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Consensus control of feedforward nonlinear multi-agent systems: a time-varying gain method

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Abstract

In this paper, the leader–follower consensus of feedforward nonlinear multi-agent systems is achieved by designing the distributed output feedback controllers with a time-varying gain. The agents dynamics are assumed to be in upper triangular structure and satisfy Lipschitz conditions with an unknown constant multiplied by a time-varying function. A time-varying gain, which increases monotonously and tends to infinity, is proposed to construct a compensator for each follower agent. Based on a directed communication topology, the distributed output feedback controller with a time-varying gain is designed for each follower agent by only using the output information of the follower and its neighbors. It is proved by the Lyapunov theorem that the leader–follower consensus of the multi-agent system is achieved by the proposed consensus protocol. The effectiveness of the proposed time-varying gain method is demonstrated by a circuit system.

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References

  1. Ren, W., Beard, R. W., & Atkins, E. M. (2007). Information consensus in multivehicle cooperative control. IEEE Control Systems Magazine, 27(2), 71–82.

    Article  Google Scholar 

  2. Liu, W., & Huang, J. (2017). Adaptive leader-following rendezvous and flocking for a class of uncertain second-order nonlinear multi-agent systems. Control Theory and Technology, 15(4), 354–363.

    Article  MathSciNet  Google Scholar 

  3. Ding, L., Han, Q.-L., Wang, L. Y., & Sindi, E. (2018). Distributed cooperative optimal control of DC microgrids with communication delays. IEEE Transactions on Industrial Informatics, 14(9), 3924–3935.

    Article  Google Scholar 

  4. Fu, J., Wen, G., Yu, W., & Ding, Z. (2018). Finite-time consensus for second-order multi-agent systems with input saturation. IEEE Transactions on Circuits and Systems II: Express Briefs, 65(11), 1758–1762.

    Article  Google Scholar 

  5. Munz, U., Papachristodoulou, A., & Allgower, F. (2011). Consensus in multi-agent systems with coupling delays and switching topology. IEEE Transactions on Automatic Control, 56(12), 2976–2982.

    Article  MathSciNet  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  7. Trentelman, H. L., Takaba, K., & Monshizadeh, N. (2013). Robust synchronization of uncertain linear multi-agent systems. IEEE Transactions on Automatic Control, 58(6), 1511–1523.

    Article  MathSciNet  Google Scholar 

  8. Zhu, W., Jiang, Z.-P., & Feng, G. (2014). Event-based consensus of multi-agent systems with general linear models. Automatica, 50(2), 552–558.

    Article  MathSciNet  Google Scholar 

  9. Xu, X., Liu, L., & Feng, G. (2018). Consensus of discrete-time linear multi-agent systems with communication, input and output delays. IEEE Transactions on Automatic Control, 63(2), 492–497.

    Article  MathSciNet  Google Scholar 

  10. Hu, Y., Su, H., & Lam, J. (2013). Adaptive consensus with a virtual leader of multiple agents governed by locally Lipschitz nonlinearity. International Journal of Robust Nonlinear Control, 23(9), 978–990.

    Article  MathSciNet  Google Scholar 

  11. Li, Z., Ren, W., Liu, X., & Fu, M. (2011). Consensus of multi-agent systems with general linear and Lipschitz nonlinear dynamics using distributed adaptive protocols. IEEE Transactions on Automatic Control, 58(7), 1786–1791.

    Article  MathSciNet  Google Scholar 

  12. Krstic, M., Kanellakopoulos, I., & Kokotovic, P. V. (1995). Nonlinear and adaptive control design. Wiley.

  13. Hua, C.-C., You, X., & Guan, X.-P. (2016). Leader-following consensus for a class of high-order nonlinear multi-agent systems. Automatica, 73, 138–144.

    Article  MathSciNet  Google Scholar 

  14. Zhang, X., Liu, L., & Feng, G. (2015). Leader-follower consensus of time-varying nonlinear multi-agent systems. Automatica, 52(2), 8–14.

    Article  MathSciNet  Google Scholar 

  15. 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  Google Scholar 

  16. Chang, L., Zhang, C., Zhang, X., & Chen, X. (2017). Decentralised regulation of nonlinear multi-agent systems with directed network topologies. International Journal of Control, 90(11), 2338–2348.

    Article  MathSciNet  Google Scholar 

  17. 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  Google Scholar 

  18. Zhu, Q., & Wang, H. (2018). Output feedback stabilization of stochastic feedforward systems with unknown control coefficients and unknown output function. Automatica, 87, 166–175.

    Article  MathSciNet  Google Scholar 

  19. Liu, Q., Zhang, X., & Li, H. (2020). Global regulation for feedforward systems with both discrete delays and distributed delays. Automatica, 113, 108753.

    Article  MathSciNet  Google Scholar 

  20. Ma, Q., Xu, S., Lewis, F. L., Zhang, B., & Zou, Y. (2016). Cooperative output regulation of singular heterogeneous multiagent systems. IEEE Transactions on Cybernetics, 46(6), 1471–1475.

    Article  Google Scholar 

  21. Xu, X., Liu, L., & Feng, G. (2016). Consensus of single integrator multi-agent systems with directed topology and communication delays. Control Theory and Technology, 14(1), 21–27.

    Article  MathSciNet  Google Scholar 

  22. Li, H., Zhang, X., & Liu, S. (2021). An improved dynamic gain method to global regulation of feedforward nonlinear systems. IEEE Transactions on Automatic Control. https://doi.org/10.1109/TAC.2021.3088787

    Article  Google Scholar 

  23. Zhou, B., & Yang, X. (2018). Global stabilization of feedforward nonlinear time-delay systems by bounded controls. Automatica, 88, 21–30.

    Article  MathSciNet  Google Scholar 

  24. Li, H., Zhang, X., & Feng, G. (2021). Event-triggered output feedback control of switched nonlinear systems with input saturation. IEEE Transactions on Cybernetics, 51(5), 2319–2326.

    Article  Google Scholar 

  25. Li, H., Liu, Q., & Zhang, X. (2021). On designing event-triggered output feedback tracking controller for feedforward nonlinear systems. IEEE Transactions on Circuits and Systems II: Express Briefs, 68(2), 677–681.

    Article  Google Scholar 

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Authors and Affiliations

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

    Hanfeng Li, Xianfu Zhang & Weihao Pan

Authors
  1. Hanfeng Li
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  2. Xianfu Zhang
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  3. Weihao Pan
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Corresponding author

Correspondence to Xianfu Zhang.

Additional information

This 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).

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Li, H., Zhang, X. & Pan, W. Consensus control of feedforward nonlinear multi-agent systems: a time-varying gain method. Control Theory Technol. 20, 46–53 (2022). https://doi.org/10.1007/s11768-022-00083-1

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  • DOI: https://doi.org/10.1007/s11768-022-00083-1

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