Skip to main content
SpringerLink
Log in

Bipartite consensus for nonlinear time-delay multiagent systems via time-varying gain control method

  • Research Article
  • Published:
Control Theory and Technology Aims and scope Submit manuscript

Abstract

The bipartite consensus problem is addressed for a class of nonlinear time-delay multiagent systems in this paper. Therein, the uncertain nonlinear dynamics of all agents satisfy a Lipschitz growth condition with unknown constants, and part of the state information cannot be measured. In this case, a time-varying gain compensator is constructed, which only utilizes the output information of the follower and its neighbors. Subsequently, a distributed output feedback control protocol is proposed on the basis of the compensator. According to Lyapunov stability theory, it is proved that the bipartite consensus can be guaranteed by means of the designed control protocol. Different from the existing literature, this paper studies the leader–follower consensus problem under a weaker connectivity condition, i.e., the signed directed graph is structurally balanced and contains a directed spanning tree. Two simulation examples are carried out to show the feasibility of the proposed control strategy.

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

Similar content being viewed by others

References

  1. You, X., Hua, C., & Guan, X. (2018). Event-triggered leader-following consensus for nonlinear multiagent systems subject to actuator saturation using dynamic output feedback method. IEEE Transactions on Automatic Control, 63(12), 4391–4396.

    Article  MathSciNet  MATH  Google Scholar 

  2. Zhao, M., Peng, C., & Tian, E. (2021). Finite-time and fixed-time bipartite consensus tracking of multi-agent systems with weighted antagonistic interactions. IEEE Transactions on Circuits and Systems I: Regular Papers, 68(1), 426–433.

    Article  MathSciNet  Google Scholar 

  3. Zhang, W., Yu, Z., & Li, S. (2021). Adaptive output consensus for heterogeneous nonlinear multi-agent systems with multi-type input constraints under switching-directed topologies. Control Theory and Technology, 19(2), 260–272.

    Article  MathSciNet  MATH  Google Scholar 

  4. Zhang, Y., Mu, C., Zhang, Y., & Feng, Y. (2021). Heuristic dynamic programming-based learning control for discrete-time disturbed multi-agent systems. Control Theory and Technology, 19(3), 339–353.

    Article  MathSciNet  MATH  Google Scholar 

  5. Olfati-Saber, R., & Murray, R. M. (2004). Consensus problems in networks of agents with switching topology and time-delays. IEEE Transactions on Automatic Control, 49(9), 1520–1533.

    Article  MathSciNet  MATH  Google Scholar 

  6. Fan, Y., Feng, G., Wang, Y., & Song, C. (2013). Distributed event-triggered control of multi-agent systems with combinational measurements. Automatica, 49(2), 671–675.

    Article  MathSciNet  MATH  Google Scholar 

  7. Abdessameud, A., & Tayebi, A. (2013). On consensus algorithms design for double integrator dynamics. Automatica, 49(1), 253–260.

    Article  MathSciNet  MATH  Google Scholar 

  8. Dong, Y., & Huang, J. (2013). A leader-following rendezvous problem of double integrator multi-agent systems. Automatica, 49(5), 1386–1391.

    Article  MathSciNet  MATH  Google Scholar 

  9. Yu, W., Chen, G., Ren, W., Kurths, J., & Zheng, W. X. (2011). Distributed higher order consensus protocols in multiagent dynamical systems. IEEE Transactions on Circuits and Systems I: Regular Papers, 58(8), 1924–1932.

    Article  MathSciNet  MATH  Google Scholar 

  10. Tian, B., Zuo, Z., & Wang, H. (2017). Leader-follower fixed-time consensus of multi-agent systems with high-order integrator dynamics. International Journal of Control, 90(7), 1420–1427.

    Article  MathSciNet  MATH  Google Scholar 

  11. Altafini, C. (2013). Consensus problems on networks with antagonistic interactions. IEEE Transactions on Automatic Control, 58(4), 935–946.

    Article  MathSciNet  MATH  Google Scholar 

  12. Hu, H.-X., Liu, A., Xuan, Q., Yu, L., & Xie, G. (2013). Second-order consensus of multi-agent systems in the cooperation-competition network with switching topologies: A time-delayed impulsive control approach. Systems and Control Letters, 62(12), 1125–1135.

    Article  MathSciNet  MATH  Google Scholar 

  13. Valcher, M. E., & Misra, P. (2014). On the consensus and bipartite consensus in high-order multi-agent dynamical systems with antagonistic interactions. Systems and Control Letters, 66(1), 94–103.

    Article  MathSciNet  MATH  Google Scholar 

  14. Zhang, H., & Chen, J. (2017). Bipartite consensus of multi-agent systems over signed graphs: State feedback and output feedback control approaches. International Journal of Robust and Nonlinear Control, 27(1), 3–14.

    Article  MathSciNet  MATH  Google Scholar 

  15. Zheng, S., Ahn, C. K., Shi, P., & Xie, Y. (2021). Prescribed finite-time consensus with severe unknown nonlinearities and mismatched disturbances. Systems and Control Letters, 157, 105047.

    Article  MathSciNet  MATH  Google Scholar 

  16. Li, H., Zhang, X., & Pan, W. (2022). Consensus control of feedforward nonlinear multi-agent systems: A time-varying gain method. Control Theory and Technology, 20(1), 46–53.

    Article  MathSciNet  MATH  Google Scholar 

  17. Zhang, X., Liu, L., & Feng, G. (2015). Leader-follower consensus of time-varying nonlinear multi-agent systems. Automatica, 52, 8–14.

    Article  MathSciNet  MATH  Google Scholar 

  18. Li, K., Hua, C.-C., You, X., & Guan, X.-P. (2020). Output feedback-based consensus control for nonlinear time delay multiagent systems. Automatica, 111, 108669.

    Article  MathSciNet  MATH  Google Scholar 

  19. Li, H., Xia, S., Mu, R., & Zhang, X. (2021). On designing a distributed event-triggered output feedback consensus protocol for nonlinear multiagent systems. International Journal of Robust and Nonlinear Control, 31(15), 7173–7185.

    Article  MathSciNet  Google Scholar 

  20. Li, H., Liu, Q., Feng, G., & Zhang, X. (2021). Leader-follower consensus of nonlinear time-delay multiagent systems: A time-varying gain approach. Automatica, 126, 109444.

    Article  MathSciNet  MATH  Google Scholar 

  21. Duan, Z., Zhang, X., Liu, S., & Wei, A. (2021). \(H_{\infty }\) output feedback control for large-scale nonlinear systems with time delay in both state and input. Control Theory and Technology, 19(3), 384–391.

    Article  MathSciNet  MATH  Google Scholar 

  22. Hua, C.-C., Li, K., & Guan, X.-P. (2019). Semi-global/global output consensus for nonlinear multiagent systems with time delays. Automatica, 103, 480–489.

    Article  MathSciNet  MATH  Google Scholar 

  23. Li, Y., Park, J. H., Hua, C., & Liu, G. (2021). Distributed adaptive output feedback containment control for time-delay nonlinear multiagent systems. Automatica, 127, 109545.

    Article  MathSciNet  MATH  Google Scholar 

  24. Li, K., Hua, C., You, X., & Ahn, C. K. (2021). Output feedback predefined-time bipartite consensus control for high-order nonlinear multiagent systems. IEEE Transactions on Circuits and Systems I: Regular Papers, 68(7), 9415871.

    Article  Google Scholar 

  25. Ning, B., Han, Q.-L., & Zuo, Z. (2021). Bipartite consensus tracking for second-order multiagent systems: A Time-varying function-based preset-time approach. IEEE Transactions on Automatic Control, 66(6), 2739–2745.

    Article  MathSciNet  MATH  Google Scholar 

  26. Wen, G., Zhao, Y., Duan, Z., Yu, W., & Chen, G. (2016). Containment of higher-order multi-leader multi-agent systems: A dynamic output approach. IEEE Transactions on Automatic Control, 61(4), 1135–1140.

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Control Science and Engineering, Shandong University, Jinan 250061, Shandong, China

    Haiou Zhao, Yanan Qi, Yanjie Chang & Xianfu Zhang

Authors
  1. Haiou Zhao
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yanan Qi
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Yanjie Chang
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Xianfu Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Xianfu Zhang.

Additional information

The work was supported by the National Natural Science Foundation of China (Nos. 61973189, 62073190), the Research Fund for the Taishan Scholar Project of Shandong Province of China (No. ts20190905), and the Natural Science Foundation of Shandong Province of China (No. ZR2020ZD25)

Rights and permissions

Springer Nature or its licensor 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

Zhao, H., Qi, Y., Chang, Y. et al. Bipartite consensus for nonlinear time-delay multiagent systems via time-varying gain control method. Control Theory Technol. 20, 504–513 (2022). https://doi.org/10.1007/s11768-022-00112-z

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11768-022-00112-z

Keywords

Search

Navigation