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Distributed Finite-Time Cooperative Control of Multi-agent Systems

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Complex Systems and Networks

Part of the book series: Understanding Complex Systems ((UCS))

Abstract

The distributed finite-time consensus problems for second-order multi-agent systems are studied in Sect. 7.1. Then, in Sect. 7.2, the distributed finite-time containment protocols are designed for second-order multi-agent systems with multiple nonlinear dynamic leaders. Finally, for multiple Euler-Lagrange systems, some finite-time tracking protocols are proposed in Sect. 7.3.

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References

  1. Hong, Y., Chen, G., Bushnell, L.: Distributed observers design for leader-following control of multi-agent networks. Automatica 44(3), 846–850 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  2. Ji, M., Ferrari-Trecate, G., Egerstedt, M., Buffa, A.Y.: Containment control in mobile networks. IEEE Trans. Autom. Control 53(8), 1972–1975 (2008)

    Article  MathSciNet  Google Scholar 

  3. Li, Z., Duan, Z., Chen, G., Huang, L.: Consensus of multi-agent systems and synchronization of complex networks: a unified viewpoint. IEEE Trans. Circuits Syst. I: Regul. Pap. 57(1), 213–224 (2010)

    Article  MathSciNet  Google Scholar 

  4. Ren, W., Beard, R., Atkins, E.M.: Information consensus in multivehicle cooperative control. IEEE Control Syst. Mag. 27(20), 71–82 (2007)

    Article  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  7. Vicsek, T., Czirók, A., Ben-Jacob, E., Cohen, I., Shochet, O.: Novel type of phase transition in a system of self-driven particles. Phys. Rev. Lett. 75(6), 1226–1229 (1995)

    Article  Google Scholar 

  8. Cao, M., Morse, A.S., Anderson, B.D.O.: Agreeing asynchronously. IEEE Trans. Autom. Control 53(8), 1826–1838 (2008)

    Article  MathSciNet  Google Scholar 

  9. Ren, W., Beard, R.: Consensus seeking in multi-agent systems under dynamically changing interaction topologies. IEEE Trans. Autom. Control 50(5), 655–661 (2005)

    Article  MathSciNet  Google Scholar 

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

    Book  MATH  Google Scholar 

  11. Xiao, F., Wang, L., Chen, J., Gao, Y.: Finite-time formation control for multi-agent systems. Automatica 45(11), 2605–2611 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  12. Yu, W., Chen, G., Cao, M.: Some necessary and sufficient conditions for second-order consensus in multi-agent dynamical systems. Automatica 46(6), 1089–1095 (2007)

    Article  MathSciNet  Google Scholar 

  13. Wen, G., Duan, Z., Yu, W., Chen, G.: Consensus in multi-agent systems with communication constraints. Int. J. Robust Nonlinear Control 22(1), 170–182 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  14. Zhao, Y., Duan, Z., Wen, G., Chen, G.: Distributed \({\rm H}_\infty \) consensus of multi-agent systems: a performance region-based approach. Int. J. Control 85(3), 332–341 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  15. Cao, Y., Ren, W.: Distributed coordinated tracking with reduced interaction via a variable structure approach. IEEE Trans. Autom. Control 57(1), 33–48 (2012)

    Article  MathSciNet  Google Scholar 

  16. Ren, W.: Multi-vehicle consensus with a time-varying reference state. Syst. Control Lett. 56(7–8), 474–483 (2007)

    Google Scholar 

  17. Li, Z., Liu, X., Ren, W., Xie, L.: Distributed tracking control for linear multi-agent systems with a leader of bounded unknown input. IEEE Trans. Autom. Control 58(2), 518–523 (2013)

    Article  MathSciNet  Google Scholar 

  18. Cao, Y., Stuart, D., Ren, W., Meng, Z.: Distributed containment control for multiple autonomous vehicles with double-integrator dynamics: algorithms and experiments. IEEE Trans. Control Syst. Technol. 19(4), 929–938 (2011)

    Article  Google Scholar 

  19. Lou, Y., Hong, Y.: Multi-leader set coordination of multi-agent systems with random switching topologies. In: Proceedings of the 49th IEEE Conference on Decision and Control, pp. 3820–3825 (2010)

    Google Scholar 

  20. Notarstefano, G., Egerstedt, M., Haque, M.: Containment in leader-follower networks with switching communication topologies. Automatica 47(5), 1035–1040 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  21. Mei, J., Ren, W., Ma, G.: Containment control for multiple Euler-Lagrange systems with parametric uncertainties in directed networks. In: Proceedings of the 2011 American Control Conference, pp. 2186–2191 (2011)

    Google Scholar 

  22. Mei, J., Ren, W., Ma, G.: Distributed containment control for multiple nonlinear systems with identical dynamics. In: Proceedings of the 30th Chinese Control Conference, pp. 6544–6549 (2011)

    Google Scholar 

  23. Kim, Y., Mesbahi, M.: On maximizing the second smallest eigenvalue of a state-dependent graph Laplacian. IEEE Trans. Autom. Control 51(1), 116–120 (2006)

    Article  MathSciNet  Google Scholar 

  24. Li, Z., Duan, Z., Chen, G.: On \({\rm H}_{\infty }\) and \({\rm H}_{2}\) performance regions of multi-agent systems. Automatica 47(4), 797–803 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  25. Olfati-Saber, R.: Ultrafast consensus in small-world networks. In: Proceedings of the 2005 American Control Conference, pp. 2371–2378 (2005)

    Google Scholar 

  26. Xiao, L., Boyd, S.: Fast linear iterations for distributed averaging. Syst. Control Lett. 53(1), 65–78 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  27. Cortés, J.: Finite-time convergent gradient flows with applications to network consensus. Automatica 42(11), 1993–2000 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  28. Cao, Y., Ren, W., Chen, F., Zong, G.: Finite-time consensus of multi-agent networks with inherent nonlinear dynamics under an undirected interaction graph. In: Proceedings of the 2011 American Control Conference, pp. 4020–4025 (2011)

    Google Scholar 

  29. Wang, X., Hong, Y.: Finite-time consensus for multi-agent networks with second-order agent dynamics. In: Proceedings of the 17th World Congress, IFAC, pp. 15185–15190 (2008)

    Google Scholar 

  30. Cao, Y., Ren, W., Meng, Z.: Decentralized finite-time sliding mode estimators and their applications in decentralized finite-time formation tracking. Syst. Control Lett. 59(9), 522–529 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  31. Li, S., Du, H., Lin, X.: Finite-time consensus algorithm for multi-agent systems with double-integrator dynamics. Automatica 47(8), 1706–1712 (2011)

    Article  MathSciNet  Google Scholar 

  32. Zhao, Y., Duan, Z., Wen, G., Zhang, Y.: Distributed finite-time tracking control for multi-agent systems: an observer-based approach. Syst. Control Lett. 62(1), 22–28 (2013)

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  Google Scholar 

  34. Hong, Y., Xu, Y., Huang, J.: Finite-time control for robot manipulators. Syst. Control Lett. 46(4), 243–253 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  35. Chu, T., Wang, L., Chen, T., Mu, S.: Complex emergent dynamics of anisotropic swarms: convergence versus oscillation. Chaos Solitons Fractals 30(4), 875–885 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  36. Chen, G., Lewis, F., Xie, L.: Finite-time distributed consensus via binary control protocols. Automatica 47(5), 1962–1968 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  37. Osborn, G.: Mnemonic for hyperbolic formulae. Math. Gaz. 2(34), 189 (1902)

    Google Scholar 

  38. Zhao, Y., Duan, Z., Wen, G.: Finite-time consensus for second-order multi-agent systems with saturated control protocols. IET Control Theory Appl. 9(3), 312–319 (2014)

    Google Scholar 

  39. Filippov, A.: Differential Equations with Discontinuous Righthand Side. Kluwer, Norwell (1988)

    Book  Google Scholar 

  40. Levant, A.: Principles of 2-sliding mode design. Automatica 43(4), 576–586 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  41. Davila, A., Moreno, J. A., Fridman, L.: Optimal Lyapunov function section for reaching time estimation of super twisting algorithm. In: Proceedings of the 48th IEEE Conference on Decision and Control, pp. 8405–8410 (2009)

    Google Scholar 

  42. Zhao, Y., Duan, Z.: Distributed finite-time containment control for multi-agent systems with multiple dynamic leaders. In: Proceedings of the 25th Chinese Control and Decision Conference, pp. 298–303 (2013)

    Google Scholar 

  43. Zhao, Y., Duan, Z., Wen, G., Chen, G.: Distributed finite-time tracking for a multi-agent system under a leader with bounded unknown acceleration. Syst. Control Lett. 81(7), 8–13 (2015)

    Google Scholar 

  44. Zhao, Y., Duan, Z.: Finite-time containment control without velocity and acceleration measurements. Nonlinear Dynamics (2015) doi:10.1007/s11071-015-2154-6

    Google Scholar 

  45. Wang, L., Xiao, F.: Finite-time consensus problems for networks of dynamic agents. IEEE Trans. Autom. Control 55(4), 950–955 (2010)

    Article  MathSciNet  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  47. Davila, J., Fridman, L., Levant, A.: Second-order sliding-mode observer for mechanical systems. IEEE Trans. Autom. Control 50(11), 1785–1789 (2005)

    Article  MathSciNet  Google Scholar 

  48. Zhao, Y., Duan, Z., Wen, G.: Distributed finite-time tracking of multiple Euler-Lagrange dynamics without velocity measurements. Int. J. Robust Nonlinear Control 25(11), 1688–1703 (2014)

    Article  Google Scholar 

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Author information

Authors and Affiliations

  1. School of Automation, Northwestern Polytechnical University, Xi’an, 710072, People’s Republic of China

    Yu Zhao

  2. Department of Mathematics, Southeast University, Nanjing, 210096, People’s Republic of China

    Guanghui Wen

  3. Department of Electronic Engineering, City University of Hong Kong, Hong Kong SAR, China

    Guanrong Chen

Authors
  1. Yu Zhao
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  2. Guanghui Wen
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  3. Guanrong Chen
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Corresponding author

Correspondence to Yu Zhao .

Editor information

Editors and Affiliations

  1. Institute of Systems Science, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China

    Jinhu Lü

  2. School of Electrical and Computer Engineering, RMIT University, Melbourne, Australia

    Xinghuo Yu

  3. Department of Electronic Engineering, City University of Hong Kong, Hong Kong, China

    Guanrong Chen

  4. Department of Mathematics, Southeast University, Nanjing, China

    Wenwu Yu

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Zhao, Y., Wen, G., Chen, G. (2016). Distributed Finite-Time Cooperative Control of Multi-agent Systems. In: Lü, J., Yu, X., Chen, G., Yu, W. (eds) Complex Systems and Networks. Understanding Complex Systems. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-47824-0_7

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  • DOI: https://doi.org/10.1007/978-3-662-47824-0_7

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-47823-3

  • Online ISBN: 978-3-662-47824-0

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