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Formation-Containment Control of Swarm Systems

  • Xiwang DongEmail author
Chapter
Part of the Springer Theses book series (Springer Theses)

Abstract

This chapter studies state and output formation-containment control problems for high-order linear time-invariant (LTI) swarm systems. First, protocols are presented for leaders and followers, respectively, to drive the states of leaders to realize the predefined time-varying state formation and propel the states of followers, to converge to the convex hull formed by states of leaders. State formation-containment problems of swarm systems are transformed into asymptotic stability problems, and an explicit expression of the formation reference function is derived. Sufficient conditions for swarm systems to achieve state formation-containment are proposed. Necessary and sufficient conditions for swarm systems to achieve state containment and time-varying state formation are presented respectively as special cases. An approach to determine the gain matrices in the state formation-containment protocols is given. Then, output formation-containment control problems for high-order LTI swarm systems are dealt with. Sufficient conditions for swarm systems to achieve output formation-containment are proposed. An approach to determine the gain matrices in the output formation-containment protocols for swarm systems to achieve output formation-containment is given. It is revealed that state formation-containment, state/output containment, state/output formation control, state/output consensus, and state/output consensus tracking problems can be unified in the framework of output formation-containment problems. Finally, numerical simulations are provided to demonstrate theoretical results.

Keywords

Swarm Systems Consensus Tracking Problem State Containment Asymptotic Stability Problem Reference Formulation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 1.
    Ji M, Ferrari-Trecate G, Egerstedt M et al (2008) Containment control in mobile networks. IEEE Trans Autom Control 53(8):1972–1975MathSciNetCrossRefGoogle Scholar
  2. 2.
    Meng ZY, Ren W, You Z (2010) Distributed finite-time attitude containment control for multiple rigid bodies. Automatica 46(12):2092–2099MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Notarstefano G, Egerstedt M, Haque M (2011) Containment in leader-follower networks with switching communication topologies. Automatica 47(5):1035–1040MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Cao YC, Ren W, Egerstedt M (2012) Distributed containment control with multiple stationary or dynamic leaders in fixed and switching directed networks. Automatica 48(8):1586–1597MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Liu HY, Xie GM, Wang L (2012) Necessary and sufficient conditions for containment control of networked multi-agent systems. Automatica 48(7):1415–1422MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Lou YC, Hong YG (2012) Target containment control of multi-agent systems with random switching interconnection topologies. Automatica 48(5):879–885MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Liu HY, Xie GM, Wang L (2012) Containment of linear multi-agent systems under general interaction topologies. Syst Control Lett 61(4):528–534MathSciNetCrossRefGoogle Scholar
  8. 8.
    Li ZK, Ren W, Liu XD et al (2013) Distributed containment control of multi-agent systems with general linear dynamics in the presence of multiple leaders. Int J Robust Nonlinear Control 23(5):534–547MathSciNetCrossRefGoogle Scholar
  9. 9.
    Dong XW, Xi JX, Lu G et al (2014) Containment analysis and design for high-order linear time-invariant singular swarm systems with time delays. Int J Robust Nonlinear Control 24(7):1189–1204MathSciNetCrossRefGoogle Scholar
  10. 10.
    Dong XW, Shi ZY, Lu G et al (2015) Output containment analysis and design for high-order linear time-invariant swarm systems. Int J Robust Nonlinear Control 25(6):900–913MathSciNetCrossRefGoogle Scholar
  11. 11.
    Ferrari-Trecate G, Egerstedt M, Buffa A, et al (2006) Laplacian sheep: a hybrid, stop-go policy for leader-based containment control. In: Proceedings of Hybrid Systems: Computation and Control, pp 212–226Google Scholar
  12. 12.
    Dimarogonas DV, Egerstedt M, Kyriakopoulos KJ (2006) A leader-based containment control strategy for multiple unicycles. In: Proceedings of the 45th IEEE Conference on Decision and Control, pp 5968–5973Google Scholar
  13. 13.
    Xi JX, Cai N, Zhong YS (2010) Consensus problems for high-order linear time-invariant swarm systems. Physica A 389(24):5619–5627CrossRefGoogle Scholar
  14. 14.
    Ni W, Cheng DZ (2010) Leader-following consensus of multi-agent systems under fixed and switching topologies. Syst Control Lett 59(3–4):209–217MathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    Lafferriere G, Williams A, Caughman J et al (2005) Decentralized control of vehicle formations. Syst Control Lett 54(9):899–910MathSciNetCrossRefzbMATHGoogle Scholar
  16. 16.
    Ma CQ, Zhang JF (2012) On formability of linear continuous-time multi-agent systems. J Syst Sci Complex 25(1):13–29MathSciNetCrossRefzbMATHGoogle Scholar
  17. 17.
    He Y, Wang Q (2006) An improved ILMI method for static output feedback control with application to multivariable PID control. IEEE Trans Autom Control 51(10):1678–1683CrossRefGoogle Scholar
  18. 18.
    Dong XW, Shi ZY, Lu G, et al (2014) Formation-containment analysis and design for high-order linear time-invariant swarm systems. Int J Robust Nonlinear Control, in press.doi: 10.1002/rnc.3274 Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.School of Automation Science and Electronic EngineeringBeihang UniversityBeijingChina

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