng, Event-triggered asynchronous guaranteed cost control for markov jump discrete-time neural networks with distributed delay and channel fading. IEEE Trans. Neural Netw. Learn. Syst. 29(8), 3588–3598 (2018)

    Article  MathSciNet  Google Scholar 

  40. X. Yang, J. Cao, J. Lu, Synchronization of randomly coupled neural networks with Markovian jumping and time-delay. IEEE Trans. Circuits Syst. I. Regul. Pap. 60(2), 363–376 (2013)

    Article  MathSciNet  Google Scholar 

  41. X. Yang, Z. Feng, J. Feng, J. Cao, Synchronization of discrete-time neural networks with delays and Markov jump topologies based on tracker information. Neural Netw. 85, 157–164 (2017)

    Article  Google Scholar 

  42. T. Yu, J. Liu, Y. Zeng, X. Zhang, Q. Zeng, L. Wu, Stability analysis of genetic regulatory networks with switching parameters and time delays. IEEE Trans. Neural Netw. Learn. Syst. 29(7), 3047–3058 (2018)

    MathSciNet  Google Scholar 

  43. D.D. Yue, Z.H. Guan, T. Li, R.Q. Liao, F. Liu, Q. Lai, Event-based cluster synchronization of coupled genetic regulatory networks. Physica A Stat. Mech. Appl. 482, 649–665 (2017)

    Article  MathSciNet  Google Scholar 

  44. D. Zhang, Q.-G. Wang, D. Srinivasan, H. Li, L. Yu, Asynchronous state estimation for discrete-time switched complex networks with communication constraints. IEEE Trans. Neural Netw. Learn. Syst. 29(5), 1732–1746 (2018)

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgements

This work was jointly supported by the National Natural Science Foundation of China under Grant No. 61573201, Project of Flagship-Major Construction of Jiangsu Higher Education Institutions of China under Grant No. PPZY2015B135, Postgraduate Research and Practice Innovation Program of Jiangsu Province under Grant Nos. KYCX17\(_{-}\)1915 and KYCX18\(_{-}\)2423, and Applied Basic Research-Industrial Innovation Project of Nantong City under Grant No. GY12017025.

Author information

Authors and Affiliations

  1. School of Information Science and Technology, Nantong University, Nantong, 226019, China

    Suying Sheng, Xiaomei Zhang & Qingqing Lu

  2. School of Electrical Engineering, Nantong University, Nantong, 226019, China

    Guoping Lu

Authors
  1. Suying Sheng
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Xiaomei Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Qingqing Lu
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Guoping Lu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Xiaomei Zhang.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Appendix A

Appendix A

The event-triggered parameters and the estimator gains are given as

$$\begin{aligned} U_1= & {} \begin{bmatrix} 0.0023&\quad -\,0.0067\\ -\,0.0067&\quad 0.0200 \end{bmatrix}, U_2=\begin{bmatrix} 0.0002&\quad 0.0008\\ 0.0008&\quad 0.0065 \end{bmatrix},\\ U_3= & {} \begin{bmatrix} 0.0010&\quad -0.0012\\ -\,0.0012&\quad 0.0017 \end{bmatrix}, A_{1f1}=\begin{bmatrix} 0.0680&\quad 0.4452&\quad 0.7029&\quad -\,0.7867\\ -\,0.4647&\quad 1.1069&\quad 0.5471&\quad -\,0.6486\\ -\,0.3780&\quad 0.6515&\quad 1.0854&\quad -\,0.7946\\ -\,0.4017&\quad 0.7698&\quad 0.3564&\quad 0.0467 \end{bmatrix},\\ A_{2f1}= & {} \begin{bmatrix} 0.6122&\quad -\,0.4157&\quad -\,0.1012&\quad 0.3131\\ -\,0.0165&\quad 0.3306&\quad -\,0.0032&\quad 0.1549\\ 0.2878&\quad -\,0.2409&\quad 0.3251&\quad 0.0574\\ 0.1053&\quad -\,0.1432&\quad -\,0.3478&\quad 0.9406 \end{bmatrix},\\ A_{3f1}= & {} \begin{bmatrix} 0.7058&\quad -\,0.4571&\quad -\,0.3184&\quad 0.6256\\ -\,0.0786&\quad 0.5091&\quad -\,0.1825&\quad 0.2790\\ 0.3069&\quad -\,0.3220&\quad 0.1344&\quad 0.4256\\ 0.0243&\quad -\,0.0098&\quad -\,0.2552&\quad 0.8769 \end{bmatrix},\\ G_{1f1}= & {} \begin{bmatrix} 0.0074&\quad 1.1864&\quad 1.1279&\quad -\,1.3413\\ -\,0.4896&\quad 1.4504&\quad 0.8266&\quad -\,0.7351\\ -\,0.7367&\quad 1.0441&\quad 1.8424&\quad -\,0.9246\\ -\,0.5387&\quad 0.8027&\quad 0.8533&\quad 0.1982 \end{bmatrix},\\ G_{2f1}= & {} \begin{bmatrix} 1.0053&\quad -\,0.8937&\quad -\,0.1585&\quad 0.4102\\ 0.1064&\quad 0.2852&\quad -\,0.0501&\quad 0.1027\\ 0.2100&\quad -\,0.6078&\quad 0.8754&\quad -\,0.1136\\ 0.3789&\quad -\,0.7475&\quad -\,0.6250&\quad 1.6746 \end{bmatrix},\\ G_{3f1}= & {} \begin{bmatrix} 0.7963&\quad -\,0.1944&\quad -\,0.4551&\quad -\,0.2871\\ -\,0.3050&\quad 1.1184&\quad -\,0.6247&\quad -\,0.1386\\ -\,0.1745&\quad -\,0.0415&\quad 0.3783&\quad -\,0.3539\\ -\,0.2277&\quad 0.1923&\quad -\,0.3842&\quad 0.6582 \end{bmatrix},\\ B_{1f1}= & {} \begin{bmatrix} 0.2240&\quad 0.1478\\ 0.1701&\quad 0.1231\\ 0.2425&\quad 0.1566\\ 0.1374&\quad 0.1146 \end{bmatrix}, B_{2f1}=\begin{bmatrix} 0.1385&\quad -\,0.0647\\ 0.1239&\quad -\,0.0856\\ 0.1459&\quad -\,0.0734\\ 0.1066&\quad -\,0.0970 \end{bmatrix}, \\ B_{3f1}= & {} \begin{bmatrix} 0.0801&\quad 0.0862\\ 0.0683&\quad 0.0536\\ 0.0838&\quad 0.0830\\ 0.0564&\quad 0.0481 \end{bmatrix}, \ A_{1f2}=\begin{bmatrix} 0.0765&\quad 0.5008&\quad 0.7907&\quad -\,0.8850\\ -\,0.5227&\quad 1.2453&\quad 0.6155&\quad -\,0.7296\\ -\,0.4252&\quad 0.7330&\quad 1.2210&\quad -\,0.8939\\ -\,0.4519&\quad 0.8660&\quad 0.4010&\quad 0.0525 \end{bmatrix},\\ A_{2f2}= & {} \begin{bmatrix} 0.6887&\quad -\,0.4677&\quad -\,0.1139&\quad 0.3522\\ -\,0.0186&\quad 0.3719&\quad -\,0.0036&\quad 0.1742\\ 0.3238&\quad -\,0.2710&\quad 0.3658&\quad 0.0645\\ 0.1185&\quad -\,0.1611&\quad -\,0.3912&\quad 1.0581 \end{bmatrix},\\ A_{3f2}= & {} \begin{bmatrix} 0.7940&\quad -\,0.5143&\quad -\,0.3582&\quad 0.7038\\ -\,0.0884&\quad 0.5727&\quad -\,0.2053&\quad 0.3139\\ 0.3452&\quad -\,0.3622&\quad 0.1512&\quad 0.4788\\ 0.0274&\quad -\,0.0110&\quad -\,0.2871&\quad 0.9866 \end{bmatrix},\\ G_{1f2}= & {} \begin{bmatrix} 0.0084&\quad 1.3347&\quad 1.2689&\quad -\,1.5090\\ -\,0.5508&\quad 1.6317&\quad 0.9299&\quad -\,0.8270\\ -\,0.8287&\quad 1.1747&\quad 2.0727&\quad -\,1.0402\\ -\,0.6060&\quad 0.9031&\quad 0.9599&\quad 0.2230 \end{bmatrix},\\ G_{2f2}= & {} \begin{bmatrix} 1.1310&\quad -\,1.0054&\quad -\,0.1783&\quad 0.4615\\ 0.1197&\quad 0.3209&\quad -\,0.0564&\quad 0.1156\\ 0.2363&\quad -\,0.6838&\quad 0.9848&\quad -\,0.1278\\ 0.4263&\quad -\,0.8410&\quad -\,0.7031&\quad 1.8839 \end{bmatrix},\\ G_{3f2}= & {} \begin{bmatrix} 0.8959&\quad -\,0.2187&\quad -\,0.5120&\quad -\,0.3229\\ -\,0.3431&\quad 1.2582&\quad -\,0.7028&\quad -\,0.1559\\ -\,0.1963&\quad -\,0.0467&\quad 0.4256&\quad -\,0.3981\\ -\,0.2562&\quad 0.2164&\quad -\,0.4322&\quad 0.7405 \end{bmatrix},\ B_{1f2}=\begin{bmatrix} -\,0.1986&\quad -\,0.1312\\ -\,0.1509&\quad -\,0.1091\\ -\,0.2150&\quad -\,0.1391\\ -\,0.1219&\quad -\,0.1014 \end{bmatrix}, \\ B_{2f2}= & {} \begin{bmatrix} -\,0.1228&\quad 0.0574\\ -\,0.1098&\quad 0.0760\\ -\,0.1294&\quad 0.0651\\ -\,0.0945&\quad 0.0860 \end{bmatrix},\ B_{3f2}=\begin{bmatrix} -\,0.0710&\quad -\,0.0764\\ -\,0.0605&\quad -\,0.0476\\ -\,0.0744&\quad -\,0.0736\\ -\,0.0500&\quad -\,0.0427 \end{bmatrix}. \end{aligned}$$

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Sheng, S., Zhang, X., Lu, Q. et al. Event-Triggered \(H_\infty \) State Estimation for Coupled and Switched Genetic Regulatory Networks. Circuits Syst Signal Process 38, 4420–4445 (2019). https://doi.org/10.1007/s00034-019-01073-6

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00034-019-01073-6

Keywords

Search

Navigation