Skip to main content
SpringerLink
Log in

Non-fragility of multi-agent controllability

  • Research Paper
  • Published:
Science China Information Sciences Aims and scope Submit manuscript

Abstract

Controllability of multi-agent systems is determined by the interconnection topologies. In practice, losing agents can change the topologies of multi-agent systems, which may affect the controllability. In order to preserve controllability, this paper first introduces the concept of non-fragility of controllability. In virtue of the notion of cutsets, necessary and sufficient conditions are established from a graphic perspective, for almost surely strongly/weakly preserving controllability, respectively. Then, the problem of leader selection to preserve controllability is proposed. The tight bounds of the fewest leaders to achieve strongly preserving controllability are estimated in terms of the diameter of the interconnection topology, and the cardinality of the node set. Correspondingly, the tight bounds of the fewest leaders to achieve weakly preserving controllability are estimated in terms of the cutsets of the interconnection topology. Furthermore, two algorithms are established for selecting the fewest leaders to strongly/weakly preserve the controllability. In addition, the algorithm for leaders’ locations to maximize non-fragility is also designed. Simulation examples are provided to illuminate the theoretical results and exhibits how the algorithms proceed.

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.

Similar content being viewed by others

References

  1. Xiao F, Wang L, Chen J. Partial state consensus for networks of second-order dynamic agents. Syst Control Lett, 2010, 59: 775–781

    Article  MathSciNet  MATH  Google Scholar 

  2. Wang L, Xiao F. Finite-time consensus problems for networks of dynamic agents. IEEE Trans Autom Control, 2010, 55: 950–955

    Article  MathSciNet  MATH  Google Scholar 

  3. Zhang Z, Zhang L, Hao F, et al. Leader-following consensus for linear and lipschitz nonlinear multiagent systems with quantized communication. IEEE Trans Cyber, 2016, 47: 1970–1982

    Article  Google Scholar 

  4. Jing G, Zheng Y, Wang L. Consensus of multiagent systems with distance-dependent communication networks. IEEE Trans Neural Netw Learn Syst, 2017, 28: 2712–2726

    Article  Google Scholar 

  5. Xiao F, Wang L, Chen J, et al. Finite-time formation control for multi-agent systems. Automatica, 2009, 45: 2605–2611

    Article  MathSciNet  MATH  Google Scholar 

  6. Olfati-Saber R. Flocking for multi-agent dynamic systems: algorithms and theory. IEEE Trans Autom Control, 2006, 51: 401–420

    Article  MathSciNet  MATH  Google Scholar 

  7. Jing G, Zheng Y, Wang L. Flocking of multi-agent systems with multiple groups. Int J Control, 2014, 87: 2573–2582

    Article  MathSciNet  MATH  Google Scholar 

  8. Guan Y, Ji Z, Zhang L, et al. Decentralized stabilizability of multi-agent systems under fixed and switching topologies. Syst Control Lett, 2013, 62: 438–446

    Article  MathSciNet  MATH  Google Scholar 

  9. Guan Y, Ji Z, Zhang L, et al. Controllability of heterogeneous multi-agent systems under directed and weighted topology. Int J Control, 2016, 89: 1009–1024

    Article  MathSciNet  MATH  Google Scholar 

  10. Guan Y Q, Wang L. Structural controllability of multi-agent systems with absolute protocol under fixed and switching topologies. Sci China Inf Sci, 2017, 60: 092203

    Article  MathSciNet  Google Scholar 

  11. Guan Y Q, Ji Z, Zhang L, et al. Controllability of multi-agent systems under directed topology. Int J Robust Nonlin Control, 2017. doi: 10.1002/rnc.3798

    Google Scholar 

  12. Lu Z, Zhang L, Ji Z, et al. Controllability of discrete-time multi-agent systems with directed topology and input delay. Int J Control, 2016, 89: 179–192

    Article  MathSciNet  MATH  Google Scholar 

  13. Ma J, Zheng Y, Wu B, et al. Equilibrium topology of multi-agent systems with two leaders: a zero-sum game perspective. Automatica, 2016, 73: 200–206

    Article  MathSciNet  MATH  Google Scholar 

  14. Tanner H. On the controllability of nearest neighbor interconnections. In: Proceedings of the 43rd IEEE Conference on Decision and Control, Nassau, 2004. 2467–2472

    Google Scholar 

  15. Wang L, Jiang F C, Xie G M,et al. Controllability of multi-agent systems based on agreement protocols. Sci China Ser F-Inf Sci, 2009, 52: 2074–2088

    Article  MathSciNet  MATH  Google Scholar 

  16. Zhao B, Guan Y, Wang L. Controllability improvement for multi-agent systems: leader selection and weight adjustment. Int J Control, 2016, 89: 2008–2018

    Article  MathSciNet  MATH  Google Scholar 

  17. Ji Z, Lin H, Yu H. Protocols design and uncontrollable topologies construction for multi-agent networks. IEEE Trans Autom Control, 2015, 60: 781–786

    Article  MathSciNet  MATH  Google Scholar 

  18. Rahmani A, Ji M, Mesbahi M, et al. Controllability of multi-agent systems from a graph-theoretic perspective. SIAM J Control Optim, 2009, 48: 162–186

    Article  MathSciNet  MATH  Google Scholar 

  19. Ji Z, Lin H, Yu H. Leaders in multi-agent controllability under consensus algorithm and tree topology. Syst Control Lett, 2012, 61: 918–925

    Article  MathSciNet  MATH  Google Scholar 

  20. Parlangeli G, Notarstefano G. On the reachability and observability of path and cycle graphs. IEEE Trans Autom Control, 2012, 57: 743–748

    Article  MathSciNet  MATH  Google Scholar 

  21. Notarstefano G, Parlangeli G. Controllability and observability of grid graphs via reduction and symmetries. IEEE Trans Autom Control, 2013, 58: 1719–1731

    Article  MathSciNet  MATH  Google Scholar 

  22. Partovi A, Lin H, Ji Z. Structural controllability of high order dynamic multi-agent systems. In: Proceedings of IEEE Conference on Robotics Automation and Mechatronics, Singapore, 2010. 327–332

    Google Scholar 

  23. Zamani M, Lin H. Structural controllability of multi-agent systems. In: Proceedings of the 2009 American Control Conference, St. Louis, 2009. 5743–5748

    Chapter  Google Scholar 

  24. Lou Y, Hong Y. Controllability analysis of multi-agent systems with directed and weighted interconnection. Int J Control, 2012, 85: 1486–1496

    Article  MathSciNet  MATH  Google Scholar 

  25. Goldin D, Raisch J. On the weight controllability of consensus algorithms. In: Proceedings of European Control Conference, Zurich, 2013. 233–238

    Google Scholar 

  26. Jafari S, Ajorlou A, Aghdam A G. Leader selection in multi-agent systems subject to partial failure. In: Proceedings of the 2011 American Control Conference, San Francisco, 2011. 5330–5335

    Chapter  Google Scholar 

  27. Rahimian M A, Aghdam A G. Structural controllability of multiagent networks: robustness against simultaneous failures. Automatica, 2013, 49: 3149–3157

    Article  MathSciNet  MATH  Google Scholar 

  28. Wilson R J. Introduction to Graph Theory. 4th ed. Upper Saddle River: Prentice Hall, 1996

    Google Scholar 

  29. Mayeda H, Yamada T. Strong structural controllability. SIAM J Control Opt, 1979, 17: 123–128

    Article  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgements

This work was supported by National Natural Science Foundation of China (Grant Nos. 61375120, 61603288).

Author information

Authors and Affiliations

  1. Center for Systems and Control, College of Engineering, Peking University, Beijing, 100871, China

    Bin Zhao & Long Wang

  2. Center for Complex Systems, School of Mechano-Electronic Engineering, Xidian University, Xi’an, 710071, China

    Yongqiang Guan

Authors
  1. Bin Zhao
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yongqiang Guan
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Long Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Long Wang.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zhao, B., Guan, Y. & Wang, L. Non-fragility of multi-agent controllability. Sci. China Inf. Sci. 61, 052202 (2018). https://doi.org/10.1007/s11432-017-9129-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11432-017-9129-y

Keywords

Search

Navigation