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Two Consensus Problems

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Cooperative Control of Multi-agent Systems

Part of the book series: Advances in Industrial Control ((AIC))

Abstract

As we pointed out in Chap. 1, depending on the nature of various global objectives of a multi-agent system, there are a variety of cooperative control problems of multi-agent systems such as consensus/synchronization, formation, cooperative output regulation, connectivity preservation, distributed estimation, distributed optimization, and so on. Fundamental to all cooperative control problems of multi-agent systems is the consensus problem. There are two types of consensus problems, namely the leaderless consensus problem and the leader-following consensus problem. The leaderless consensus problem is to design a distributed control law such that the state vector of each subsystem asymptotically synchronizes to the same trajectory regardless of the time profile of the trajectory.

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References

  1. Olfati-Saber R, Fax JA, Murray RM (2007) Consensus and cooperation in networked multi-agent systems. Proc IEEE 95(1):215–223

    Article  Google Scholar 

  2. Qu Z (2008) Cooperative control of dynamical systems: applications to autonomous vehicles. Springer, London

    MATH  Google Scholar 

  3. Ren W, Beard RW (2008) Distributed consensus in multi-vehicle cooperative control: theory and applications. Springer, London

    Book  Google Scholar 

  4. Hu J, Hong Y (2007) Leader-following coordination of multi-agent systems with coupling time delays. Phys A: Stat Mech Appl 374(2):853–863

    Article  MathSciNet  Google Scholar 

  5. Olfati-Saber R, Murray RM (2004) Consensus problems in networks of agents with switching topology and time-delays. IEEE Trans Autom Control 49(9):1520–1533

    Article  MathSciNet  Google Scholar 

  6. Ren W, Beard RW (2005) Consensus seeking in multiagent systems under dynamically changing interaction topologies. IEEE Trans Autom Control 50(5):655–661

    Article  MathSciNet  Google Scholar 

  7. Tuna SE (2008) LQR-based coupling gain for synchronization of linear systems. arXiv:0801.3390

  8. Wang J, Cheng D, Hu X (2008) Consensus of multi-agent linear dynamic systems. Asian J Cortrol 10(2):144–155

    Article  MathSciNet  Google Scholar 

  9. Jadbabaie A, Lin J, Morse AS (2003) Coordination of groups of mobile autonomous agents using nearest neighbor rules. IEEE Trans Autom Control 48(6):988–1001

    Article  MathSciNet  Google Scholar 

  10. Su S, Lin Z (2016) Distributed consensus control of multi-agent systems with higher order agent dynamics and dynamically changing directed interaction topologies. IEEE Trans Autom Control 61(2):515–519

    MathSciNet  MATH  Google Scholar 

  11. Ni W, Cheng D (2010) Leader-following consensus of multi-agent systems under fixed and switching topologies. Syst & Control Lett 59(3):209–217

    Article  MathSciNet  Google Scholar 

  12. Cheng D, Wang J, Hu X (2008) An extension of LaSalle’s invariance principle and its application to multi-agent consensus. IEEE Trans Autom Control 53(7):885–890

    Article  MathSciNet  Google Scholar 

  13. Su Y, Huang J (2012) Stability of a class of linear switching systems with applications to two consensus problems. IEEE Trans Autom Control 57(6):1420–1430

    Article  MathSciNet  Google Scholar 

  14. Su Y, Huang J (2012) Two consensus problems for discrete-time multi-agent systems with switching network topology. Automatica 48(9):1988–1997

    Article  MathSciNet  Google Scholar 

  15. Lin Z (2005) Coupled dynamic systems: from structure towards stability and stabilizability, PhD dissertation, University of Toronto, Toronto, Canada

    Google Scholar 

  16. Moreau L (2004) Stability of continuous-time distributed consensus algorithms. In: Proceedings of the 41st IEEE conference on decision and control, pp 3998–4003

    Google Scholar 

  17. Lee T, Tan Y, Su Y, Mareels I (2021) Invariance principles and observability in switched systems with an application in consensus. IEEE Trans Autom Control 66(11): 5128–5143.

    Google Scholar 

  18. Tuna SE (2008) Synchronizing linear systems via partial-state coupling. Automatica 44:2179–2184

    Article  MathSciNet  Google Scholar 

  19. You K, Xie L (2011) Network topology and communication data rate for consensusability of discrete-time multi-agent systems. IEEE Trans Autom Control 56(10):2262–2275

    Article  MathSciNet  Google Scholar 

  20. Hengster-Movric K, You K, Lewis FL, Xie L (2013) Synchronization of discrete-time multi-agent systems on graphs using Riccati design. Automatica 49:414–423

    Article  MathSciNet  Google Scholar 

  21. Liu J, Huang J (2019) A spectral property of a graph matrix and its application to the leader-following consensus problem of discrete-time multi-agent systems. IEEE Trans Autom Control 64(6):2583–2589

    Article  Google Scholar 

  22. Qin J, Gao H, Yu C (2014) On discrete-time convergence for general linear multi-agent systems under dynamic topology. IEEE Trans Autom Control 59(4):1054–1059

    Article  MathSciNet  Google Scholar 

  23. Huang J (2017) The consensus for discrete-time linear multi-agent systems under directed switching networks. IEEE Trans Autom Control 62(8):4086–4092

    Article  MathSciNet  Google Scholar 

  24. Lee T, Xia W, Su Y, Huang J (2018) Exponential consensus of discrete-time systems based on a novel Krasovskii–LaSalle theorem under directed switching networks. Automatica 97:189–199

    Article  MathSciNet  Google Scholar 

  25. Liu J, Huang J (2021) Discrete-time leader-following consensus over switching digraphs with general system modes. IEEE Trans Autom Control 66(3):1238–1245

    Article  MathSciNet  Google Scholar 

  26. Liu T, Huang J (2021) Discrete-time distributed observers over jointly connected switching networks and an application. IEEE Trans Autom Control 66(4):1918–1924

    Article  MathSciNet  Google Scholar 

  27. Klamkin MS, Newman DJ (1971) Cyclic pursuit or the three bugs problem. Amer Math Mon 78(6):631–639

    MathSciNet  MATH  Google Scholar 

  28. Bruckstein AM, Cohen N, Efrat A (1991) Ants, crickets and frogs in cyclic pursuit. Center for intelligent systems. Technical Report #9105, Technion-Israel Institute of Technology, Haifa, Israel

    Google Scholar 

  29. Richardson TJ (2001) Non-mutual captures in cyclic pursuit. Ann Math Artif Intell 31:127–146

    Article  MathSciNet  Google Scholar 

  30. Marshall JA, Broucke ME, Francis BA (2004) Formations of vehicles in cyclic pursuit. IEEE Trans Autom Control 49(11):1963–1974

    Article  MathSciNet  Google Scholar 

  31. Liu T, Lee T, Huang J (2019) An exponential stability result for a class of linear switched systems and its application. In: IEEE conference on decision and control, pp 1551–1556

    Google Scholar 

  32. He C, Huang J (2022) Adaptive distributed observer for general linear leader systems over periodic switching digraphs. Automatica 137(3):110021

    Google Scholar 

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Author information

Authors and Affiliations

  1. School of Automation Science and Engineering, South China University of Technology, Guangzhou, Guangdong, China

    He Cai

  2. College of Computer and Data Science, Fuzhou University, Fuzhou, Fujian, China

    Youfeng Su

  3. Department of Mechanical and Automation Engineering, The Chinese University of Hong Kong, Shatin, Hong Kong, China

    Jie Huang

Authors
  1. He Cai
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  2. Youfeng Su
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  3. Jie Huang
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Corresponding author

Correspondence to He Cai .

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Cai, H., Su, Y., Huang, J. (2022). Two Consensus Problems. In: Cooperative Control of Multi-agent Systems. Advances in Industrial Control. Springer, Cham. https://doi.org/10.1007/978-3-030-98377-2_3

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