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Distributed prescribed-time leader–follower tracking consensus control for high-order nonlinear MASs

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Abstract

A novel distributed prescribed-time leader–follower tracking consensus control strategy is proposed for high-order nonlinear multi-agent systems with lower triangular time-varying dynamics in directed communication topology. Firstly, a distributed prescribed-time state observer (DPTSO) is presented for each follower to estimate the states of the leader. Based on the DPTSO, the consensus problem is transformed into a tracking control problem; that is, the follower tracks the estimations of the DPTSO. Then, a distributed prescribed-time controller is developed by using the cascade control framework and dynamic control, which avoids the problem of differential explosion in traditional back-stepping control. The convergence time of the DPTSO and distributed prescribed-time controller is not only explicitly pre-specified but also determined regardless of the initial states of the system and control parameters. Finally, it is demonstrated that the closed-loop systems realize prescribed-time full-state leader–follower tracking consensus. Simulation results show that the method is effective and feasible.

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The data that support the findings of this study are available on request from the corresponding author. The data are not publicly available due to privacy or ethical restrictions.

References

  1. Li, W.B., Chiu, P.W., Li, Z.: An accelerated finite-time convergent neural network for visual servoing of a flexible surgical endoscope with physical and RCM constraints. IEEE Trans. Neural Netw. Learn. Syst. 31(12), 5272–5284 (2020). https://doi.org/10.1109/TNNLS.2020.2965553

    Article  MathSciNet  Google Scholar 

  2. Yu, Z.Q., Liu, Z.X., Zhang, Y.M., Qu, Y.H., Su, C.Y.: Distributed finite-time fault-tolerant containment control for multiple unmanned aerial vehicles. IEEE Trans. Neural Netw. Learn. Syst. 31(6), 2077–2091 (2020). https://doi.org/10.1109/TNNLS.2019.2927887

    Article  MathSciNet  Google Scholar 

  3. Zhang, S., Guo, Y., Liu, Z.G., Wang, S.C., Hu, X.X.: Finite-time cooperative guidance strategy for impact angle and time control. IEEE Trans. Aerosp. Electron. Syst. 57(2), 806–819 (2021). https://doi.org/10.1109/TAES.2020.3037958

    Article  Google Scholar 

  4. Li, S.H., Du, H.B., Lin, X.Z.: Finite-time consensus algorithm for multi-agent systems with double-integrator dynamics. Automatica 47, 1706–1712 (2011). https://doi.org/10.1016/j.automatica.2011.02.045

    Article  MathSciNet  Google Scholar 

  5. Du, H.B., Wen, G.H., Chen, G.R., Cao, J.D., Alsaadi, F.E.: A distributed finite-time consensus algorithm for higher-order leaderless and leader-following multiagent systems. IEEE Trans. Syst. Man Cybern. Syst. 47(7), 1625–1634 (2017). https://doi.org/10.1109/TSMC.2017.2651899

    Article  Google Scholar 

  6. Hu, B., Guan, Z.H., Fu, M.Y.: Distributed event-driven control for finite-time consensus. Automatica 103, 88–95 (2019). https://doi.org/10.1016/j.automatica.2019.01.026

    Article  MathSciNet  Google Scholar 

  7. Wang, J.A., Bi, C.Y., Wang, D.D., Kuang, Q.B., Wang, C.Y.: Finite-time distributed event-triggered formation control for quadrotor UAVs with experimentation. ISA Trans. 126, 585–596 (2022). https://doi.org/10.1016/j.isatra.2021.07.049

    Article  Google Scholar 

  8. Yu, S., Long, X.: Finite-time consensus for second-order multi-agent systems with disturbances by integral sliding mode. Automatica 54, 158–165 (2015). https://doi.org/10.1016/j.automatica.2015.02.001

    Article  MathSciNet  Google Scholar 

  9. Du, H., Wen, G., Wu, D., Cheng, Y., Lv, J.: Distributed fixed-time consensus for nonlinear heterogeneous multi-agent systems. Automatica 113, 108797 (2020). https://doi.org/10.1016/j.automatica.2019.108797

    Article  MathSciNet  Google Scholar 

  10. Liu, Y., Zhang, F., Huang, P.F., Lu, Y.B.: Fixed-time consensus tracking control with connectivity preservation for strict-feedback nonlinear multi-agent systems. ISA Trans. 123, 14–24 (2022). https://doi.org/10.1016/j.isatra.2021.06.003

    Article  Google Scholar 

  11. Zuo, Z.Y.: Nonsingular fixed-time consensus tracking for second-order multi-agent networks. Automatica 54, 305–309 (2015). https://doi.org/10.1016/j.ins.2018.12.037

    Article  MathSciNet  Google Scholar 

  12. Zhao, K., Song, Y.D., Wang, Y.J.: Regular error feedback based adaptive practical prescribed time tracking control of normal form nonaffine systems. J. Frankl. Inst. 356(5), 2759–2779 (2019). https://doi.org/10.1016/j.jfranklin.2019.02.015

    Article  MathSciNet  Google Scholar 

  13. Song, Y.D., Wang, Y.J., Holloway, J., Krstic, M.: Time-varying feedback for regulation of normal-form nonlinear systems in prescribed finite time. Automatica 83, 243–251 (2017). https://doi.org/10.1016/j.automatica.2017.06.008

    Article  MathSciNet  Google Scholar 

  14. Gong, X., Cui, Y.K., Shen, J., Shu, Z., Huang, T.W.: Distributed prescribed-time interval bipartite consensus of multi-agent systems on directed graphs: theory and experiment. IEEE Trans. Netw. Sci. Eng. 8(1), 613–624 (2021). https://doi.org/10.1109/TNSE.2020.3047232

    Article  MathSciNet  Google Scholar 

  15. Zhao, Y., Liu, Y.F., Wen, G.H., Ren, W., Chen, G.R.: Designing distributed specified-time consensus protocols for linear multiagent systems over directed graphs. IEEE Trans. Autom. Control 64(7), 2945–2952 (2019). https://doi.org/10.1109/TAC.2018.2872534

    Article  MathSciNet  Google Scholar 

  16. Ren, Y.H., Zhou, W.N., Li, Z.W., Liu, L., Sun, Y.Q.: Prescribed-time consensus tracking of multiagent systems with nonlinear dynamics satisfying time-varying Lipschitz growth rates. IEEE Trans. Cybern. (2021). https://doi.org/10.1109/TCYB.2021.3109294

    Article  Google Scholar 

  17. Ren, Y.H., Zhou, W.N., Li, Z.W., Liu, L., Sun, Y.Q.: Prescribed-time cluster lag consensus control for second-order non-linear leader-following multiagent systems. ISA Trans. 109, 49–60 (2021). https://doi.org/10.1016/j.isatra.2020.09.012

    Article  Google Scholar 

  18. Wang, Y.J., Song, Y.D., Hill, D.J.: Zero-error consensus tracking with preassignable convergence for nonaffine multiagent systems. IEEE Trans. Cybern. 51(3), 1300–1310 (2021). https://doi.org/10.1109/TCYB.2019.2893461

    Article  Google Scholar 

  19. Wang, Y.J., Song, Y.D.: Leader-following control of high-order multi-agent systems under directed graphs: pre-specified finite time approach. Automatica 87, 113–120 (2018). https://doi.org/10.1016/j.automatica.2017.09.017

    Article  MathSciNet  Google Scholar 

  20. Liu, D.C., Liu, Z., Chen, C.L.P., Zhang, Y.: Prescribed-time containment control with prescribed performance for uncertain nonlinear multi-agent systems. J. Frankl. Inst. 358(3), 1782–1811 (2021). https://doi.org/10.1016/j.jfranklin.2020.12.021

    Article  MathSciNet  Google Scholar 

  21. Yao, H.J., Gao, F.Z., Huang, J.C., Wu, Y.Q.: Global prescribed-time stabilization via time-scale transformation for switched nonlinear systems subject to switching rational powers. Appl. Math. Comput. 393, 125766 (2021). https://doi.org/10.1016/j.amc.2020.125766

    Article  MathSciNet  Google Scholar 

  22. Chen, Z.C., Wang, J.H., Zhang, L., Mad, K.M., Liu, Y.H.: Event-triggered prescribed settling time consensus control of uncertain nonlinear multiagent systems with given transient performance. ISA Trans. 129, 24–35 (2021). https://doi.org/10.1016/j.isatra.2021.12.018

    Article  Google Scholar 

  23. Liu, D.C., Liu, Z., Chen, C.L.P., Zhang, Y.: Distributed adaptive fuzzy control approach for prescribed-time containment of uncertain nonlinear multi-agent systems with unknown hysteresis. Nonlinear Dyn. 105(1), 257–275 (2021). https://doi.org/10.1007/s11071-021-06304-7

    Article  Google Scholar 

  24. Chen, X.D., Zhang, X.F., Liu, Q.R.: Prescribed-time decentralized regulation of uncertain nonlinear multi-agent systems via output feedback. Syst. Control Lett. 137, 104640 (2020). https://doi.org/10.1016/j.sysconle.2020.104640

    Article  MathSciNet  Google Scholar 

  25. Ding, Z.: Distributed adaptive consensus output regulation of network-connected heterogeneous unknown linear systems on directed graphs. IEEE Trans. Autom. Control 62(9), 4683–4690 (2017). https://doi.org/10.1109/TAC.2016.2628643

    Article  MathSciNet  Google Scholar 

  26. Mazenc, F., Praly, L., Dayawansa, W.P.: Global stabilization by output feedback: examples and counterexamples. Syst. Control Lett. 23(2), 119–125 (1994). https://doi.org/10.1016/0167-6911(94)90041-8

    Article  MathSciNet  Google Scholar 

  27. Li, K., Hua, C.C., You, X., Guan, X.P.: Distributed consensus control for nonlinear multiagent systems under directed graphs of dynamic frequency switches. IEEE Trans. Autom. Control 66(2), 841–848 (2020). https://doi.org/10.1109/TAC.2020.2987302

    Article  MathSciNet  Google Scholar 

  28. Wang, W., Wen, C.Y., Huang, J.S., Li, Z.G.: Hierarchical decomposition based consensus tracking for uncertain interconnected systems via distributed adaptive output feedback control. IEEE Trans. Autom. Control 61(7), 1938–1945 (2016). https://doi.org/10.1109/TAC.2015.2479535

  29. Zhang, H.W., Lewis, F.L.: Adaptive cooperative tracking control of higher-order nonlinear systems with unknown dynamics. Automatica 48, 1432–1439 (2012). https://doi.org/10.1016/j.automatica.2012.05.008

    Article  MathSciNet  Google Scholar 

  30. Cui, L., Jin, N.: Prescribed-time ESO-based prescribed-time control and its application to partial IGC design. Nonlinear Dyn. 106(1), 491–508 (2021). https://doi.org/10.1007/s11071-021-06859-5

    Article  Google Scholar 

  31. Ding, Z.T., Li, Z.K.: Distributed adaptive consensus control of nonlinear output-feedback systems on directed graphs. Automatica 72, 46–52 (2016). https://doi.org/10.1016/j.automatica.2016.05.014

    Article  MathSciNet  Google Scholar 

  32. Wang, F., Chen, B., Lin, C., Zhang, J., Meng, X.Z.: Adaptive neural network finite-time output feedback control of quantized nonlinear systems. IEEE Trans. Cybern. 48(6), 1839–1848 (2018). https://doi.org/10.1109/TCYB.2017.2715980

    Article  Google Scholar 

  33. Cai, Y.L., Dai, J., Zhang, H.G., Wang, Y.C.: Fixed-time leader-following/containment consensus of nonlinear multi-agent systems based on event-triggered mechanism. Appl. Math. Comput. 396, 125881 (2021). https://doi.org/10.1016/j.amc.2020.125881

    Article  MathSciNet  Google Scholar 

  34. You, X., Hua, C.C., Li, K., Jia, X.C.: Fixed-time leader-following consensus for high-order time-varying nonlinear multiagent systems. IEEE Trans. Autom. Control 65(12), 5510–5516 (2020). https://doi.org/10.1109/TAC.2020.3005154

    Article  MathSciNet  Google Scholar 

  35. Praly, L., Jiang, Z.P.: Linear output feedback with dynamic high gain for nonlinear systems. Syst. Control Lett. 53(2), 107–116 (2004). https://doi.org/10.1016/J.SYSCONLE.2004.02.025

    Article  MathSciNet  Google Scholar 

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Acknowledgements

The work was supported by the National Natural Science Foundation of China under Grant 61773334 and the Natural Science Fund of Hebei Province under Grant F2020203079.

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Author notes

  1. Li Li and Yuanqing Xia have contributed equally to this work.

Authors and Affiliations

  1. Engineering Research Center of the Ministry of Education for Intelligent Control System and Intelligent Equipment, School of Electrical Engineering, Yanshan University, Qinhuangdao, 066004, Hebei Province, China

    Jiaping Qiang & Li Li

  2. School of Automation, Beijing Institute of Technology, Beijing, 100081, China

    Yuanqing Xia

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  1. Jiaping Qiang
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  2. Li Li
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Correspondence to Li Li.

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Qiang, J., Li, L. & Xia, Y. Distributed prescribed-time leader–follower tracking consensus control for high-order nonlinear MASs. Nonlinear Dyn 112, 491–505 (2024). https://doi.org/10.1007/s11071-023-09051-z

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