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Consensus of second-order nonlinear multi-agent systems under state-controlled switching topology

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Abstract

This paper studies the consensus problem of second-order multi-agent systems under both fixed and switching directed topologies in a more general framework. Specifically, each agent incorporates an intrinsic nonlinear dynamics and the communication topology switches in a state-controlled manner. Novel distributed consensus protocols are proposed based only on relative position information and local velocity information. Through constructing appropriate Lyapunov functions, it is shown that the proposed protocols are feasible for achieving consensus, even under switching topology jointly containing a spanning tree. Moreover, some easily manageable algebraic criteria are presented to unravel the underlying mechanism for reaching consensus. In the special case of multi-agent systems with double-integrator dynamics, we further derive a necessary and sufficient condition for the consensus problem. Finally, two numerical examples are provided to validate the effectiveness of theoretical results.

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References

  1. Ren, W., Beard, R.W.: Distributed Consensus in Multi-Vehicle Cooperative Control. Springer, London (2008)

    Book  MATH  Google Scholar 

  2. Lewis, F.L., Zhang, H., Hengster-Movric, K., Das, A.: Cooperative Control of Multi-Agent Systems-Optimal and Adaptive Design Approaches. Springer, London (2014)

    Book  MATH  Google Scholar 

  3. Tan, S., Lu, J., Hill, D.J.: Towards a theoretical framework for analysis and intervention of random drift on general networks. IEEE Trans. Autom. Control 60, 576–581 (2015)

    Article  MathSciNet  Google Scholar 

  4. Olfati-Saber, R., Fax, J.A., Murray, R.M.: Consensus and cooperation in networked multi-agent systems. Proc. IEEE 95, 215–233 (2007)

    Article  Google Scholar 

  5. Cao, Y., Yu, W., Ren, W., Chen, G.: An overview of recent progress in the study of distributed multi-agent coordination. IEEE Trans. Ind. Inf. 9, 427–438 (2013)

    Article  Google Scholar 

  6. Zhou, B., Liao, X.: Leader-following second-order consensus in multi-agent systems with sampled data via pinning control. Nonlinear Dyn. 78, 555–569 (2014)

    Article  MathSciNet  Google Scholar 

  7. Huang, J., Dou, L., Fang, H., Chen, J., Yang, Q.: Distributed backstepping-based adaptive fuzzy control of multiple high-order nonlinear dynamics. Nonlinear Dyn. (2015). doi:10.1007/s11071-015-1973-9

  8. Vicsek, T., Czirók, A., Jacob, E.B., Cohen, I., Schochet, O.: Novel type of phase transitions in a system of self-driven particles. Phys. Rev. Lett. 75, 1226–1229 (1995)

    Article  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  10. Chen, Y., Lü, J., Lin, Z.: Consensus of discrete-time multi-agent systems with transmission nonlinearity. Automatica 49, 1768–1775 (2013)

    Article  Google Scholar 

  11. Chen, Y., Lü, J., Yu, X., Lin, Z.: Consensus of discrete-time second-order multiagent systems based on infinite products of general stochastic matrices. SIAM J. Control Optim. 51, 3274–3301 (2013)

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  14. Moreau, L.: Stability of multiagent systems with time-dependent communication links. IEEE Trans. Autom. Control 50, 169–182 (2005)

    Article  MathSciNet  Google Scholar 

  15. Cao, M., Morse, A.S., Anderson, B.D.O.: Reaching a consensus in a dynamically changing environment: a graphical approach. SIAM J. Control Optim. 47, 575–600 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  16. Proskurnikov, A.V.: Average consensus in networks with nonlinearly delayed couplings and switching topology. Automatica 49, 2928–2932 (2013)

    Article  MathSciNet  Google Scholar 

  17. Lee, D., Spong, M.W.: Stable flocking of multiple inertial agents on balanced graphs. IEEE Trans. Autom. Control. 52, 1469–1475 (2007)

    Article  MathSciNet  Google Scholar 

  18. Ren, W., Beard, R.W.: On consensus algorithms for double-integrator dynamics. IEEE Trans. Autom. Control. 53, 1503–1509 (2008)

    Article  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  20. Abdessameud, A., Tayebi, A.: On consensus algorithms for double-integrator dynamics without velocity measurements and with input constraints. Syst. Control Lett. 59, 812–821 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  21. Meng, Z., Ren, W., Cao, Y., You, Z.: Leaderless and leader-following consensus with communication and input delays under a directed network topology. IEEE Trans. Syst. Man Cybern. B 41, 75–88 (2011)

    Article  Google Scholar 

  22. Cheng, L., Hou, Z.-G., Tan, M., Wang, X.: Necessary and sufficient conditions for consensus of double-integrator multi-agent systems with measurement noises. IEEE Trans. Autom. Control 56, 1958–1963 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  23. Li, H., Liao, X., Dong, T., Xiao, L.: Second-order consensus seeking in directed networks of multi-agent dynamical systems via generalized linear local interaction protocols. Nonlinear Dyn. 70, 2213–2226 (2012)

    Article  MathSciNet  Google Scholar 

  24. Xu, X., Wang, J.: Finite-time consensus tracking for second-order multiagent systems. Asian J. Control 15, 1246–1250 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  25. Yu, W., Chen, G., Cao, M.: Some necessary and sufficient conditions for second-order consensus in multi-agent dynamical systems. Automatica 46, 1089–1095 (2010)

    Article  MathSciNet  Google Scholar 

  26. Song, Q., Cao, J., Yu, W.: Second-order leader-following consensus of nonlinear multi-agent systems via pinning control. Syst. Control Lett. 59, 553–562 (2010)

    Article  MathSciNet  Google Scholar 

  27. Qian, Y., Wu, X., Lü, J., Lu, J.-A.: Consensus of second-order multi-agent systems with nonlinear dynamics and time delay. Nonlinear Dyn. 78, 495–503 (2014)

    Article  MATH  Google Scholar 

  28. Mei, J., Ren, W., Ma, G.: Distributed coordination for second-order multi-agent systems with nonlinear dynamics using only relative position measurements. Automatica 49, 1419–1427 (2013)

    Article  MathSciNet  Google Scholar 

  29. Meng, Z., Lin, Z., Ren, W.: Robust cooperative tracking for multiple non-identical second-order nonlinear systems. Automatica 49, 2363–2372 (2013)

    Article  MathSciNet  Google Scholar 

  30. Qian, Y., Wu, X., Lü, J., Lu, J.: Second-order consensus of multi-agent systems with nonlinear dynamics via impulsive control. Neurocomputing 125, 142–147 (2014)

    Article  Google Scholar 

  31. Qin, W., Liu, Z., Chen, Z.: A novel observer-based formation for nonlinear multi-agent systems with time delay and intermittent communication. Nonlinear Dyn. 79, 1651–1664 (2015)

    Article  MathSciNet  Google Scholar 

  32. Das, A., Lewis, F.L.: Cooperative adaptive control for synchronization of second-order systems with unknown nonlinearities. Int. J. Robust Nonlinear Control 21, 1509–1524 (2011)

    Article  MathSciNet  Google Scholar 

  33. Su, H., Chen, G., Wang, X., Lin, Z.: Adaptive second-order consensus of networked mobile agents with nonlinear dynamics. Automatica 47, 368–375 (2011)

    Article  MathSciNet  Google Scholar 

  34. Yu, W., Ren, W., Zheng, W.X., Chen, G., Lü, J.: Distributed control gains design for consensus in multi-agent systems with second-order nonlinear dynamics. Automatica 49, 2107–2115 (2013)

    Article  Google Scholar 

  35. Lü, J., Yu, X., Chen, G., Cheng, D.: Characterizing the synchronizability of small-world dynamical networks. IEEE Trans. Circuits Syst. I Regul. Pap. 51, 787–796 (2004)

    Article  MathSciNet  Google Scholar 

  36. Lü, J., Chen, G.: A time-varying complex dynamical network model and its controlled synchronization criteria. IEEE Trans. Autom. Control. 50, 841–846 (2005)

    Article  MATH  Google Scholar 

  37. Ma, J., Yang, L.-J., Wu, Y., Zhang, C.R.: Spiral wave in the small-world networks of Hodgkin–Huxley neurons. Commun. Theor. Phys. 54, 583–588 (2010)

    Article  Google Scholar 

  38. Ma, J., Wu, Y., Wu, N.J., Guo, H.Y.: Detection of ordered wave in the networks of neurons with changeable connection. Sci. China Phys. Mech. Astron. 56, 952–959 (2013)

    Article  Google Scholar 

  39. Qin, H.X., Ma, J., Wang, C.N., Chu, R.T.: Autapse-induced target wave, spiral wave in regular network of neurons. Sci. China Phys. Mech. Astron. 57, 1918–1926 (2014)

    Article  Google Scholar 

  40. Li, H., Liao, X., Lei, X., Huang, T., Zhu, W.: Second-order consensus seeking in multi-agent systems with nonlinear dynamics over random switching directed networks. IEEE Trans. Circuits Syst. I Regul. Pap. 60, 1595–1607 (2013)

    Article  MathSciNet  Google Scholar 

  41. Chen, K., Wang, J., Zhang, Y., Liu, Z.: Second-order consensus of nonlinear multi-agent systems with restricted switching topology and time delay. Nonlinear Dyn. 78, 881–887 (2014)

    Article  MathSciNet  Google Scholar 

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

    Article  Google Scholar 

  43. Sun, Z., Ge, S.S.: Switched Linear Systems: Control and Design. Springer, London (2005)

    Book  Google Scholar 

  44. Qin, J., Gao, H., Zheng, W.X.: Second-order consensus for multi-agent systems with switching topology and communication delay. Syst. Control Lett. 60, 390–397 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  45. Wu, C.W.: Synchronization in arrays of coupled nonlinear systems with delay and nonreciprocal time-varying coupling. IEEE Trans. Circuits Syst. II Express Briefs 52, 282–286 (2005)

    Article  Google Scholar 

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Acknowledgments

This work was jointly supported by the Training Program for Outstanding Young Teachers in University of Guangdong Province under Grant Yq2013065, the China Postdoctoral Science Foundation under Grant 2013M540648 and the Business Intelligence Key Team of Guangdong University of Foreign Studies under Grant TD1202.

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Authors and Affiliations

  1. Faculty of Automation, Guangdong University of Technology, Guangzhou, 510006, China

    Kairui Chen, Yun Zhang & Zhi Liu

  2. Department of Applied Mathematics, Guangdong University of Foreign Studies, Guangzhou, 510006, China

    Junwei Wang

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  1. Kairui Chen
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  2. Junwei Wang
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  3. Yun Zhang
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  4. Zhi Liu
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Correspondence to Junwei Wang.

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Chen, K., Wang, J., Zhang, Y. et al. Consensus of second-order nonlinear multi-agent systems under state-controlled switching topology. Nonlinear Dyn 81, 1871–1878 (2015). https://doi.org/10.1007/s11071-015-2112-3

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  • DOI: https://doi.org/10.1007/s11071-015-2112-3

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