Table of Contents Author Guidelines Submit a Manuscript
Mathematical Problems in Engineering
Volume 2013, Article ID 762861, 10 pages
http://dx.doi.org/10.1155/2013/762861
Research Article

Impulsive Consensus for Leader-Following Multiagent Systems with Fixed and Switching Topology

1Department of Automation, Wuhan University, Wuhan 430072, China
2College of Automation, Huazhong University of Science and Technology, Wuhan 430074, China

Received 29 March 2013; Accepted 2 June 2013

Academic Editor: Chuandong Li

Copyright © 2013 Zhi-Wei Liu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. F. Bullo, J. Cortés, and S. Martínez, Distributed Control of Robotic Networks, Princeton Series in Applied Mathematics, Princeton University Press, Princeton, NJ, USA, 2009. View at Zentralblatt MATH · View at MathSciNet
  2. Z.-H. Guan, Z.-W. Liu, G. Feng, and Y.-W. Wang, “Synchronization of complex dynamical networks with time-varying delays via impulsive distributed control,” IEEE Transactions on Circuits and Systems. I, vol. 57, no. 8, pp. 2182–2195, 2010. View at Publisher · View at Google Scholar · View at MathSciNet
  3. R. Carli, A. Chiuso, L. Schenato, and S. Zampieri, “Distributed Kalman filtering based on consensus strategies,” IEEE Journal on Selected Areas in Communications, vol. 26, no. 4, pp. 622–633, 2008. View at Publisher · View at Google Scholar · View at Scopus
  4. A. Kashyap, T. Başar, and R. Srikant, “Quantized consensus,” Automatica, vol. 43, no. 7, pp. 1192–1203, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. R. Olfati-Saber and R. M. Murray, “Consensus problems in networks of agents with switching topology and time-delays,” IEEE Transactions on Automatic Control, vol. 49, no. 9, pp. 1520–1533, 2004. View at Publisher · View at Google Scholar · View at MathSciNet
  6. L. Moreau, “Stability of multiagent systems with time-dependent communication links,” IEEE Transactions on Automatic Control, vol. 50, no. 2, pp. 169–182, 2005. View at Publisher · View at Google Scholar · View at MathSciNet
  7. F. Xiao and L. Wang, “Asynchronous consensus in continuous-time multi-agent systems with switching topology and time-varying delays,” IEEE Transactions on Automatic Control, vol. 53, no. 8, pp. 1804–1816, 2008. View at Publisher · View at Google Scholar · View at MathSciNet
  8. Z. Lin, B. Francis, and M. Maggiore, “State agreement for continuous-time coupled nonlinear systems,” SIAM Journal on Control and Optimization, vol. 46, no. 1, pp. 288–307, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. Q. Hui and W. M. Haddad, “Distributed nonlinear control algorithms for network consensus,” Automatica, vol. 44, no. 9, pp. 2375–2381, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. Z.-W. Liu, Z.-H. Guan, T. Li, X.-H. Zhang, and J.-W. Xiao, “Quantized consensus of multi-agent systems via broadcast gossip algorithms,” Asian Journal of Control, vol. 14, no. 6, pp. 1634–1642, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  11. T. Li and J.-F. Zhang, “Consensus conditions of multi-agent systems with time-varying topologies and stochastic communication noises,” IEEE Transactions on Automatic Control, vol. 55, no. 9, pp. 2043–2057, 2010. View at Publisher · View at Google Scholar · View at MathSciNet
  12. P. Lin and Y. Jia, “Consensus of second-order discrete-time multi-agent systems with nonuniform time-delays and dynamically changing topologies,” Automatica, vol. 45, no. 9, pp. 2154–2158, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  13. W. Yu, G. Chen, and M. Cao, “Some necessary and sufficient conditions for second-order consensus in multi-agent dynamical systems,” Automatica, vol. 46, no. 6, pp. 1089–1095, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  14. Y. Hong, J. Hu, and L. Gao, “Tracking control for multi-agent consensus with an active leader and variable topology,” Automatica, vol. 42, no. 7, pp. 1177–1182, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  15. D. V. Dimarogonas, P. Tsiotras, and K. J. Kyriakopoulos, “Leader-follower cooperative attitude control of multiple rigid bodies,” in Proceedings of the American Control Conference, pp. 801–806, Seattle, Wash, USA, 2008. View at Publisher · View at Google Scholar
  16. A. Jadbabaie, J. Lin, and A. S. Morse, “Coordination of groups of mobile autonomous agents using nearest neighbor rules,” IEEE Transactions on Automatic Control, vol. 48, no. 6, pp. 988–1001, 2003. View at Publisher · View at Google Scholar · View at MathSciNet
  17. Y. Cao and W. Ren, “Distributed coordinated tracking with reduced interaction via a variable structure approach,” IEEE Transactions on Automatic Control, vol. 57, no. 1, pp. 33–48, 2012. View at Publisher · View at Google Scholar · View at Scopus
  18. H. Su, X. Wang, and Z. Lin, “Flocking of multi-agents with a virtual leader,” IEEE Transactions on Automatic Control, vol. 54, no. 2, pp. 293–307, 2009. View at Publisher · View at Google Scholar · View at MathSciNet
  19. W. Zhu and D. Cheng, “Leader-following consensus of second-order agents with multiple time-varying delays,” Automatica, vol. 46, no. 12, pp. 1994–1999, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  20. Z. Meng, W. Ren, Y. Cao, and Z. You, “Leaderless and leader-following consensus with communication and input delays under a directed network topology,” IEEE Transactions on Systems, Man, and Cybernetics B, vol. 41, no. 1, pp. 75–88, 2011. View at Publisher · View at Google Scholar · View at Scopus
  21. T. Li and J. Zhang, “Sampled-data based average consensus with measurement noises: convergence analysis and uncertainty principle,” Science in China F, vol. 52, no. 11, pp. 2089–2103, 2009. View at Publisher · View at Google Scholar · View at MathSciNet
  22. Y. Cao and W. Ren, “Sampled-data discrete-time coordination algorithms for double-integrator dynamics under dynamic directed interaction,” International Journal of Control, vol. 83, no. 3, pp. 506–515, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  23. Y. Zhang and Y.-P. Tian, “Consensus of data-sampled multi-agent systems with random communication delay and packet loss,” IEEE Transactions on Automatic Control, vol. 55, no. 4, pp. 939–943, 2010. View at Publisher · View at Google Scholar · View at MathSciNet
  24. H. Liu, G. Xie, and L. Wang, “Necessary and sufficient conditions for solving consensus problems of double-integrator dynamics via sampled control,” International Journal of Robust and Nonlinear Control, vol. 20, no. 15, pp. 1706–1722, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  25. Y. Gao and L. Wang, “Consensus of multiple double-integrator agents with intermittent measurement,” International Journal of Robust and Nonlinear Control, vol. 20, no. 10, pp. 1140–1155, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  26. X. Liu and K. Rohlf, “Impulsive control of a Lotka-Volterra system,” IMA Journal of Mathematical Control and Information, vol. 15, no. 3, pp. 269–284, 1998. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  27. J. E. Prussing and J.-H. Chiu, “Optimal multiple-impulse time-fixed rendezvous between circular orbits,” Journal of Guidance, Control, and Dynamics, vol. 9, no. 1, pp. 17–22, 1986. View at Google Scholar · View at Scopus
  28. J. F. Eastham and K. J. Hastings, “Optimal impulse control of portfolios,” Mathematics of Operations Research, vol. 13, no. 4, pp. 588–605, 1988. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  29. G. Zhang, Z. Liu, and Z. Ma, “Synchronization of complex dynamical networks via impulsive control,” Chaos, vol. 17, no. 4, Article ID 043126, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  30. B. Liu, X. Liu, G. Chen, and H. Wang, “Robust impulsive synchronization of uncertain dynamical networks,” IEEE Transactions on Circuits and Systems. I, vol. 52, no. 7, pp. 1431–1441, 2005. View at Publisher · View at Google Scholar · View at MathSciNet
  31. J. Lu, D. W. C. Ho, and J. Cao, “A unified synchronization criterion for impulsive dynamical networks,” Automatica, vol. 46, no. 7, pp. 1215–1221, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  32. Q. Zhang, S. Chen, and C. Yu, “Impulsive consensus problem of second-order multi-agent systems with switching topologies,” Communications in Nonlinear Science and Numerical Simulation, vol. 17, no. 1, pp. 9–16, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  33. Y. Qian, X. Wu, J. Lu, and J.-A. Lu, “Second-order consensus of multi-agent systems with nonlinear dynamics via impulsive control,” Neurocomputing, 2013. View at Publisher · View at Google Scholar
  34. Z.-H. Guan, Z.-W. Liu, G. Feng, and M. Jian, “Impulsive consensus algorithms for second-order multi-agent networks with sampled information,” Automatica, vol. 48, no. 7, pp. 1397–1404, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  35. Z.-W. Liu, Z.-H. Guan, X. Shen, and G. Feng, “Consensus of multi-agent networks with aperiodic sampled communication via impulsive algorithms using position-only measurements,” IEEE Transactions on Automatic Control, vol. 57, no. 10, pp. 2639–2643, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  36. K. Ogata, Discrete-Time Control Systems, Prentice-Hall, Englewood Cliffs, NJ, USA, 2nd edition, 1995.
  37. P. Parks and V. Hahn, Stability Theory, Prentice Hall, Englewood Cliffs, NJ, USA, 1993.
  38. W. Yu, W. X. Zheng, G. Chen, W. Ren, and J. Cao, “Second-order consensus in multi-agent dynamical systems with sampled position data,” Automatica, vol. 47, no. 7, pp. 1496–1503, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  39. J. Wolfowitz, “Products of indecomposable, aperiodic, stochastic matrices,” Proceedings of the American Mathematical Society, vol. 14, pp. 733–737, 1963. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  40. W. Ren and R. W. Beard, “Consensus seeking in multiagent systems under dynamically changing interaction topologies,” IEEE Transactions on Automatic Control, vol. 50, no. 5, pp. 655–661, 2005. View at Publisher · View at Google Scholar · View at MathSciNet