Distributed Robust Control of Uncertain Multi-agent Systems with Directed Networks

Conference paper
First Online:
Part of the Lecture Notes in Electrical Engineering book series (LNEE, volume 367)

Abstract

This paper investigates the distributed robust control problem of a class of uncertain linear time invariant multi-agent systems with directed networks. It is assumed that the agents have identical nominal dynamics while subject to different norm-bounded parameter uncertainties. Based on relative states information of the neighbor agents and a subset of absolute states of the agents, distributed robust controllers are constructed. Sufficient conditions are proposed based on bounded real lemma and algebraic graph theory. The effectiveness of the theoretical results is illustrated via a numerical simulation.

Keywords

Multi-agent systems Robust control Directed networks Bounded real lemma 
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References

  1. 1.
    Jadbabaie A, Lin J, Morse AS (2003) Coordination of groups of mobile autonomous agents using nearest neighbor rules. IEEE Trans Autom Control 48:988–1001MathSciNetCrossRefGoogle Scholar
  2. 2.
    Fax JA, Murry RM (2004) Information flow and cooperative control of vehicle formations. IEEE Trans Autom Control 49:1465–1476MathSciNetCrossRefGoogle Scholar
  3. 3.
    Borrelli F, Keviczeky T (2008) Distributed LQR design for identical dynamically decoupled systems. IEEE Trans Autom Control 53:1901–1912MathSciNetCrossRefGoogle Scholar
  4. 4.
    Ajorlou A, Momeni A, Aghdam AG (2010) A class of bounded distributed control strategies for connectivity preservation in multi-agent systems. IEEE Trans Autom Control 55:2828–2833MathSciNetCrossRefGoogle Scholar
  5. 5.
    Olfati-Saber R (2006) Flocking for multi-agent dynamic systems: algorithms and theory. IEEE Trans Autom Control 51:401–420MathSciNetCrossRefGoogle Scholar
  6. 6.
    Vicsek T, Cziro´k A, Jacob EB, Cohen I, Schochet O (1995) Novel type of phase transitions in a system of self-driven particles. Phys Rev Lett 75:1226–1229Google Scholar
  7. 7.
    Ren W, Beard RW (2005) Consensus seeking in multiagent systems under dynamically changing interaction topologies. IEEE Trans Autom Control 50:655–661MathSciNetCrossRefGoogle Scholar
  8. 8.
    Tuna SE (2008) Synchronizing linear systems via partial-state coupling. Automatica 44:2179–2184MathSciNetCrossRefMATHGoogle Scholar
  9. 9.
    Li Z, Duan Z, Chen G, Huang L (2010) Consensus of multiagent systems and synchronization of complex networks: A unified viewpoint. IEEE Trans Circuits Syst–I Reg Pap 57:213–224MathSciNetCrossRefGoogle Scholar
  10. 10.
    Wen G, Yu W, Cao J, Hu G, Chen G (2013) Consensus control of switching directed networks with general linear node dynamics. In: Proceedings of the 9th Asian control conference, pp 1–6Google Scholar
  11. 11.
    Massioni P, Verhaegen M (2009) Distributed control for identical dynamically coupled systems: a decomposition approach. IEEE Trans Autom Control 54:124–135MathSciNetCrossRefGoogle Scholar
  12. 12.
    Li Z, Duan Z, Huang L (2009) H ∞ control of networked multi-agent systems. J syst Sci Complex 22:35–48MathSciNetCrossRefMATHGoogle Scholar
  13. 13.
    Li Z, Duan Z, Chen G (2011) On H ∞ and H 2 performance regions of multi-agent systems. Automatica 57:213–224Google Scholar
  14. 14.
    Wang J, Duan Z, Zhao Y, Qin G, Yan Y (2013) H ∞ and H 2 control of multi-agent systems with transient performance improvement. Int J Control 86:2131–2145MathSciNetCrossRefMATHGoogle Scholar
  15. 15.
    Wang J, Duan Z, Wen G, Chen G (2015) Distributed robust control of uncertain linear multi-agent systems. Int J Robust Nonlin 25:2162–2179MathSciNetMATHGoogle Scholar
  16. 16.
    Li Z, Duan Z, Xie L (2012) Distributed robust control of linear multi-agent systems with parameter uncertainties. Int J Control 85:384–396MathSciNetCrossRefGoogle Scholar
  17. 17.
    Zhou K, Doyle J (1998) Essential of robust control. Prentice Hall, Upper Saddle RiverGoogle Scholar
  18. 18.
    Gahinet P, Apkarian P (1994) A linear matrix inequality approach to H ∞ control. Int J Robust Nonlinear Control 4:421–448MathSciNetCrossRefMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.Department of Control EngineeringNaval Aeronautical and Astronautical UniversityYantaiChina

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