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Volume 9 Issue 5
May  2022

IEEE/CAA Journal of Automatica Sinica

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W. C. Huang, H. L. Liu, and J. Huang, “Distributed robust containment control of linear heterogeneous multi-agent systems: An output regulation approach,” IEEE/CAA J. Autom. Sinica, vol. 9, no. 5, pp. 864–877, May 2022. doi: 10.1109/JAS.2022.105560
Citation: W. C. Huang, H. L. Liu, and J. Huang, “Distributed robust containment control of linear heterogeneous multi-agent systems: An output regulation approach,” IEEE/CAA J. Autom. Sinica, vol. 9, no. 5, pp. 864–877, May 2022. doi: 10.1109/JAS.2022.105560

Distributed Robust Containment Control of Linear Heterogeneous Multi-Agent Systems: An Output Regulation Approach

doi: 10.1109/JAS.2022.105560
Funds:  This work was supported by the National Science Foundation of China (51977040)
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  • In this paper, we consider the robust output containment problem of linear heterogeneous multi-agent systems under fixed directed networks. A distributed dynamic observer based on the leaders’ measurable output was designed to estimate a convex combination of the leaders’ states. First, for the case of followers with identical state dimensions, distributed dynamic state and output feedback control laws were designed based on the state-coupled item and the internal model compensator to drive the uncertain followers into the leaders’ convex hull within the output regulation framework. Subsequently, we extended theoretical results to the case where followers have nonidentical state dimensions. By establishing virtual errors between the dynamic observer and followers, a new distributed dynamic output feedback control law was constructed using only the states of the compensator to solve the robust output containment problem. Finally, two numerical simulations verified the effectiveness of the designed schemes.

     

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  • 1 This paper has two types of dynamic output feedback law, the footnote is to distinguish so as not to confuse.
    2 This footnote is for the same purpose as Footnote 1.
  • [1]
    G. A. Kaminka, R. Schechter-Glick, and V. Sadov, “Using sensor morphology for multirobot formations,” IEEE Trans. Robotics, vol. 24, no. 2, pp. 271–282, 2008. doi: 10.1109/TRO.2008.918054
    [2]
    P. Hernandez-Leon, J. Dvila, S. Salazar, and X. Ping, “Distance-based formation maneuvering of non-holonomic wheeled mobile robot multi-agent system,” IFAC Proceedings Volumes, vol. 53, no. 2, pp. 5665–5670, 2020.
    [3]
    B. Alberto, V. G. Gabriel, D. P. Juan, L. Alvaro, and B. Javier, “Combination of multi-agent systems and wireless sensor networks for the monitoring of cattle,” Sensors, vol. 18, no. 2, pp. 108–124, 2018. doi: 10.3390/s18010108
    [4]
    S. Wang, W. Yang, and H. Shi, “Consensus-based filtering algorithm with packet-dropping,” Acta Automatica Sinica, vol. 36, no. 12, pp. 1689–1696, 2010.
    [5]
    Y. Su and J. Huang, “Cooperative output regulation of linear multi-agent systems,” IEEE Trans. Automatic Control, vol. 57, no. 4, pp. 1062–1066, 2012. doi: 10.1109/TAC.2011.2169618
    [6]
    X. Wang, Y. Hong, J. Huang, and Z. Jiang, “A distributed control approach to a robust output regulation problem for multi-agent linear systems,” IEEE Trans. Automatic Control, vol. 55, no. 12, pp. 2891–2895, 2010. doi: 10.1109/TAC.2010.2076250
    [7]
    X. Liu, Y. Xie, F. Li, P. Shi, W. Gui, and W. Li, “Formation control of singular multi-agent systems with switching topologies,” Int. Journal of Robust and Nonlinear Control, vol. 2, no. 30, pp. 1–13, 2020.
    [8]
    H. Liu, G. Xie, and L. Wang, “Necessary and sufficient conditions for containment control of networked multi-agent systems,” Automatica, vol. 48, no. 7, pp. 1415–1422, 2012. doi: 10.1016/j.automatica.2012.05.010
    [9]
    A. T. Koru, S. B. Sarsilmaz, Selahattin, T. Yucelen, and E. N. Johnson, “Cooperative output regulation of heterogeneous multi-agent systems: A global distributed control synthesis approach,” IEEE Trans. Automatic Control, vol. 66, no. 9, pp. 4289–4296, 2021. doi: 10.1109/tac.2020.3032496
    [10]
    T. Liu, J. Qi, and Z. Jiang, “Distributed containment control of multi-agent systems with velocity and acceleration saturations,” Automatica, vol. 117, pp. 1–10, 2020.
    [11]
    J. Qin, Q. Ma, X. Yu, and Y. Kang, “Output containment control for heterogeneous linear multi-agent systems with fixed and switching topologies,” IEEE Trans. Cybernetics, vol. 49, no. 12, pp. 4117–4128, 2019. doi: 10.1109/TCYB.2018.2859159
    [12]
    H. Haghshenas, M. A. Badamchizadeh, and M. Baradarannia, “Containment control of heterogeneous linear multi-agent systems,” Automatica, vol. 54, pp. 210–216, 2015. doi: 10.1016/j.automatica.2015.02.002
    [13]
    H. Chu, L. Gao, and W. Zhang, “Distributed adaptive containment control of heterogeneous linear multi-agent systems: An output regulation approach,” IET Control Theory and Applications, vol. 10, no. 1, pp. 95–102, 2016. doi: 10.1049/iet-cta.2015.0398
    [14]
    W. Wang, S. Tong, and D. Wang, “Adaptive fuzzy containment control of nonlinear systems with unmeasurable states,” IEEE Trans. Cybernetics, vol. 49, no. 3, pp. 961–973, 2019. doi: 10.1109/TCYB.2018.2789917
    [15]
    Y. Cao, W. Ren, and M. Egerstedt, “Distributed containment control with multiple stationary or dynamic leaders in fixed and switching directed networks,” Automatica, vol. 48, no. 8, pp. 1586–1597, 2012. doi: 10.1016/j.automatica.2012.05.071
    [16]
    J. Shao, L. Shi, M. Cao, and H. Xia, “Distributed containment control for asynchronous discrete-time second-order multi-agent systems with switching topologies,” Applied Mathematics &Computation, vol. 336, pp. 47–59, 2018.
    [17]
    K. Chen, J. Wang, Y. Zhang, and Z. Liu, “Consensus of second-order nonlinear multi-agent systems under state-controlled switching topology,” Nonlinear Dynamics, vol. 81, no. 4, pp. 1871–1878, 2015. doi: 10.1007/s11071-015-2112-3
    [18]
    P. Wang and Y. Jia, “Distributed containment control of second-order multi-agent systems with inherent non-linear dynamics,” IET Control Theory and Applications, vol. 8, no. 4, pp. 277–287, 2014. doi: 10.1049/iet-cta.2013.0686
    [19]
    F. Wang, Z. Liu, Z. Chen, and S. Wang, “Containment control for second-order nonlinear multi-agent systems with intermittent communications,” Int. Journal of Systems Science, vol. 50, no. 5, pp. 919–934, 2019. doi: 10.1080/00207721.2019.1585997
    [20]
    T. Li, Z. Li, S. Fei, and Z. Ding, “Second-order event-triggered adaptive containment control for a class of multi-agent systems,” ISA Transactions, vol. 96, pp. 132–142, 2020. doi: 10.1016/j.isatra.2019.06.003
    [21]
    H. Xia, W. X. Zheng, and J. Shao, “Event-triggered containment control for second-order multi-agent systems with sampled position data,” ISA Transactions, vol. 73, pp. 91–99, 2018. doi: 10.1016/j.isatra.2017.11.001
    [22]
    Y. Zheng and L. Wang, “Containment control of heterogeneous multi-agent systems,” Int. Journal of Control, vol. 87, no. 1, pp. 1–8, 2014. doi: 10.1080/00207179.2013.814074
    [23]
    R. Liao, L. Han, X. Dong, Q. Li, and Z. Ren, “Finite-time formation-containment tracking for second-order multi-agent systems with a virtual leader of fully unknown input,” Neurocomputing, vol. 415, pp. 234–246, 2020. doi: 10.1016/j.neucom.2020.07.067
    [24]
    X. He, Q. Wang, and W. Yu, “Distributed finite-time containment control for second-order nonlinear multi-agent systems,” Applied Mathematics and Computation, vol. 268, pp. 509–521, 2015. doi: 10.1016/j.amc.2015.06.101
    [25]
    F. Wang, Y. Ni, Z. Liu, and Z. Chen, “Fully distributed containment control for second-order multi-agent systems with communication delay,” ISA Transactions, vol. 99, pp. 123–129, 2020. doi: 10.1016/j.isatra.2019.09.009
    [26]
    L. Han, X. Dong, Q. Li, and Z. Ren, “Formation-containment control for second-order multi-agent systems with time-varying delays,” Neurocomputing, vol. 218, pp. 439–447, 2016. doi: 10.1016/j.neucom.2016.09.001
    [27]
    K. Liu, G. Xie, and L. Wang, “Containment control for second-order multi-agent systems with time-varying delays,” Systems &Control Letters, vol. 67, pp. 24–34, 2014.
    [28]
    D. Wang, D. Wang, and W. Wei, “Necessary and sufficient conditions for containment control of multi-agent systems with time delay,” Automatica, vol. 103, pp. 418–423, 2019. doi: 10.1016/j.automatica.2018.12.029
    [29]
    Q. Song, F. Liu, H. Su, and A. V. Vasilakos, “Semi-global and global containment control of multi-agent systems with second-order dynamics and input saturation,” Int. Journal of Robust &Nonlinear Control, vol. 26, no. 16, pp. 3460–3480, 2016.
    [30]
    C. Xu, B. Li, and L. Yang, “Semi-global containment of discrete-time high-order multi-agent systems with input saturation via intermittent control,” IET Control Theory and Applications, vol. 14, no. 16, pp. 2303–2309, 2020. doi: 10.1049/iet-cta.2020.0110
    [31]
    T. Liu, J. Qi and Z. P. Jiang, “ Distributed containment control of multi-agent systems with velocity and acceleration saturations,” Automatica, vol. 117, p. 108992, 2020.
    [32]
    G. Wen, Y. Zhao, and Z. Duan, “Containment of higher-order multi-leader multi-agent systems: A dynamic output approach,” IEEE Trans. Automatic Control, vol. 61, no. 4, pp. 1135–1140, 2016. doi: 10.1109/TAC.2015.2465071
    [33]
    S. Zuo, Y. Song, F. Lewis, and A. Davoudi, “Adaptive output containment control of heterogeneous multi-agent systems with unknown leaders,” Automatica, vol. 92, pp. 235–239, 2018. doi: 10.1016/j.automatica.2018.02.004
    [34]
    J. Zhang and H. Su, “Formation-containment control for multi-agent systems with sampled data and time delays,” Neurocomputing, vol. 424, pp. 125–131, 2021. doi: 10.1016/j.neucom.2019.11.030
    [35]
    X. Dong, Q. Li, Z. Ren, and Y. Zhong, “Formation-containment control for high-order linear time-invariant multi-agent systems with time delays,” Journal of the Franklin Institute, vol. 352, pp. 3564–3584, 2015. doi: 10.1016/j.jfranklin.2015.05.008
    [36]
    G. Wen, G. Hu, Z. Zuo, Y. Zhao, and J. Cao, “Robust containment of uncertain linear multi-agent systems under adaptive protocols,” Int. Journal of Robust and Nonlinear Control, vol. 27, no. 12, pp. 2053–2069, 2017. doi: 10.1002/rnc.3670
    [37]
    G. Wen, P. Wang, T. Huang, W. Yu, and J. Sun, “Robust neuro-adaptive containment of multileader multi-agent systems with uncertain dynamics,” IEEE Trans. Systems,Man,and Cybernetics:Systems, vol. 99, pp. 1–12, 2017.
    [38]
    X. Wang, Y. Hong, and H. Ji, “Adaptive multi-agent containment control with multiple parametric uncertain leaders,” Automatica, vol. 50, no. 9, pp. 2366–2372, 2014. doi: 10.1016/j.automatica.2014.07.019
    [39]
    J. Chen, Z. Guan, C. Yang, T. Li, D. He, and X. Zhang, “Distributed containment control of fractional-order uncertain multi-agent systems,” Journal of the Franklin Institute, vol. 353, no. 7, pp. 1672–1688, 2016. doi: 10.1016/j.jfranklin.2016.02.002
    [40]
    P. Li, F. Jabbari and X. M. Sun, “Containment control of multi-agent systems with input saturation and unknown leader inputs,” Automatica, vol. 130, p. 109677, 2021.
    [41]
    L. Wang, T. Han, X. S. Zhan, J. Wu, and H. Yan, “Bipartite containment for linear multi-agent systems subject to unknown exogenous disturbances,” Asian Journal of Control, DOI: 10.1002/asjc.2580, 2021.
    [42]
    T. Han, B. Xiao, X. S. Zhan, and H. Yan, “Bipartite containment of descriptor multi-agent systems via an observer-based approach,” IET Control Theory and Applications, vol. 14, no. 9, pp. 3047–3051, 2020.
    [43]
    J. Huang, Nonlinear Output Regulation: Theory and Applications, Philadelphia, PA: SIAM, 2004.
    [44]
    H. Liang, H. Zhang, Z. Wang, and J. Wang, “Output regulation of state-coupled linear multi-agent systems with globally reachable topologies,” Neurocomputing, vol. 123, pp. 337–343, 2014. doi: 10.1016/j.neucom.2013.07.028
    [45]
    Y. Su and J. Huang, “Cooperative output regulation of linear multi-agent systems by output feedback,” Systems &Control Letters, vol. 61, pp. 1248–1253, 2012.
    [46]
    Y. Su, Y. Hong, and J. Huang, “A general result on the robust cooperative output regulation for linear uncertain multi-agent systems,” IEEE Trans. Automatic Control, vol. 58, no. 5, pp. 1275–1279, 2013. doi: 10.1109/TAC.2012.2229837
    [47]
    S. Li, J. Zhang, M. Er, X. Luo, Z. Yang, and N. Wang, “Robust containment control of heterogeneous non-linear multi-agent systems via power series approach,” IET Control Theory and Applications, vol. 13, no. 4, pp. 496–505, 2019. doi: 10.1049/iet-cta.2018.5385
    [48]
    S. E. Tuna, “LQR-based coupling gain for synchronization of linear systems”, 2008. [Online]. Available: http://arxiv.org/abs/0801.3390. Accessed on: May 21, 2019.
    [49]
    S. Boyd, L. E. Ghaoui, E. Feron, and V. Balakrishnan, Linear Matrix Inequality in Systems and Control Theory, Philadelphia, PA: SIMA, 1994.
    [50]
    B. A. Francis and W. M. Wonham, “The internal model principle for linear multivariable regulators,” Applied Mathematics and Optimization, vol. 2, no. 2, pp. 170–194, 1975. doi: 10.1007/BF01447855
    [51]
    B. A. Francis and W. M. Wonham, “The internal model principle of control theory,” Automatica, vol. 12, no. 5, pp. 457–465, 1976. doi: 10.1016/0005-1098(76)90006-6
    [52]
    E. J. Davison, “The robust control of a servomechanism problem for linear time-invariant multivariable systems,” IEEE Trans. Automatic Control, vol. 21, no. 1, pp. 25–34, 1976. doi: 10.1109/TAC.1976.1101137
    [53]
    H. Liang, H. Zhang, Z. Wang, and J. Zhang, “Output regulation for heterogeneous linear multi-agent systems based on distributed internal model compensator,” Applied Mathematics &Computation, vol. 242, pp. 736–747, 2014.
    [54]
    W. Ren and R. W. Beard, “Consensus seeking in multi-agent systems under dynamically changing interaction topologies,” IEEE Trans. Automatic Control, vol. 50, no. 5, pp. 655–661, 2005. doi: 10.1109/TAC.2005.846556

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    Highlights

    • For the robust output containment control problem with the uncertain followers of identical nominal dynamics, based on the internal model principle and the compensator technique, the distributed dynamic state and output feedback control laws were introduced to drive the uncertain followers to enter the convex hull spanned by the leaders under the output regulation framework. Among them, the nonsingular transformation and a Lyapunov inequality method was used to analysis the closed-loop system stabilization
    • By introducing the distributed observer systems, we extended the theoretical results to a more general case where the followers have nonidentical state dimensions. In this section, the robust containment problem was converted into a new tracking problem between the distributed observer systems and the follower systems by constructing a virtual error. A distributed dynamic output feedback control law was further devised to drive the virtual error to converge to the origin asymptotically, such that multi-agent systems achieved output containment control
    • At present, most of the containment control protocols must know the relative values of the state with respect to its neighbors, so they can only deal with the situation with followers having the same state dimensions. In our research, the distributed control law has avoided the dependence on the relative states of followers by utilizing the virtual error, and is capable of solving the robust output containment problem for linear heterogeneous multi-agent systems with nonidentical state dimensions
    • We modify the conventional state observer to produce an estimate of the convex combination of the leaders’ states by applying a directed network, which lends itself to the design of the distributed protocols. Moreover, the distributed observer can also be viewed as an extension of the compensators associated with the leaders’ states in some relevant literature, because these compensators can be regarded as a special case of our observer when the output matrix of the leader systems is of full column rank

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