Skip to main content
SpringerLink
Log in

Reachable set estimation of multi-agent systems under packet losses and deception attacks

  • Original Research
  • Published:
Journal of Applied Mathematics and Computing Aims and scope Submit manuscript

Abstract

This paper considers the problem of estimating reachable set in leaderless consensus for multi-agent systems with Lipschitz nonlinear dynamics and bounded external disturbances. Initially, a sampled-data control is introduced to address the consensus of nonlinear multi-agent systems vulnerable to deception attacks and packet dropouts, which occur randomly during sampling intervals. Then, aperiodic sampling in various degrees is taken into account in the primary Lyapunov term. Sufficient conditions to guarantee that all the actual states of the multi-agent, starting from the initial state, can be bounded within a given ellipsoid set are established by designing a suitable controller. Moreover, the consensus control design is established as linear matrix inequalities, utilizing a two-sided looped functional and Wirtinger’s inequality-based discontinuous Lyapunov–Krasovskii functional. Finally, the numerical section validates the applicability of the proposed control method.

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
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12

Similar content being viewed by others

References

  1. Olfati-Saber, R.: Flocking for multi-agent dynamic systems: algorithms and theory. IEEE Trans. Autom. Control 51, 401–420 (2006)

    Article  MathSciNet  Google Scholar 

  2. Cao, Y., Yu, W., Ren, W., Chen, G.: An overview of recent progress in the study of distributed multi-agent coordination. IEEE Trans. Industr. Inf. 9(1), 427–438 (2013)

    Article  Google Scholar 

  3. Cheng, Y., Shi, B., Liu, H.: An improved class of fixed-time consensus protocols for multi-agent systems. J. Appl. Math. Comput. 63(1), 439–454 (2020)

    Article  MathSciNet  Google Scholar 

  4. Wang, J., Tang, Z., Ding, D., Feng, J.: Aperiodically intermittent saturation consensus on multi-agent systems with discontinuous dynamics. ISA Trans. 133, 66–74 (2023)

    Article  Google Scholar 

  5. Cao, Y., Sun, Y.: Necessary and sufficient conditions for consensus of third-order discrete-time multi-agent systems in directed networks. J. Appl. Math. Comput. 57(1), 199–210 (2018)

    Article  MathSciNet  Google Scholar 

  6. Zhang, D., Liu, L., Feng, G.: Consensus of heterogeneous linear multiagent systems subject to aperiodic sampled-data and DoS attack. IEEE Trans. Cybern. 49(4), 1501–1511 (2019)

    Article  Google Scholar 

  7. Liu, W., Zhou, S., Qi, Y., Wu, X.: Leaderless consensus of multi-agent systems with Lipschitz nonlinear dynamics and switching topologies. Neurocomputing 173, 1322–1329 (2016)

    Article  Google Scholar 

  8. He, W., Lv, S., Wang, X., Qian, F.: Leaderless consensus of multi-agent systems via an event-triggered strategy under stochastic sampling. J. Frankl. Inst. 356, 6502–6524 (2019)

    Article  MathSciNet  Google Scholar 

  9. Rehan, M., Tufail, M., Ahmed, S.: Leaderless consensus control of nonlinear multi-agent systems under directed topologies subject to input saturation using adaptive event-triggered mechanism. J. Frankl. Inst. 358, 6217–6239 (2021)

    Article  MathSciNet  Google Scholar 

  10. Parivallal, A., Sakthivel, R., Wang, C.: Guaranteed cost leaderless consensus for uncertain Markov jumping multi-agent systems. J. Exp. Theor. Artif. Intell. 35, 257–273 (2023)

    Article  Google Scholar 

  11. Wu, Y., Wang, Y., Gunasekaran, N., Vadivel, R.: Almost sure consensus of multi-agent systems: an intermittent noise. IEEE Trans. Circuits Syst. II Express Briefs 69(6), 2897–2901 (2022)

    Google Scholar 

  12. Zhai, S., Wang, X., Zheng, W.X.: Leaderless cluster consensus of second-order general nonlinear multiagent systems under directed topology. IEEE Trans. Circuits Syst. I Regul. Pap. 70(10), 4080–4091 (2023)

    Article  Google Scholar 

  13. Lam, J., Zhang, B., Chen, Y., Xu, S.: Reachable set estimation for discrete-time linear systems with time delays. Int. J. Robust Nonlinear Control 25, 269–281 (2015)

    Article  MathSciNet  Google Scholar 

  14. Visakamoorthi, B., Subramanian, K., Muthukumar, P., Yu, S.S., Trinh, H., Lee, T.H.: Reachable set estimation and \(H_\infty \) performance for delayed fuzzy multi-agent systems under false data injection attacks. IET Control Theory Appl. (2023). https://doi.org/10.1049/cth2.12606

    Article  Google Scholar 

  15. Jiang, X., Xia, G., Feng, Z., Zheng, W.X., Su, R.: Reachable set estimation of multi-agent systems: an approximate consensus perspective. IEEE Trans. Control Netw. Syst. 11(1), 353–363 (2024)

    Article  Google Scholar 

  16. Sheng, Y., Shen, Y.: Improved reachable set bounding for linear time-delay systems with disturbances. J. Frankl. Inst. 353, 2708–2721 (2016)

    Article  MathSciNet  Google Scholar 

  17. Li, Y., He, Y., Lin, W.J., Wu, M.: Reachable set estimation for singular systems via state decomposition method. J. Frankl. Inst. 357, 7327–7342 (2020)

    Article  MathSciNet  Google Scholar 

  18. Lin, W.J., He, Y., Wu, M., Liu, Q.: Reachable set estimation for Markovian jump neural networks with time-varying delay. Neural Netw. 108, 527–532 (2018)

    Article  Google Scholar 

  19. Hu, W., Huang, W., Huang, Y., Chen, S., Wu, A.G.: On reachable set estimation of multi-agent systems. Neurocomputing 401, 69–77 (2020)

    Article  Google Scholar 

  20. Vadivel, R., Njitacke, Z.T., Shanmugam, L., Hammachukiattikul, P., Gunasekaran, N.: Dynamical analysis and reachable set estimation of T-S fuzzy system with permanent magnet synchronous motor. Commun. Nonlinear Sci. Numer. Simul. 125, 107407 (2023)

    Article  MathSciNet  Google Scholar 

  21. Huang, W., Tian, B., Chen, Y., Wang, J.: Reachable set estimation of multi-agent systems with semi-Markov switching topologies and time-delay. J. Frankl. Inst. 360, 7415–7437 (2023)

    Article  MathSciNet  Google Scholar 

  22. Fan, C., Lam, J., Lu, X., Liu, J.J., Wang, X., Kwok, K.W.: Reachable set-based consensus of positive multiagent systems. IEEE Trans. Syst. Man Cybern. Syst. 54(4), 2320–2330 (2024)

    Article  Google Scholar 

  23. Wu, Y., Ma, H., Chen, M., Li, H.: Observer-based fixed-time adaptive fuzzy bipartite containment control for multiagent systems with unknown hysteresis. IEEE Trans. Fuzzy Syst. 30, 1302–1312 (2022)

    Article  Google Scholar 

  24. Liu, Z., Huang, H., Park, J.H., Huang, J., Wang, X., Lv, M.: Adaptive fuzzy control for unknown nonlinear multi-agent systems with switching directed communication topologies. IEEE Trans. Fuzzy Syst. 31, 2487–2494 (2023)

    Article  Google Scholar 

  25. Zhang, C., Zhang, C., Zhang, X., Liang, Y.: Sampling-based event-triggered control for cluster synchronization in two-layer nonlinear networks. J. Appl. Math. Comput. 69(5), 3969–3986 (2023)

    Article  MathSciNet  Google Scholar 

  26. Liu, Y., Li, J., Fang, F., Park, J.H.: Further studies on sampled-data consensus of multi-agent systems with communication delays. IEEE Trans. Signal Inf. Process. Over Netw. 8, 920–931 (2022)

    Article  MathSciNet  Google Scholar 

  27. Saravanakumar, R., Amini, A., Datta, R., Cao, Y.: Reliable memory sampled-data consensus of multi-agent systems with nonlinear actuator faults. IEEE Trans. Circuits Syst. II Express Briefs 69(4), 2201–2205 (2021)

    Google Scholar 

  28. Zhao, G., Hua, C., Liu, S.: Sampled-data dynamic output feedback consensus control of multi-agent systems. IEEE Trans. Netw. Sci. Eng. 9(5), 3292–3301 (2022)

    Article  MathSciNet  Google Scholar 

  29. Wang, J., He, W., Fu, J., Wang, Y., Sun, J.: Sampled-data consensus control of nonlinear multi-agent systems with Markovian switching topologies based on extended looped functional. IEEE Trans. Circuits Syst. II Express Briefs 71(1), 251–255 (2024)

    Google Scholar 

  30. Stephen, A., Karthikeyan, R., Sowmiya, C., Raja, R., Agarwal, R.P.: Sampled-data controller scheme for multi-agent systems and its application to circuit network. Neural Netw. 170, 506–520 (2024)

    Article  Google Scholar 

  31. Zhang, W., Tang, Y., Huang, T., Kurths, J.: Sampled-data consensus of linear multi-agent systems with packet losses. IEEE Trans. Neural Netw. Learn. Syst. 28, 2516–2527 (2017)

    Article  MathSciNet  Google Scholar 

  32. Zhao, G., Hua, C.: Sampled-data leaderless and leader-following consensus of multiagent systems under nonidentical packet losses. IEEE Trans. Netw. Sci. Eng. 9, 795–806 (2022)

    Article  MathSciNet  Google Scholar 

  33. Cui, Y., Liu, Y., Zhang, W., Alsaadi, F.E.: Sampled-based consensus for nonlinear multiagent systems with deception attacks: the decoupled method. IEEE Trans. Syst. Man Cybern. Syst. 51, 561–573 (2018)

    Article  Google Scholar 

  34. Jeong, J., Lim, Y., Parivallal, A.: An asymmetric Lyapunov–Krasovskii functional approach for event-triggered consensus of multi-agent systems with deception attacks. Appl. Math. Comput. 439, 127584 (2023)

    MathSciNet  Google Scholar 

  35. Sheng, Z., Xu, S.: A sampled-data control method related to time for Takagi–Sugeno fuzzy systems via novel sampling-dependent functional approach. IEEE Trans. Fuzzy Syst. 32(2), 460–469 (2024)

    Article  MathSciNet  Google Scholar 

  36. Zhang, R., Zeng, D., Park, J.H., Liu, Y., Zhong, S.: A new approach to stabilization of chaotic systems with nonfragile fuzzy proportional retarded sampled-data control. IEEE Trans. Cybern. 49, 3218–3229 (2019)

    Article  Google Scholar 

  37. Zeng, H.B., Teo, K.L., He, Y.: A new looped-functional for stability analysis of sampled-data systems. Automatica 82, 328–331 (2017)

    Article  MathSciNet  Google Scholar 

  38. Shanmugam, L., Joo, Y.H.: Further stability and stabilization condition for sampled-data control systems via looped-functional method. IEEE Trans. Circuits Syst. II Express Briefs 68, 301–305 (2021)

    Google Scholar 

Download references

Acknowledgements

The first author in this article was supported by the University Grants Commission (UGC) under the scheme of Savitribai Jyotirao Phule Single Girl Child Fellowship (SJSGC) 2022-2023, UGC Award Letter - F. No. 82-7/2022(SA-III) dated 07th February 2023 and UGC-Ref.No. UGCES-22-OB-TAMF-SJSGC-2920.

Author information

Authors and Affiliations

  1. Department of Mathematics, The Gandhigram Rural Institute (Deemed to be University), Gandhigram, Tamil Nadu, 624 302, India

    V. M. Janani & P. Muthukumar

  2. School of Electronic and Electrical Engineering, Kyungpook National University, Daegu, 41566, South Korea

    B. Visakamoorthi & Sung-ho Hur

Authors
  1. V. M. Janani
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. B. Visakamoorthi
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. P. Muthukumar
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Sung-ho Hur
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

V. M. Janani: Conceptualization, Methodology, Software, Writing - original draft. B. Visakamoorthi: Conceptualization, Methodology, Software, Writing - review & editing. P. Muthukumar: Conceptualization, Supervision, Writing - original draft, Writing - review & editing. S. Hur: Validation, Investigation, Formal analysis, Writing - review & editing.

Corresponding author

Correspondence to P. Muthukumar.

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

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Janani, V.M., Visakamoorthi, B., Muthukumar, P. et al. Reachable set estimation of multi-agent systems under packet losses and deception attacks. J. Appl. Math. Comput. (2024). https://doi.org/10.1007/s12190-024-02111-6

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s12190-024-02111-6

Keywords

Mathematics Subject Classification

Search

Navigation