Skip to main content
SpringerLink
Log in

Finite-time synchronization control for uncertain Markov jump neural networks with input constraints

  • Original Paper
  • Published:
Nonlinear Dynamics Aims and scope Submit manuscript

Abstract

This paper is concerned with the problem of finite-time synchronization control for uncertain Markov jump neural networks in the presence of constraints on the control input amplitude. The parameter uncertainties under consideration are assumed to belong to a fixed convex polytope. By using a parameter-dependent Lyapunov functional and a simple matrix decoupling method, a sufficient condition is proposed to ensure that the considered networks are stochastically synchronized over a finite-time interval. The desired mode-independent controller parameters can be computed via solving a convex optimization problem. Finally, two chaos neural networks are employed to demonstrate the effectiveness of our proposed approach.

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

Access this article

Log in via an institution

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

Similar content being viewed by others

References

  1. Amato, F., Ambrosino, R., Cosentino, C., Tommasi, G.: Input–output finite-time stabilization of linear systems. Automatica 46, 1558–1562 (2010)

    Article  MATH  Google Scholar 

  2. Arik, S.: An analysis of exponential stability of delayed neural networks with time varying delays. Neural Netw. 17, 1027–1031 (2004)

    Article  MATH  Google Scholar 

  3. Balasubramaniam, P., Nagamani, G., Rakkiyappan, R.: Passivity analysis for neural networks of neutral type with Markovian jumping parameters and time delay in the leakage term. Commun. Nonlinear Sci. Numer. Simul. 16, 4422–4437 (2011)

    Article  MATH  MathSciNet  Google Scholar 

  4. Balasubramaniam, P., Vembarasan, V., Rakkiyappan, R.: Delay-dependent robust asymptotic state estimation of Takagi–Sugeno fuzzy hopfield neural networks with mixed interval time-varying delays. Expert Syst. Appl. 39, 472–481 (2012)

  5. Chen, Y., Zheng, W.: Stochastic state estimation for neural networks with distributed delays and Markovian jump. Neural Netw. 25, 14–20 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  6. de Oliveira, P., Oliveira, R., Leite, V., Montagner, V., Peres, P.: \(H_{\infty }\) guaranteed cost computation by means of parameter-dependent lyapunov functions. Automatica 35, 305–315 (2004)

    MATH  MathSciNet  Google Scholar 

  7. Farges, C., Moze, M., Sabatier, J.: Pseudo-state feedback stabilization of commensurate fractional order systems. Automatica 46, 1730–1734 (2010)

    Article  MATH  MathSciNet  Google Scholar 

  8. Gao, H., Meng, X., Chen, T.: A new design of robust \(H_2\) filters for uncertain systems. Syst. Control Lett. 57, 585–593 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  9. Huang, H., Huang, T., Chen, X.: A mode-dependent approach to state estimation of recurrent neural networks with Markovian jumping parameters and mixed delays. Neural Netw. 46, 50–61 (2013)

    Article  Google Scholar 

  10. Jin, X., Yang, G.: Adaptive synchronization of a class of uncertain complex networks against network deterioration. IEEE Trans. Circuits Syst. I. Reg. Papers 58, 1396–1409 (2011)

    Article  MathSciNet  Google Scholar 

  11. Jin, X., Yang, G., Che, W.: Adaptive pinning control of deteriorated nonlinear coupling networks with circuit realization. IEEE Trans. Neural Netw. Learn. Syst. 23, 1345–1355 (2012)

    Google Scholar 

  12. Li, H., Chen, B., Zhou, Q., Qian, W.: Robust stability for uncertain delayed fuzzy Hopfield neural networks with Markovian jumping parameters. IEEE Trans. Syst. Man Cybern. B 39, 94–102 (2009)

    Article  Google Scholar 

  13. Liao, X., Wang, J., Zeng, Z.: Global asymptotic stability and global exponential stability of delayed cellular neural networks. IEEE Trans. Circuits Syst. II Exp. Briefs 52, 403–409 (2005)

  14. Liu, Q., Dang, C., Cao, J.: A novel recurrent neural network with one neuron and finite-time convergence for k-winners-take-all operation. IEEE Trans. Neural Netw. 21, 1140–1148 (2010)

    Google Scholar 

  15. Liu, X., Chen, T., Cao, J., Lu, W.: Dissipativity and quasi-synchronization for neural networks with discontinuous activations and parameter mismatches. Neural Netw. 24, 1013–1021 (2011)

    Article  MATH  Google Scholar 

  16. Liu, Y., Wang, Z., Liang, J., Liu, X.: Synchronization of coupled neutral-type neural networks with jumping-mode-dependent discrete and unbounded distributed delays. IEEE Trans. Cybern. 43, 102–114 (2013)

    Article  Google Scholar 

  17. Ma, Q., Wang, Z., Lu, J.: Finite-time synchronization for complex dynamical networks with time-varying delays. Nonlinear Dyn. 70(1), 841–848 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  18. Ma, Q., Xu, S., Zou, Y., Shi, G.: Synchronization of stochastic chaotic neural networks with reaction-diffusion terms. Nonlinear Dyn. 67(3), 2183–2196 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  19. Shen, H., Huang, X., Zhou, J., Wang, Z.: Global exponential estimates for uncertain Markovian jump neural networks with reaction-diffusion terms. Nonlinear Dyn. 69, 473–486 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  20. Shen, H., Xu, S., Lu, J., Zhou, J.: Passivity based control for uncertain stochastic jumping systems with mode-dependent round-trip time delays. J. Frankl. Inst. 349, 1665–1680 (2012)

  21. Shen, H., Xu, S., Zhou, J., Lu, J.: Fuzzy \({\cal H}_{\infty }\) filtering for nonlinear Markovian jump neutral systems. Int. J. Syst. Sci. 42, 767–780 (2011)

    Article  MATH  MathSciNet  Google Scholar 

  22. Shen, H., Song, X., Wang, Z.: Robust fault tolerant control of uncertain fractional-order systems against actuator faults. IET Control Theory Appl. 7(9), 1233–1241 (2013)

    Article  MathSciNet  Google Scholar 

  23. Shen, H., Park, J.H., Zhang, L.X., Wu, Z.: Robust extended dissipative control for sampled-data Markov jump systems. Int. J. Control (2014). doi:10.1080/00207179.2013.878478

  24. Shen, J., Cao, J.: Finite-time synchronization of coupled neural networks via discontinuous controllers. Cogn. Neurodyn. 5, 373–385 (2011)

    Article  Google Scholar 

  25. Shen, Y., Li, C.: LMI-based finite-time boundedness analysis of neural networks with parametric uncertainties. Neurocomputing 71, 502–507 (2008)

    Article  Google Scholar 

  26. Shen, Y., Wang, J.: Almost sure exponential stability of recurrent neural networks with Markovian switching. IEEE Trans. Neural Netw. 20, 840–855 (2009)

    Google Scholar 

  27. Wang, Z., Liu, Y., Yu, L., Liu, H.: Exponential stability of delayed recurrent neural networks with Markovian jumping parameters. Phys. Lett. A 356, 346–352 (2006)

    Article  MATH  Google Scholar 

  28. Wu, L., Yao, X., Zheng, W.: Generalized \(H_{2}\) fault detection for Markovian jumping two-dimensional systems. Automatica 48, 1741–1750 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  29. Wu, Z., Shi, P., Su, H., Chu, J.: Passivity analysis for discrete-time stochastic Markovian jump neural networks with mixed time delays. IEEE Trans. Neural Netw. 22, 1566–1575 (2011)

    Google Scholar 

  30. Wu, Z., Shi, P., Su, H., Chu, J.: Asynchronous \(l_{2}-l_{\infty }\) filtering for discrete-time stochastic Markov jump systems with randomly occurred sensor nonlinearities. Automatica. 50, 180–186 (2014)

  31. Wu, Z., Shi, P., Su, H., Chu, J.: Stochastic synchronization of Markovian jump neural networks with time-varying delay using sampled data. IEEE Trans. Cybern. 43, 1796–1806 (2013)

  32. Xu, S., Zheng, W., Zou, Y.: Passivity analysis of neural networks with time-varying delays. IEEE Trans. Circuits Syst. II. Exp. Briefs 56, 325–329 (2009)

    Google Scholar 

  33. Yang, X., Wu, Z., Cao, J.: Finite-time synchronization of complex networks with nonidentical discontinuous nodes. Nonlinear Dyn. 73(4), 2313–2327 (2013)

    Article  MATH  MathSciNet  Google Scholar 

  34. Yang, X., Cao, J., Lu, J.: Synchronization of Markovian coupled neural networks with nonidentical node-delays and random coupling strengths. IEEE Trans. Neural Netw. Learn. Syst. 23, 60–71 (2012)

    MathSciNet  Google Scholar 

  35. Zeng, Z., Wang, J.: Analysis and design of associative memories based on recurrent neural networks with linear saturation activation functions and time varying delays. Neural Comput. 19, 2149–2182 (2006)

    Article  MathSciNet  Google Scholar 

  36. Zhang, B., Zheng, W., Xu, S.: Filtering of Markovian jump delay systems based on a new performance index. IEEE Trans. Circuits Syst. I. Reg. Papers 60, 1250– 1263 (2013)

    MathSciNet  Google Scholar 

  37. Zhang, D., Yu, L.: Exponential state estimation for Markovian jumping neural networks with time-varying discrete and distributed delays. Neural Netw. 35, 103–111 (2012)

    Article  Google Scholar 

  38. Zhang, H., Wang, Y.: Stability analysis of Markovian jumping stochastic Cohen–Grossberg neural networks with mixed time delays. IEEE Trans. Neural Netw. 19, 366–371 (2008)

    Google Scholar 

  39. Zhang, L.X., Lam, J.: Necessary and sufficient conditions for analysis and synthesis of Markov jump linear systems with incomplete transition descriptions. IEEE Trans. Autom. Control 55, 1695–1701 (2010)

    Article  MathSciNet  Google Scholar 

  40. Zhu, Q., Cao, J.: Robust exponential stability of Markovian jump impulsive stochastic Cohen-Grossberg neural networks with mixed time delays. IEEE Trans. Neural Netw. 21, 1314–1325 (2010)

  41. Zhu, Q., Cao, J.: \(p\)th moment exponential synchronization for stochastic delayed Cohen–Grossberg neural networks with Markovian switching. Nonlinear Dyn. 67(1), 829–845 (2012)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Acknowledgments

This work of H. Shen was supported by the National Natural Science Foundation of China under grant 61304066,61104007,61304072, the Natural Science Foundation of Anhui Province under Grant 1308085QF119, the Key Foundation of Natural Science for Colleges and Universities in Anhui province under grant KJ2012A049. Also, this research of J.H. Park was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (2013R1A1A2A10005201). Dr. J.H. Park gives special thanks to his friend, Dr. M.H. Seo, for continuous support and encouragement in his work.

Author information

Authors and Affiliations

  1. School of Electrical Engineering and Information, Anhui University of Technology, Ma’anshan, 243002, China

    Hao Shen

  2. Department of Electrical Engineering, Yeungnam University, 280 Daehak-Ro, Kyongsan, 712-749, Republic of Korea

    Hao Shen & Ju H. Park

  3. National Laboratory of Industrial Control Technology, Institute of Cyber-Systems and Control, Zhejiang University, Hangzhou , 310027, Zhejiang, China

    Zheng-Guang Wu

Authors
  1. Hao Shen
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ju H. Park
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Zheng-Guang Wu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ju H. Park.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Shen, H., Park, J.H. & Wu, ZG. Finite-time synchronization control for uncertain Markov jump neural networks with input constraints. Nonlinear Dyn 77, 1709–1720 (2014). https://doi.org/10.1007/s11071-014-1412-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11071-014-1412-3

Keywords

Search

Navigation