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Cooperative output regulation for linear uncertain MIMO multi-agent systems by output feedback

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In this paper, we study the cooperative output regulation problem for a class of general linear uncertain multi-input multi-output (MIMO) multi-agent systems subject to a well-defined vector relative degree. By proposing some suitable internal model, the problem is first converted into the auxiliary cooperative stabilization problem of the augmented system in the so-called strict feedback normal form. This auxiliary problem is then solved by some developed robust control techniques, such as multiple high-gain feedback and mixed distributed observer, leading to an effective distributed output feedback regulator synthesis for the original cooperative output regulation problem.

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  1. 1

    Cai H, Huang J. Leader-following adaptive consensus of multiple uncertain rigid spacecraft systems. Sci China Inf Sci, 2016, 59: 010201

  2. 2

    Chen J, Gan MG, Huang J, et al. Formation control of multiple Euler-Lagrange systems via null-space-based behavioral control. Sci China Inf Sci, 2016, 59: 010202

  3. 3

    Liu T F, Lu X S, Jiang Z P. A junction-by-junction feedback-based strategy with convergence analysis for dynamic traffic assignment. Sci China Inf Sci, 2016, 59: 010203

  4. 4

    Peng K M, Lin F, Chen B M. Online schedule for autonomy of multiple unmanned aerial vehicles. Sci China Inf Sci, 2017, 60: 072203

  5. 5

    Yu X, Liu L. Leader-follower formation of vehicles with velocity constraints and local coordinate frames. Sci China Inf Sci, 2017, 60: 070206

  6. 6

    Wang X L, Hong Y G, Huang J, et al. A distributed control approach to a robust output regulation problem for multi-agent linear systems. IEEE Trans Autom Control, 2010, 55: 2891–2895

  7. 7

    Francis B A, Wonham W M. The internal model principle of control theory. Automatica, 1976, 12: 457–465

  8. 8

    Grip H F, Yang T, Saberi A, et al. Output synchronization for heterogeneous networks of non-introspective agents. Automatica, 2012, 48: 2444–2453

  9. 9

    Su Y F, Huang J. Cooperative output regulation of linear multi-agent systems. IEEE Trans Autom Control, 2012, 57: 1062–1066

  10. 10

    Xiang J, Wei W, Li Y J. Synchronized output regulation of linear networked systems. IEEE Trans Autom Control, 2009, 54: 1336–1341

  11. 11

    Su Y F, Hong Y G, Huang J. A general result on the robust cooperative output regulation for linear uncertain multi-agent systems. IEEE Trans Autom Control, 2013, 58: 1275–1279

  12. 12

    Wang X L, Han F L. Robust coordination control of switching multi-agent systems via output regulation approach. Kybernetika, 2011, 47: 755–772

  13. 13

    Tuna S E. LQR-based coupling gain for synchronization of linear systems. Mathematics, 2008. https://arxiv.org/abs/0801.3390

  14. 14

    Chen C T. Linear System Theory and Design. Oxford: Oxford University Press, 1984

  15. 15

    Shi L R, Zhao Z Y, Lin Z L. Robust semi-global leader-following practical consensus of a group of linear systems with imperfect actuators. Sci China Inf Sci, 2017, 60: 072201

  16. 16

    Chen Z Y, Huang J. Stabilization and Regulation of Nonlinear Systems — A Robust and Adaptive Approach. Berlin: Springer, 2015

  17. 17

    Kim H, Shim H, Seo J H. Output consensus of heterogeneous uncertain linear multi-agent systems. IEEE Trans Autom Control, 2011, 56: 200–206

  18. 18

    Liu W, Huang J. Cooperative robust output regulation of linear minimum-phase multi-agent systems under switching network. In: Proceedings of the 10th Asian Control Conference (ASCC), Kota Kinabalu, 2015. 1–5

  19. 19

    Wang X H, Xu D B, Ji H B. Robust almost output consensus in networks of nonlinear agents with external disturbances. Automatica, 2016, 70: 303–311

  20. 20

    Su Y F. Output feedback cooperative control for linear uncertain multi-agent systems with nonidentical relative degrees. IEEE Trans Autom Control, 2016, 61: 4027–4033

  21. 21

    Wang X H, Su Y F, Xu D B. Internal model-based synthesis for networks of multiple multivariable systems. In: Proceedings of the 29th Chinese Control and Decision Conference (CCDC), Chongqing, 2017. 5539–5544

  22. 22

    Mueller M. Normal form for linear systems with respect to its vector relative degree. Linear Algebra Appl, 2009, 430: 1292–1312

  23. 23

    Su Y F, Huang J. Cooperative robust output regulation of a class of heterogeneous linear uncertain multi-agent systems. Int J Robust Nonlinear Control, 2014, 24: 2819–2839

  24. 24

    Nikiforov V O. Adaptive non-linear tracking with complete compensation of unknown disturbances. Eur J Control, 1998, 4: 132–139

  25. 25

    Berman A, Plemmons R J. Nonnegative Matrices in the Mathematical Sciences. Cambridge: Academic Press, 1979

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This work was supported by National Natural Science Foundation of China (Grant No. 61403082) and Natural Science Foundation of Fujian Province (Grant No. 2016J06014).

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Correspondence to Youfeng Su.

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Zhang, Y., Su, Y. Cooperative output regulation for linear uncertain MIMO multi-agent systems by output feedback. Sci. China Inf. Sci. 61, 092206 (2018). https://doi.org/10.1007/s11432-017-9255-2

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  • cooperative control
  • output regulation
  • MIMO
  • output feedback
  • vector relative degrees