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Volume 11 Issue 4
Apr.  2024

IEEE/CAA Journal of Automatica Sinica

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H. Wang and  Q.-L. Han,  “Designing proportional-integral consensus protocols for second-order multi-agent systems using delayed and memorized state information,” IEEE/CAA J. Autom. Sinica, vol. 11, no. 4, pp. 878–892, Apr. 2024. doi: 10.1109/JAS.2024.124308
Citation: H. Wang and  Q.-L. Han,  “Designing proportional-integral consensus protocols for second-order multi-agent systems using delayed and memorized state information,” IEEE/CAA J. Autom. Sinica, vol. 11, no. 4, pp. 878–892, Apr. 2024. doi: 10.1109/JAS.2024.124308

Designing Proportional-Integral Consensus Protocols for Second-Order Multi-Agent Systems Using Delayed and Memorized State Information

doi: 10.1109/JAS.2024.124308
Funds:  This work was supported in part by the National Natural Science Foundation of China (NSFC) (61703086, 61773106) and the IAPI Fundamental Research Funds (2018ZCX27)
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  • This paper is concerned with consensus of a second-order linear time-invariant multi-agent system in the situation that there exists a communication delay among the agents in the network. A proportional-integral consensus protocol is designed by using delayed and memorized state information. Under the proportional-integral consensus protocol, the consensus problem of the multi-agent system is transformed into the problem of asymptotic stability of the corresponding linear time-invariant time-delay system. Note that the location of the eigenvalues of the corresponding characteristic function of the linear time-invariant time-delay system not only determines the stability of the system, but also plays a critical role in the dynamic performance of the system. In this paper, based on recent results on the distribution of roots of quasi-polynomials, several necessary conditions for Hurwitz stability for a class of quasi-polynomials are first derived. Then allowable regions of consensus protocol parameters are estimated. Some necessary and sufficient conditions for determining effective protocol parameters are provided. The designed protocol can achieve consensus and improve the dynamic performance of the second-order multi-agent system. Moreover, the effects of delays on consensus of systems of harmonic oscillators/double integrators under proportional-integral consensus protocols are investigated. Furthermore, some results on proportional-integral consensus are derived for a class of high-order linear time-invariant multi-agent systems.

     

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  • [1]
    R. Olfati-Saber and R. M. Murray, “Consensus problems in networks of agents with switching topology and time-delays,” IEEE Trans. Autom. Control, vol. 49, no. 9, pp. 1520–1533, Sept. 2004. doi: 10.1109/TAC.2004.834113
    [2]
    H. Yang, Q.-L. Han, X. Ge, L. Ding, Y. Xu, B. Jiang, and D. Zhou, “Fault tolerant cooperative control of multi-agent systems: A survey of trends and methodologies,” IEEE Trans. Ind. Inform., vol. 16, no. 1, pp. 4–17, Jan. 2020. doi: 10.1109/TII.2019.2945004
    [3]
    Y. Ju, D. Ding, X. He, Q.-L. Han, and G. Wei, “Consensus control of multi-agent systems using fault-estimation-in-the-loop: Dynamic event-triggered case,” IEEE/CAA J. Autom. Sinica, vol. 9, no. 8, pp. 1440–1451, Aug. 2022. doi: 10.1109/JAS.2021.1004386
    [4]
    P. Yu, K. Liu, X. Liu, X. Li, M. Wu, and J. She, “Robust consensus tracking control of uncertain multi-agent systems with local disturbance rejection,” IEEE/CAA J. Autom. Sinica, vol. 10, no. 2, pp. 427–438, Feb. 2023. doi: 10.1109/JAS.2023.123231
    [5]
    G.-P. Liu, “Tracking control of multi-agent systems using a networked predictive PID tracking scheme,” IEEE/CAA J. Autom. Sinica, vol. 10, no. 1, pp. 216–225, Jan. 2023. doi: 10.1109/JAS.2023.123030
    [6]
    S. Hara, T. Hayakawa, and H. Sugata, “LTI systems with generalized frequency variables: A unified framework for homogeneous multi-agent dynamical systems,” SICE J. Control,Meas.,Syst. Integr., vol. 2, no. 5, pp. 299–306, Sept. 2009. doi: 10.9746/jcmsi.2.299
    [7]
    U. T. Jönsson and C.-Y. Kao, “Consensus of heterogeneous LTI agents,” IEEE Trans. Autom. Control, vol. 57, no. 8, pp. 2133–2139, Aug. 2012. doi: 10.1109/TAC.2012.2183178
    [8]
    P. Wieland, J.-S. Kim, H. Scheu, and F. Allgöwer, “On consensus in multi-agent systems with linear high-order agents,” IFAC Proceedings Volumes, vol. 41, no. 2, pp. 1541–1546, Jul. 2008. doi: 10.3182/20080706-5-KR-1001.00263
    [9]
    C.-Q. Ma and J.-F. Zhang, “Necessary and sufficient conditions for consensusability of linear multi-agent systems,” IEEE Trans. Autom. Control, vol. 55, no. 5, pp. 1263–1268, May 2010. doi: 10.1109/TAC.2010.2042764
    [10]
    P.-A. Blimana and G. Ferrari-Trecate, “Average consensus problems in networks of agents with delayed communications,” Automatica, vol. 44, no. 8, pp. 1985–1995, Aug. 2008. doi: 10.1016/j.automatica.2007.12.010
    [11]
    K. Gu and S.-I. Niculescu, “Survey on recent results in the stability and control of time-delay systems,” J. Dyn. Syst.,Meas.,Control, vol. 125, no. 2, pp. 158–165, Jun. 2003. doi: 10.1115/1.1569950
    [12]
    J. Li, S. Xu, Y. Chu, and H. Wang, “Distributed average consensus control in networks of agents using outdated states,” IET Control Theory Appl., vol. 4, no. 5, pp. 746–758, May 2010. doi: 10.1049/iet-cta.2008.0531
    [13]
    Y. Cao and W. Ren, “Multi-agent consensus using both current and outdated states with fixed and undirected interaction,” J. Intell. Robot Syst., vol. 58, no. 1, pp. 95–106, Apr. 2010. doi: 10.1007/s10846-009-9337-7
    [14]
    Z. Meng, Y. Cao, and W. Ren, “Stability and convergence analysis of multi-agent consensus with information reuse,” Int. J. Control, vol. 83, no. 5, pp. 1081–1092, May 2010. doi: 10.1080/00207170903581603
    [15]
    Q. Song, W. Yu, J. Cao, and F. Liu, “Reaching synchronization in networked harmonic oscillators with outdated position data,” IEEE Trans. Cybern., vol. 46, no. 7, pp. 1566–1578, Jul. 2016. doi: 10.1109/TCYB.2015.2451651
    [16]
    Q. Song, F. Liu, G. Wen, J. Cao, and Y. Tang, “Synchronization of coupled harmonic oscillators via sampled position data control,” IEEE Trans. Circuits Syst. I,Reg. Papers, vol. 63, no. 7, pp. 1079–1088, Jul. 2016. doi: 10.1109/TCSI.2016.2552718
    [17]
    W. Yu, G. Chen, M. Cao, and W. Ren, “Delay-induced consensus and quasi-consensus in multi-agent dynamical systems,” IEEE Trans. Circuits Syst. I,Reg. Papers, vol. 60, no. 10, pp. 2679–2687, Oct. 2013. doi: 10.1109/TCSI.2013.2244357
    [18]
    D. Ma, R. Tian, A. Zulfiqar, J. Chen, and T. Chai, “Bounds on delay consensus margin of second-order multiagent systems with robust position and velocity feedback protocol,” IEEE Trans. Autom. Control, vol. 64, no. 9, pp. 3780–3787, Sept. 2019. doi: 10.1109/TAC.2018.2884154
    [19]
    W. Yu, W. X. Zheng, G. Chen, W. Ren, and J. Cao, “Second-order consensus in multi-agent dynamical systems with sampled position data,” Automatica, vol. 47, no. 7, pp. 1496–1503, Jul. 2011. doi: 10.1016/j.automatica.2011.02.027
    [20]
    Q. Ma and S. Xu, “Consensus switching of second-order multiagent systems with time delay,” IEEE Trans. Cybern., vol. 52, no. 5, pp. 3349–3353, May 2022. doi: 10.1109/TCYB.2020.3011448
    [21]
    W. Hou, M. Fu, H. Zhang, and Z. Wu, “Consensus conditions for general second-order multi-agent systems with communication delay,” Automatica, vol. 75, pp. 293–298, Jan. 2017. doi: 10.1016/j.automatica.2016.09.042
    [22]
    L. Li, M. Fu, H. Zhang, and R. Lu, “Consensus control for a network of high order continuous-time agents with communication delays,” Automatica, vol. 89, pp. 144–150, Mar. 2018. doi: 10.1016/j.automatica.2017.12.006
    [23]
    H. Wang and Q.-L. Han, “Distribution of roots of quasi-polynomials of neutral type and its application–Part I: Determination of the number of roots and Hurwitz stability criteria,” IEEE Trans. Autom. Control, Jul. 2023. DOI: 10.1109/TAC.2023.3300348
    [24]
    H. Wang and Q.-L. Han, “Distribution of roots of quasi-polynomials of neutral type and its application–Part Ⅱ: Consensus protocol design of multi-agent systems using delayed state information,” IEEE Trans. Autom. Control, Dec. 2023. DOI: 10.1109/TAC.2023.3345794
    [25]
    L. Cossi, Introduction to Stability of Quasipolynomials, Time-Delay Systems, Prof. Dragutin Debeljkovic (Ed.), InTech, 2011, Available at: http://www.intechopen.com/books/time-delay-systems/introduction-to-stability-of-quasipolynomials.
    [26]
    H. Wang, J. Liu, and Y. Zhang, “New results on eigenvalue distribution and controller design for time delay systems,” IEEE Trans. Autom. Control, vol. 62, no. 6, pp. 2886–2901, Jun. 2017. doi: 10.1109/TAC.2016.2637002
    [27]
    L. Ou, W. Zhang, and L. Yu, “Low-order stabilization of LTI systems with time delay,” IEEE Trans. Autom. Control, vol. 54, no. 4, pp. 774–787, Apr. 2009. doi: 10.1109/TAC.2009.2014935

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    Highlights

    • New results on Hurwitz stability for a class of quasi-polynomials
    • Consensus design for LTI multi-agent systems via eigenvalue assignment
    • Improving the dynamic performance in addition to achieving the consensus
    • Analysis about effects of delays on consensus of harmonic oscillators/double integrators

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