Location via proxy:   [ UP ]  
[Report a bug]   [Manage cookies]                
Skip to main content

Advertisement

Springer Nature Link
Log in

Mixed Time-Delayed Nonlinear Multi-agent Dynamic Systems for Asymptotic Stability and Non-fragile Synchronization Criteria

  • Published:
Neural Processing Letters Aims and scope Submit manuscript

Abstract

In this manuscript, we are concerned with mixed (discrete and distributed) time-delayed both stability and non-fragile synchronization of nonlinear multi-agent systems (MASs). We shall find stability criteria for the unknown parameter value of nonlinear multi-agent systems using the Lyapunov–Krasovskii functions, Lemma, the analytical techniques, the Kronecker product, and the general specifications for asymptotic stability of selected MASs are obtained. Moreover, criteria for the synchronization of leader–follower unknown parameter value of nonlinear MASs with non-fragile controllers are discussed. At last, we provide two numerical calculations along with the computational simulations to check the validity of the theoretical findings reported in this manuscript.

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
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12

Similar content being viewed by others

Explore related subjects

Discover the latest articles, news and stories from top researchers in related subjects.

References

  1. Agha G (1986) A model of concurrent computation in distributed systems, ACTORS. MIT Press, Cambridge

    Book  Google Scholar 

  2. Ali MS, Usha M, Zhu QX, Shanmugam S (2020) Synchronization analysis for stochastic T–S fuzzy complex networks with Markovian jumping parameters and mixed time-varying delays via impulsive control. Math Probl Eng 2020:27

    Article  MathSciNet  Google Scholar 

  3. Beard RW, McLain TW, Goodrich MA, Anderson EP (2002) Coordinated target assignment and intercept for unmanned-air-vehicles. IEEE Trans Robot Autom 18(6):911–922

    Article  Google Scholar 

  4. Boyd S, Ghaoui L, Feron E, Balakrishnan V (1994) Linear matrix inequalities in system and control theory. SIAM, Philadelphia

    Book  Google Scholar 

  5. Fax A, Murray RM (2004) Information flow and cooperative control of vehicle formations. IEEE Trans Autom Control 49(9):1465–1476

    Article  MathSciNet  Google Scholar 

  6. Gu K (2000) An integral inequality in the stability problem of time delay systems. In: Proceedings of the 39th IEEE conference on decision control, pp 2805–2810

  7. Guo L, Pan H, Nian X (2016) Adaptive pinning control of cluster synchronization in complex networks with Lurie-type nonlinear dynamics. Neurocomputing 182(19):294–303

    Article  Google Scholar 

  8. He W, Zhang B, Han QL, Qian F, Kurths J, Cao J (2017) Leader-Following consensus of nonlinear multiagent systems with stochastic sampling. IEEE Trans Cybernet 47(2):327–338

    Google Scholar 

  9. Holland JH (1975) Adaptation in natural and artificial systems, 2nd ed. MIT Press, Cambridge, 1992 (1st ed)

  10. Hu C, Jiang H (2015) Pinning synchronization for directed networks with node balance via adaptive intermittent control. Nonlinear Dyn 80(1–2):295–307

    Article  Google Scholar 

  11. Hu JQ, Yu J, Cao JD (2016) Distributed containment control for nonlinear multi-agent systems with time-delayed protocol. Asian J Control 18(2):747–756

    Article  MathSciNet  Google Scholar 

  12. Hu J, Cao J, Yuan K, Hayat T (2016) Cooperative tracking for nonlinear multi-agent systems with hybrid time-delayed protocol. Neurocomputing 171:171–178

    Article  Google Scholar 

  13. Insperger T, Stépán G (2011) Semi-discretization for time-delay systems: stability and engineering applications. Springer, p 178

  14. Jia Q, Tang WKS, Halang WA (2011) Leader following of nonlinear agents with switching connective network and coupling delay. IEEE Trans Circuits Syst I Regul Pap 58(10):2508–2519

    Article  MathSciNet  Google Scholar 

  15. Jiang X, Xia G, Feng Z, Li T (2020) Non-fragile \(H_{\infty }\) consensus tracking of nonlinear multi-agent systems with switching topologies and transmission delay via sampled-data control. Inf Sci 509:210–226

    Article  MathSciNet  Google Scholar 

  16. Kaviarasan B, Kwon OM, Park MJ, Sakthivel R (2021) Stochastic faulty estimator-based non-fragile tracking controller for multi-agent systems with communication delay. Appl Math Comput 392:125704

    MathSciNet  MATH  Google Scholar 

  17. Kong F, Zhu Q (2021) New fixed-time synchronization control of discontinuous inertial neural networks via indefinite Lyapunov–Krasovskii functional method. Int J Robust Nonlinear Control 31(2):471–495

    Article  MathSciNet  Google Scholar 

  18. Kwon OM, Park MJ, Park JuH, Lee SM, Cha EJ (2014) On stability analysis for neural networks with interval time-varying delays via some new augmented Lyapunov–Krasovskii functional. Commun Nonlinear Sci Numer Simul 19(9):3184–3201

    Article  MathSciNet  Google Scholar 

  19. Li H (2016) Leader-following consensus of nonlinear multi-agent systems with mixed delays and uncertain parameters via adaptive pinning intermittent control. Nonlinear Anal Hybrid Syst 22:202–214

    Article  MathSciNet  Google Scholar 

  20. Li W, Zhou H, Liu ZW, Qin Y, Wang Z (2016) Impulsive coordination of nonlinear multi-agent systems with multiple leaders and stochastic disturbance. Neurocomputing 171:73–81

    Article  Google Scholar 

  21. Li Z, Duan Z, Chen G, Huang L (2010) Consensus of multiagent systems and synchronization of complex networks: a unified viewpoint. IEEE Trans Circuits Syst I Regul Pap 57(1):213–224

    Article  MathSciNet  Google Scholar 

  22. Meng Z, Ren W, Cao Y, You Z (2011) Leaderless and leader-following consensus with communication and input delays under a directed network topology. IEEE Trans Syst Man Cybern B Cybern 41(1):75–88

    Article  Google Scholar 

  23. Moulay E, Dambrine M, Yeganefar N (2008) Finite-time stability and stabilization of time-delay systems. Syst Control Lett 57(7):561–566

    Article  MathSciNet  Google Scholar 

  24. Ni W, Cheng D (2010) Leader-following consensus of multi-agent systems under fixed and switching topologies. Syst Control Lett 59(3–4):209–217

    Article  MathSciNet  Google Scholar 

  25. Pecora L, Carrol T (1990) Synchronization in chaotic systems. Phys Rev Lett 64:821–824

    Article  MathSciNet  Google Scholar 

  26. Qin W, Liu ZX, Chen ZQ (2015) Impulsive observer-based consensus control for multi-agent systems with time delay. Int J Control 88(9):1789–1804

    Article  MathSciNet  Google Scholar 

  27. Rakkiyappan R, Kaviarasan B, Cao J (2015) Leader-following consensus of multi-agent systems via sampled data control with randomly missing data. Neurocomputing 161:132–147

    Article  Google Scholar 

  28. Ren F, Cao J (2008) Asymptotic and robust stability of genetic regulatory networks with time-varying delays. Neurocomputing 71(4):834–842

    Article  Google Scholar 

  29. Ren W, Sorensen N (2008) Distributed coordination architecture for multi-robot formation control. Robot Autonom Syst 56(4):324–333

    Article  Google Scholar 

  30. Saravanakumar T, Muoi NH, Zhu Q (2020) Finite-time sampled-data control of switched stochastic model with non-deterministic actuator faults and saturation nonlinearity. J Frankl Inst 357(18):13637–13665

    Article  MathSciNet  Google Scholar 

  31. Senthil R, Raja R, Samidurai R, Cao J, Li X (2018) Passivity analysis of uncertain stochastic neural network with leakage and distributed delays under impulsive perturbations. Kybernetika 54(1):3–29

    MathSciNet  MATH  Google Scholar 

  32. Song R, Wang B, Zhu Q (2021) Delay-dependent stability of nonlinear hybrid neutral stochastic differential equations with multiple delays. Int J Robust Nonlinear Control 31(1):250–267

    Article  MathSciNet  Google Scholar 

  33. Su H, Rong Z, Chen MZQ, Wang X, Chen G, Wang H (2013) Decentralized adaptive pinning control for cluster synchronization of complex dynamical networks. IEEE Trans Cybern 43(1):394–399

    Article  Google Scholar 

  34. Subramanian K, Muthukumar P, Hoon Joo Y (2019) Leader-following consensus of nonlinear multi-agent systems via reliable control with time-varying communication delay. Int J Control Autom Syst 17:1–9

    Article  Google Scholar 

  35. Syed Ali M, Agalya R, Shekher V, Hoon Joo Y (2020) Non-fragile sampled data control for stabilization of non-linear multi-agent system with additive time varying delays, Markovian jump and uncertain parameters. Nonlinear Anal Hybrid Syst 36:100830

    Article  MathSciNet  Google Scholar 

  36. Wang CY, Zuo ZY, Lin ZL, Ding ZT (2015) Consensus control of a class of Lipschitz nonlinear systems with input delay. IEEE Trans Circuits Syst I Regul Pap 62(11):2730–2738

    Article  MathSciNet  Google Scholar 

  37. Wang Y, Cao J, Wang H, Alsaedi A, Alsaadi FU (2018) Exponential consensus for nonlinear multi-agent system with communication and input delays via hybrid controller. Asian J Control 20(5):1–12

    MathSciNet  MATH  Google Scholar 

  38. Wang YL, Cao JD, Hu JQ (2014) Pinning consensus for multi-agent systems with non-linear dynamics and time-varying delay under directed switching topology. IET Control Theory Appl 8(17):1931–1939

    Article  Google Scholar 

  39. Xi Q, Si J (2014) Existence, uniqueness and stability analysis of impulsive neural networks with mixed time delays. Hindawi Publishing Corporation, p 14

  40. Zheng M, Li L, Peng H, Xiao J, Yang Y, Zhao H (2017) Finite-time stability analysis for neutral-type neural networks with hybrid time-varying delays without using Lyapunov method. Neurocomputing 238:67–75

    Article  Google Scholar 

  41. Zhou B, Liao XF, Huang TW, Chen G (2015) Leader-following exponential consensus of general linear multi-agent systems via event-triggered control with combinational measurements. Appl Math Lett 40(2):35–39

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgements

The article has been written with the joint partial financial support of RUSA-Phase 2.0 grant sanctioned vide letter No.F 24-51/2014-U, Policy (TN Multi-Gen), Dept. of Edn. Govt. of India, UGC-SAP (DRS-I) vide letter No.F.510/8/DRS-I/2016(SAP-I) and DST (FIST-Phase I) vide letter No.SR/FIST/MS-I/2018-17, the National Science Centre in Poland Grant DEC-2017/25/B/ST7/02888 and J. Alzabut would like to thank Prince Sultan University for supporting this work through research group Nonlinear Analysis Methods in Applied Mathematics (NAMAM) group number RG-DES-2017-01-17.

Author information

Authors and Affiliations

  1. Department of Mathematics, Alagappa University, Karaikudi, 630 004, India

    A. Stephen

  2. Ramanujan Centre for Higher Mathematics, Alagappa University, Karaikudi, 630 004, India

    R. Raja

  3. Department of Mathematics and General Sciences, Prince Sultan University, Riyadh, 12435, Saudi Arabia

    J. Alzabut

  4. Department of Industrial Engineering, OSTİM Technical University, Ankara, 06374, Turkey

    J. Alzabut

  5. School of Mathematics and Statistics, Hunan Normal University, Hunan, 410081, People’s Republic of China

    Quanxin Zhu

  6. Department of Automatic Control and Robotics, Faculty of Automatic Control, Electronics and Computer Science, Silesian University of Technology, Akademicka 16, Gliwice, 44-100, Poland

    M. Niezabitowski

  7. Department of Electronics, Computing and Mathematics, University of Derby, Derby, UK

    O. Bagdasar

Authors
  1. A. Stephen
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. R. Raja
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. J. Alzabut
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Quanxin Zhu
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. M. Niezabitowski
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. O. Bagdasar
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Quanxin Zhu.

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

Stephen, A., Raja, R., Alzabut, J. et al. Mixed Time-Delayed Nonlinear Multi-agent Dynamic Systems for Asymptotic Stability and Non-fragile Synchronization Criteria. Neural Process Lett 54, 43–74 (2022). https://doi.org/10.1007/s11063-021-10619-2

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11063-021-10619-2

Keywords

Search

Navigation