Skip to main content

Advertisement

Springer Nature Link
Log in

Stabilization of stochastic delayed networks with Markovian switching via intermittent control: an averaging technique

  • Original Article
  • Published:
Neural Computing and Applications Aims and scope Submit manuscript

Abstract

This paper considers the stabilization of stochastic delayed networks with Markovian switching via aperiodically intermittent control (AIC). The concepts of average control ratio and average control period are proposed to characterize the distributions of control and rest intervals of AIC. It should be noted that the averaging technique used here is more general and less restrictive than the quasi-periodicity condition and minimum control ratio condition used in previous works. Then two kinds of stabilization criteria are obtained: (1) the upper bound of time delay should be less than the average control width; (2) the upper bound of time delay has no relationship with the average control width. Finally, the results are applied to studying the stabilization of coupled stochastic neural networks with Markovian switching via AIC. Numerical simulations are provided to show the effectiveness of obtained results.

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

Similar content being viewed by others

Explore related subjects

Discover the latest articles and news from researchers in related subjects, suggested using machine learning.

References

  1. Boccaletti S, Latora V, Moreno Y, Chavez M, Hwang DU (2006) Complex networks: structure and dynamics. Phys Rep Rev Sec Phys Lett 424(4–5):175–308

    MathSciNet  MATH  Google Scholar 

  2. Chen WH, Zhong J, Zheng WX (2016) Delay-independent stabilization of a class of time-delay systems via periodically intermittent control. Automatica 71:89–97

    MathSciNet  MATH  Google Scholar 

  3. Cheng L, Chen X, Qiu J, Lu J, Cao J (2018) Aperiodically intermittent control for synchronization of switched complex networks with unstable modes via matrix omega-measure approach. Nonlinear Dyn 92(3):1091–1102

    MATH  Google Scholar 

  4. Ciuchi S, De Pasquale F, Spagnolo B (1996) Self-regulation mechanism of an ecosystem in a non-gaussian fluctuation regime. Phys Rev E 54(1):706

    Google Scholar 

  5. De Persis C, Tesi P (2015) Input-to-state stabilizing control under denial-of-service. IEEE Trans Autom Control 60(11):2930–2944

    MathSciNet  MATH  Google Scholar 

  6. De Persis C, Tesi P (2016) Networked control of nonlinear systems under denial-of-service. Syst Control Lett 96:124–131

    MathSciNet  MATH  Google Scholar 

  7. Ding S, Wang Z, Zhang H (2019) Quasi-synchronization of delayed memristive neural networks via region-partitioning-dependent intermittent control. IEEE Trans Cybern 49(12):4066–4077

    Google Scholar 

  8. Dong Y, Guo L, Hao J (2020) Robust exponential stabilization for uncertain neutral neural networks with interval time-varying delays by periodically intermittent control. Neural Comput Appl 32(7):2651–2664

    Google Scholar 

  9. Falci G, La Cognata A, Berritta M, D’Arrigo A, Paladino E, Spagnolo B (2013) Design of a lambda system for population transfer in superconducting nanocircuits. Phys Rev B 87(21):214515

  10. Fiasconaro A, Valenti D, Spagnolo B (2003) Role of the initial conditions on the enhancement of the escape time in static and fluctuating potentials. Phys A 325(1–2):136–143

    MathSciNet  MATH  Google Scholar 

  11. Gan Q (2017) Exponential synchronization of generalized neural networks with mixed time-varying delays and reaction–diffusion terms via aperiodically intermittent control. Chaos 27(1):013113

    MathSciNet  MATH  Google Scholar 

  12. Gawthrop PJ, Wang L (2009) Event-driven intermittent control. Int J Control 82(12):2235–2248

    MathSciNet  MATH  Google Scholar 

  13. Guo Y, Li X, Wang P (2021) Improved results on synchronization of stochastic delayed networks under aperiodically intermittent control. J Franklin Inst 358(9):4950–4971

    MathSciNet  MATH  Google Scholar 

  14. Guo Y, Liu Y, Xu Y (2019) Synchronized stationary distribution of stochastic coupled systems based on graph theory. Math Methods Appl Sci 42(13):4444–4455

    MathSciNet  MATH  Google Scholar 

  15. Guo Y, Qian Y, Wang P (2021) Leader-following consensus of delayed multi-agent systems with aperiodically intermittent communications. Neurocomputing 466:49–57

    Google Scholar 

  16. Halanay A (1966) Differential equations: stability, oscillations, time lags. Academic, San Diego

    MATH  Google Scholar 

  17. Huang L, Mao X (2009) On input-to-state stability of stochastic retarded systems with Markovian switching. IEEE Trans Autom Control 54(8):1898–1902

    MathSciNet  MATH  Google Scholar 

  18. Li MY, Shuai Z (2010) Global-stability problem for coupled systems of differential equations on networks. J Differ Equ 248(1):1–20

    MathSciNet  MATH  Google Scholar 

  19. Li S, Lv C, Ding X (2020) Synchronization of stochastic hybrid coupled systems with multi-weights and mixed delays via aperiodically adaptive intermittent control. Nonlinear Anal Hybrid Syst 35:100819

    MathSciNet  MATH  Google Scholar 

  20. Li S, Ren X, Su H (2020) Stabilization and destabilization of nonlinear systems via aperiodically intermittent stochastic noises: average techniques and scalar functions. Chaos 30(3):033134

    MathSciNet  MATH  Google Scholar 

  21. Li W, Su H, Wang K (2011) Global stability analysis for stochastic coupled systems on networks. Automatica 47(1):215–220

    MathSciNet  MATH  Google Scholar 

  22. Liberzon D, Morse AS (1999) Basic problems in stability and design of switched systems. IEEE Control Syst Mag 19(5):59–70

    MATH  Google Scholar 

  23. Liu B, Lu W, Chen T (2014) New criterion of asymptotic stability for delay systems with time-varying structures and delays. Neural Netw 54:103–111

    MATH  Google Scholar 

  24. Liu B, Yang M, Liu T, Hill DJ (2021) Stabilization to exponential input-to-state stability via aperiodic intermittent control. IEEE Trans Autom Control 66(6):2913–2919 

    MathSciNet  MATH  Google Scholar 

  25. Liu D, Ye D (2020) Pinning-observer-based secure synchronization control for complex dynamical networks subject to dos attacks. IEEE Trans Circuits Syst I-Regul Pap 67(12):5394–5404

    MathSciNet  MATH  Google Scholar 

  26. Liu X, Chen T (2015) Synchronization of complex networks via aperiodically intermittent pinning control. IEEE Trans Autom Control 60(12):3316–3321

    MathSciNet  MATH  Google Scholar 

  27. Liu X, Chen T (2015) Synchronization of linearly coupled networks with delays via aperiodically intermittent pinning control. IEEE Trans Neural Netw Learn Syst 26(10):2396–2407

    MathSciNet  Google Scholar 

  28. Liu X, Chen T (2015) Synchronization of nonlinear coupled networks via aperiodically intermittent pinning control. IEEE Trans Neural Netw Learn Syst 26(1):113–126

    MathSciNet  Google Scholar 

  29. Mao X (2007) Stochastic differential equations and applications. Elsevier, London

    MATH  Google Scholar 

  30. Mao X, Yuan C (2006) Stochastic differential equations with Markovian switching. Imperial college press, New York

    MATH  Google Scholar 

  31. Mwanandiye ES, Wu B, Jia Q (2020) Synchronization of delayed dynamical networks with multi-links via intermittent pinning control. Neural Comput Appl 32:11277–11284

    Google Scholar 

  32. Rao H, Xu Y, Peng H, Lu R, Su C (2020) Quasi-synchronization of time delay Markovian jump neural networks with impulsive-driven transmission and fading channels. IEEE Trans Cybern 50(9):4121–4131

    Google Scholar 

  33. Sakthivel R, Wang C, Santra S, Kaviarasan B (2018) Non-fragile reliable sampled-data controller for nonlinear switched time-varying systems. Nonlinear Anal Hybrid Syst 27:62–76

    MathSciNet  MATH  Google Scholar 

  34. Spagnolo B, Dubkov A, Agudov N (2004) Enhancement of stability in randomly switching potential with metastable state. Eur Phys J B 40(3):273–281

    Google Scholar 

  35. Spagnolo B, La Barbera A (2002) Role of the noise on the transient dynamics of an ecosystem of interacting species. Phys A 315(1–2):114–124

    MATH  Google Scholar 

  36. Spagnolo B, Valenti D (2008) Volatility effects on the escape time in financial market models. Int J Bifurcat Chaos 18(09):2775–2786

    MATH  Google Scholar 

  37. Strogatz SH (2001) Exploring complex networks. Nature 410(6825):268–276

    MATH  Google Scholar 

  38. Sun XM, Liu GP, Rees D, Wang W (2008) Stability of systems with controller failure and time-varying delay. IEEE Trans Autom Control 53(10):2391–2396

    MathSciNet  MATH  Google Scholar 

  39. Wang C (2014) Existence and exponential stability of piecewise mean-square almost periodic solutions for impulsive stochastic Nicholsons blowflies model on time scales. Appl Math Comput 248:101–112

    MathSciNet  MATH  Google Scholar 

  40. Wang C, Agarwal RP (2016) Almost periodic dynamics for impulsive delay neural networks of a general type on almost periodic time scales. Commun Nonlinear Sci Numer Simul 36:238–251

    MathSciNet  MATH  Google Scholar 

  41. Wang C, Agarwal RP (2016) A classification of time scales and analysis of the general delays on time scales with applications. Math Method Appl Sci 39(6):1568–1590

    MathSciNet  MATH  Google Scholar 

  42. Wang C, Agarwal RP (2017) Almost periodic solution for a new type of neutral impulsive stochastic Lasota–Wazewska timescale model. Appl Math Lett 70:58–65

    MathSciNet  MATH  Google Scholar 

  43. Wang C, Agarwal RP, Rathinasamy S (2018) Almost periodic oscillations for delay impulsive stochastic Nicholsons blowflies timescale model. Comput Appl Math 37(3):3005–3026

    MathSciNet  MATH  Google Scholar 

  44. Wang P, Feng J, Su H (2019) Stabilization of stochastic delayed networks with Markovian switching and hybrid nonlinear coupling via aperiodically intermittent control. Nonlinear Anal Hybrid Syst 32:115–130

    MathSciNet  MATH  Google Scholar 

  45. Wang P, Jin W, Su H (2018) Synchronization of coupled stochastic complex-valued dynamical networks with time-varying delays via aperiodically intermittent adaptive control. Chaos 28(4):043114

    MathSciNet  MATH  Google Scholar 

  46. Wang P, Li S, Su H (2021) Aperiodically intermittent stabilization for complex-valued hybrid stochastic delayed systems: An average technique. Commun Nonlinear Sci Numer Simul 101:105852

    MathSciNet  MATH  Google Scholar 

  47. Wang P, Wang R, Su H (2021) Stability of time-varying hybrid stochastic delayed systems with application to aperiodically intermittent stabilization. IEEE Trans Cybern. https://doi.org/10.1109/TCYB.2021.3052042

    Article  Google Scholar 

  48. Wang P, Wang W, Su H, Feng J (2020) Stability of stochastic discrete-time piecewise homogeneous Markov jump systems with time delay and impulsive effects. Nonlinear Anal Hybrid Syst 38:100916

    MathSciNet  MATH  Google Scholar 

  49. Wang P, Zhang B, Su H (2019) Stabilization of stochastic uncertain complex-valued delayed networks via aperiodically intermittent nonlinear control. IEEE Trans Syst Man Cybern Syst 49(3):649–662

    Google Scholar 

  50. Wang Y, Zheng WX, Zhang H (2017) Dynamic event-based control of nonlinear stochastic systems. IEEE Trans Autom Control 62(12):6544–6551

    MathSciNet  MATH  Google Scholar 

  51. Xiang W, Zhai G, Briat C (2015) Stability analysis for LTI control systems with controller failures and its application in failure tolerant control. IEEE Trans Autom Control 61(3):811–816

    MathSciNet  MATH  Google Scholar 

  52. Xiao Q, Lewis FL, Zeng Z (2019) Containment control for multiagent systems under two intermittent control schemes. IEEE Trans Autom Control 64(3):1236–1243

    MathSciNet  MATH  Google Scholar 

  53. Xu Y, Gao S, Li W (2020) Exponential stability of fractional-order complex multi-links networks with aperiodically intermittent control. IEEE Trans Neural Netw Learn Syst. https://doi.org/10.1109/TNNLS.2020.3016672

    Article  Google Scholar 

  54. Zhai Y, Wang P, Su H (2021) Stabilization of stochastic complex networks with delays based on completely aperiodically intermittent control. Nonlinear Anal Hybrid Syst 42:101074

    MathSciNet  MATH  Google Scholar 

Download references

Acknowledgements

This work was supported by Shandong Province Natural Science Foundation (Nos. ZR2017MA008, ZR2017BA007 and ZR2018MA023); the Project of Shandong Province Higher Educational Science and Technology Program of China (Nos. J18KA218 and J16LI09), and Shandong Province Innovation Training Project for College Students (No. S201910429099).

Author information

Authors and Affiliations

  1. Department of Mathematics, Qingdao University of Technology, Qingdao, 266520, People’s Republic of China

    Ying Guo

  2. Shenzhen Key Laboratory of Advanced Machine Learning and Application, College of Mathematics and Statistics, Shenzhen University, Shenzhen, 518060, People’s Republic of China

    Jiqiang Feng

Authors
  1. Ying Guo
    View author publications

    You can also search for this author inPubMed Google Scholar

  2. Jiqiang Feng
    View author publications

    You can also search for this author inPubMed Google Scholar

Corresponding author

Correspondence to Jiqiang Feng.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Additional information

Publisher's Note

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

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Guo, Y., Feng, J. Stabilization of stochastic delayed networks with Markovian switching via intermittent control: an averaging technique. Neural Comput & Applic 34, 4487–4499 (2022). https://doi.org/10.1007/s00521-021-06603-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00521-021-06603-5

Keywords