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Difference-Compensated Consensus Algorithms

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Abstract

Difference feedback control described as \(u(t)=x(t)-x(t-T)\) with \(u\in R\), \(x\in R\) and \(T>0\), which is also named as time-delayed feedback control, has been an effective method for stabilizing unstable periodic orbits of chaotic dynamics [1] and stabilizing an equilibrium point for a normal dynamical system [2].

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References

  1. K. Pyragas, Continuous control of chaos by self-controlling feedback. Phys. Lett. A 170(6), 421–428 (1992)

    Article  Google Scholar 

  2. H. Kokame, K. Hirata, K. Konishi, T. Mori, Difference feedback can stabilize uncertain steady states. IEEE Trans. Autom. Control 46(12), 1908–1913 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  3. H. Nakajima, On analytical properties of delayed feedback control of chaos. Phys. Lett. A 232(3–4), 207–210 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  4. T. Ushio, Limitation of delayed feedback control in nonlinear discrete-time systems. IEEE Trans. Circuit Syst. 43(9), 815–816 (1996)

    Article  Google Scholar 

  5. K. Pyragas, V. Pyragas, I.Z. Kiss, J.L. Hudson, Stabilizing and tracking unknown steady states of dynamical systems. Phys. Rev. Lett. 89(24), 244103 (2002)

    Article  Google Scholar 

  6. W. Yu, G. Chen, M. Cao, W. Ren, Delay-induced consensus and quasi-consensus in multi-agent dynamical systems. IEEE Trans. Circuits Syst. I, Reg. Papers 60(10), 2679–2687 (2013)

    Article  MathSciNet  Google Scholar 

  7. C.L. Liu, Y.P. Tian, Formation control of multi-agent systems with heterogeneous communication delays. Int. J. Syst. Sci. 40(6), 627–636 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  8. E. Nuno, R. Ortega, L. Basanez, D. Hill, Synchronization of networks of nonidentical Euler-Lagrange systems with uncertain parameters and communication delays. IEEE Trans. Autom. Control 56(4), 935–941 (2011)

    Article  MathSciNet  Google Scholar 

  9. W. Zhu, D. Cheng, Leader-following consensus of second-order agents with multiple time-varying delays. Automatica 46(12), 1994–1999 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  10. J. Zhu, Y.P. Tian, J. Kuang, On the general consensus protocol of multi-agent systems with double-integrator dynamics. Linear Algebr. Appl. 431(5–7), 701–715 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  11. Y.P. Tian, C.L. Liu, Robust consensus of multi-agent systems with diverse input delays and asymmetric interconnection perturbations. Automatica 45(5), 1347–1353 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  12. X. Lu, F. Austin, S. Chen, Flocking in multi-agent systems with active virtual leader and time-varying delays coupling. Commun. Nonlinear Sci. Numer. Simul. 16(2), 1014–1026 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  13. W. Zhu, Consensus of multiagent systems with switching jointly reachable interconnection and time delays. IEEE Trans. Syst., Cybern. A, Syst., Humans 42(2), 348–358 (2012)

    Google Scholar 

  14. C.L. Liu, F. Liu, Dynamical consensus seeking of second-order multi-agent systems based on delayed state compensation. Syst. Control Lett. 61(12), 1235–1241 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  15. C.L. Liu, F. Liu, Asynchronously compensated consensus algorithm for discrete-time second-order multi-agent systems under communication delay. IET Control Theory A. 8(17), 2004–2012 (2014)

    Article  MathSciNet  Google Scholar 

  16. C.L. Liu, F. Liu, Delayed-compensation algorithm for second-order leader-following consensus seeking under communication delay. Entropy 17(6), 3752–3765 (2015)

    Article  MathSciNet  Google Scholar 

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Correspondence to Cheng-Lin Liu .

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Liu, CL., Liu, F. (2017). Difference-Compensated Consensus Algorithms. In: Consensus Problem of Delayed Linear Multi-agent Systems. SpringerBriefs in Electrical and Computer Engineering(). Springer, Singapore. https://doi.org/10.1007/978-981-10-2492-4_4

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  • DOI: https://doi.org/10.1007/978-981-10-2492-4_4

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  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-10-2491-7

  • Online ISBN: 978-981-10-2492-4

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