Containment Control of Swarm Systems

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


This chapter studies output containment control problems for high-order linear time-invariant (LTI) swarm systems and state containment problems for high-order LTI singular swarm systems with time delays. First, a dynamic output containment protocol is presented. Necessary and sufficient conditions for swarm systems to achieve output containment are proposed. To ensure the scalability of the criteria, a sufficient condition which only includes two linear matrix inequality constraints independent of the number of agents is further presented. An approach independent of the number of agents is proposed to determine the gain matrices in the dynamic output containment protocols by solving an algebraic Riccati equation. Second, to eliminate impulse terms in singular swarm systems and ensure that the singular swarm systems can achieve containment, time-delayed protocols are presented for leaders and followers, respectively. By model transformation, containment problems of singular swarm systems are converted into stability problems of multiple low-dimensional time-delayed systems. In terms of linear matrix inequality, sufficient conditions are presented for time-delayed singular swarm systems to achieve state containment, which are independent of the number of agents. By using the method of changing variables, an approach is provided to determine the gain matrices in the protocols. Finally, numerical simulations are presented to demonstrate theoretical results.


Swarm Systems Containment Control Problem Output Container Containment Protocols State Containment 
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.


  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):1035–1040MathSciNetCrossRefGoogle 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.
    Cao YC, Stuart D, Ren W et al (2011) Distributed containment control for multiple autonomous vehicles with double-integrator dynamics: algorithms and experiments. IEEE Trans Control Syst Technol 19(4):929–938CrossRefGoogle Scholar
  6. 6.
    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
  7. 7.
    Lou YC, Hong YG (2012) Target containment control of multi-agent systems with random switching interconnection topologies. Automatica 48(5):879–885MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    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
  9. 9.
    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):534–547MathSciNetCrossRefzbMATHGoogle 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.
    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
  12. 12.
    Dai L (1989) Singular control systems. Springer, BerlinCrossRefzbMATHGoogle Scholar
  13. 13.
    Artstein Z (1982) Linear systems with delayed control: a reduction. IEEE Trans Autom Control 27(4):869–879MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Gu K, Niculescu S (2003) Survey on recent results in the stability and control of time-delay systems. J Dyn Syst Meas Control 125(1):158–165CrossRefGoogle Scholar
  15. 15.
    Richard J (2003) Time-delay systems: an overview of some recent advances and open problems. Automatica 39(10):1667–1694MathSciNetCrossRefzbMATHGoogle Scholar
  16. 16.
    Mondie S, Michiels W (2003) Finite spectrum assignment of unstable time-delay systems with a safe implementation. IEEE Trans Autom Control 48(12):2207–2212MathSciNetCrossRefGoogle Scholar
  17. 17.
    Zhang XM, Wu M, She JH et al (2005) Delay-dependent stabilization of linear systems with time-varying state and input delays. Automatica 41(8):1405–1412MathSciNetCrossRefGoogle Scholar
  18. 18.
    Wu L, Su X, Shi P et al (2011) Model approximation for discrete-time state-delay systems in the T-S fuzzy framework. IEEE Trans Fuzzy Syst 19(2):366–378MathSciNetCrossRefGoogle Scholar
  19. 19.
    Wu L, Su X, Shi P et al (2011) A new approach to stability analysis and stabilization of discrete-time T-S fuzzy time-varying delay systems. IEEE Trans Syst Man Cybern Part B-Cybern 41(1):273–286CrossRefzbMATHGoogle Scholar
  20. 20.
    Dong XW, Meng FL, Shi ZY et al (2014) Output containment control for swarm systems with general linear dynamics: a dynamic output feedback approach. Syst Control Lett 71(1):31–37MathSciNetCrossRefzbMATHGoogle Scholar
  21. 21.
    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):1189–1204MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

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

Personalised recommendations