Skip to main content
SpringerLink
Log in

Robust Semi-Global Leaderless Consensus and Containment Control of Identical Linear Systems with Imperfect Actuators

  • Published:
Journal of Systems Science and Complexity Aims and scope Submit manuscript

Abstract

This paper investigates both the robust semi-global leaderless consensus problem and the robust semi-global containment control problem for a group of identical linear systems with imperfect actuators. The imperfect actuators are characterized by nonlinearities such as saturation and dead zone and there input output relationships are not precisely known. The dynamics of follower agents are also affected by the input additive disturbances. Low-and-high gain feedback consensus protocols are constructed to solve these problems. More specifically, it is shown that robust semi-global leaderless consensus can be achieved over a connected undirected graph and robust semi-global containment control can be achieved when each follower agent has access to the information of at least one leader agent. Numerical simulation illustrates the theoretical results.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Dimarogonas D and Kyriakopoulos K, On the rendezvous problem for multiple nonholonomic agents, IEEE Transactions on Automatic Control, 2007, 52(5): 916–922.

    Article  MathSciNet  MATH  Google Scholar 

  2. Hengster-Movric K, You K, Lewis F, et al., Synchronization of discrete-time multi-agent systems on graphs using Riccati design, Automatica, 2013, 49(2): 414–423.

    Article  MathSciNet  MATH  Google Scholar 

  3. Su H, Wang X, and Lin Z, Flocking of multi-agents with a virtual leader, IEEE Transactions on Automatic Control, 2009, 54(2): 293–307.

    Article  MathSciNet  MATH  Google Scholar 

  4. Ma C, Li T, and Zhang J, Consensus control for leader-following multi-agent systems with measurement noises, Journal of Systems Science & Complexity, 2010, 23(1): 35–49.

    Article  MathSciNet  MATH  Google Scholar 

  5. Oh K, Park M, and Ahn H, A survey of multi-agent formation control, Automatica, 2015, 53: 424–440.

    Article  MathSciNet  MATH  Google Scholar 

  6. Meng Z, Ren W, Cao Y, et al., Leaderless and leader-following consensus with communication and input delays under a directed network topology, IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics, 2011, 41(1): 75–88.

    Article  Google Scholar 

  7. Li Z, Ren W, Liu X, et al., Consensus of multi-agent systems with general linear and Lipschitz nonlinear dynamics using distributed adaptive protocols, IEEE Transactions on Automatic Control, 2013, 58(7): 1786–1791.

    Article  MathSciNet  MATH  Google Scholar 

  8. Wang L and Guo L, Robust consensus and soft control of multi-agent systems with noises, Journal of Systems Science & Complexity, 2008, 21(3): 406–415.

    Article  MathSciNet  MATH  Google Scholar 

  9. Liu Z, Chen Z, and Yuan Z, Event-triggered average-consensus of multi-agent systems with weighted and direct topology, Journal of Systems Science & Complexity, 2012, 25(5): 845–855.

    Article  MathSciNet  MATH  Google Scholar 

  10. Ren W, Distributed leaderless consensus algorithms for networked Euler-Lagrange systems, International Journal of Control, 2009, 82(11): 2137–2149.

    Article  MathSciNet  MATH  Google Scholar 

  11. Liu H, Xie G, and Wang L, Containment of linear multi-agent systems under general interaction topologies, Systems & Control Letters, 2012, 61(4): 528–534.

    Article  MathSciNet  MATH  Google Scholar 

  12. Li Z, Duan Z, Ren W, et al., Containment control of linear multi-agent systems with multiple leaders of bounded inputs using distributed continuous controllers, International Journal of Robust and Nonlinear Control, 2015, 25(13): 2101–2121.

    Article  MathSciNet  MATH  Google Scholar 

  13. Meng Z, Ren W, and You Z, Distributed finite-time attitude containment control for multiple rigid bodies, Automatica, 2010, 46(12): 2092–2099.

    Article  MathSciNet  MATH  Google Scholar 

  14. Wang Y, Cheng L, Hou Z, et al., Containment control of multi-agent systems in a noisy communication environment, Automatica, 2014, 50(7): 1922–1928.

    Article  MathSciNet  MATH  Google Scholar 

  15. Cao Y, Ren W, and Egerstedt M, Distributed containment control with multiple stationary or dynamic leaders in fixed and switching directed networks, Automatica, 2012, 48(8): 1586–1597.

    Article  MathSciNet  MATH  Google Scholar 

  16. Li Y, Xiang J, and Wei W, Consensus problems for linear time-invariant multi-agent systems with saturation constraints, IET Control Theory & Applications, 2011, 5(6): 823–829.

    Article  MathSciNet  Google Scholar 

  17. Wu Z, Li J, and Song F, Semi-global leaderless consensus with input saturation constraints via adaptive protocols, International Journal of Research in Engineering and Science, 2015, 3(10): 36–42.

    Google Scholar 

  18. Su H, Chen M Z Q, Lam J, et al., Semi-global leader-following consensus of linear multi-agent systems with input saturation via low gain feedback, IEEE Transactions on Circuits and Systems I: Regular Papers, 2013, 60(7): 1881–1889.

    Article  MathSciNet  Google Scholar 

  19. Su H, Jia G, and Chen M Z Q, Semi-global containment control of multi-agent systems with input saturation, IET Control Theory & Applications, 2014, 8(18): 2229–2237.

    Article  MathSciNet  Google Scholar 

  20. Lin Z, Low Gain Feedback, Springer, London, 1998.

    MATH  Google Scholar 

  21. Hu G, Robust consensus tracking of a class of second-order multi-agent dynamic systems, Systems & Control Letters, 2012, 61(1): 134–142.

    Article  MathSciNet  MATH  Google Scholar 

  22. Wen G, Duan Z, Zhao Y, et al., Robust containment tracking of uncertain linear multi-agent systems: A non-smooth control approach, International Journal of Control, 2014, 87(12): 2522–2534.

    Article  MathSciNet  MATH  Google Scholar 

  23. Shi L, Zhao Z, and Lin Z, Robust semi-global leader-following practical consensus of a group of linear systems with imperfect actuators, Science China Information Sciences, 2017, 60(7): 1–12.

    Article  MathSciNet  Google Scholar 

  24. Lin Z, Robust semi-global stabilization of linear systems with imperfect actuators, Systems & Control Letters, 1997, 29: 215–221.

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Automation, Shanghai Jiao Tong University, and Key Laboratory of System Control and Information Processing of Ministry of Education, Shanghai, 200240, China

    Liangren Shi

  2. Key Laboratory of Advanced Control and Optimization for Chemical Processes (East China University of Science and Technology), Ministry of Education, Shanghai, 200237, China

    Zhiyun Zhao

  3. Charles L. Brown Department of Electrical and Computer Engineering, University of Virginia, P.O. Box 400743, Charlottesville, VA, 22904-4743, USA

    Zongli Lin

Authors
  1. Liangren Shi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Zhiyun Zhao
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Zongli Lin
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Liangren Shi.

Additional information

This research was supported by the National Natural Science Foundation of China under Grant No. 61733018, Shanghai Natural Science Foundation under Grant No. 17ZR1445400, China Postdoctoral Science Foundation under Grant Nos. 2017M610233 and 2016T90373, the Fundamental Research Funds for Central Universities under Grant No. 222201714030, and the US Army Research Office under Grant No. W911NF-17-1-0535.

This paper was recommended for publication by Editor CHEN Jie.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Shi, L., Zhao, Z. & Lin, Z. Robust Semi-Global Leaderless Consensus and Containment Control of Identical Linear Systems with Imperfect Actuators. J Syst Sci Complex 31, 69–86 (2018). https://doi.org/10.1007/s11424-018-7086-z

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11424-018-7086-z

Keywords

Search

Navigation