Advertisement

A constrained consensus problem using MPC

  • Jinyoung Lee
  • Jung-Su Kim
  • Hwachang Song
  • Hyungbo Shim
Technical Notes and Correspondence

Abstract

This paper presents an MPC (Model Predictive Control) based consensus algorithm which solves a consensus problem in which constraints are imposed on the increment of the state of each agent. After making an artificial consensus trajectory using a previously designed consensus algorithm, the MPC is used to make the agent track the consensus trajectory. Simulation results demonstrate the effectiveness of the proposed algorithm.

Keywords

Consensus problem MPC tracking multi-agent systems 

References

  1. [1]
    L. Chisci and G. Zappa, “Dual mode predictive tracking of piecewise constant references for constrained linear systems,” International Journal of Control, vol. 76, pp. 61–72, 2003.MathSciNetzbMATHCrossRefGoogle Scholar
  2. [2]
    J. A. Fax and R. M. Murray, “Information flow and cooperative control of vehicle formations,” IEEE Trans. on Automatic Control, vol. 49, no. 9, pp. 1465–1476, September 2004.MathSciNetCrossRefGoogle Scholar
  3. [3]
    J. Lee, J.-S. Kim, and H. Shim, “Disc margins of the discrete-time LQR and its application to consensus problem,” International Journal of Systems Science, in press, 2011.Google Scholar
  4. [4]
    D. Limon, I. Alvarado, T. Alamo, and E. F. Camacho, “MPC for tracking piecewise constant references for constrained linear systems,” Automatica, vol. 44, pp. 2382–2387, 2008.MathSciNetzbMATHCrossRefGoogle Scholar
  5. [5]
    D. Q. Mayne, J. B. Rawlings, C. V. Rao, and P. O. N. Scokaert, “Constrained model predictive control: Stability and optimality,” Automatica, vol. 36, pp. 789–814, 2000.MathSciNetzbMATHCrossRefGoogle Scholar
  6. [6]
    R. Olfati-Saber and R. M. Murray, “Consensus problem in networks of agents with switching topology and time-delays,” IEEE Trans. on Automatic Control, vol. 49, no. 9, pp. 1520–1533, September 2004.MathSciNetCrossRefGoogle Scholar
  7. [7]
    W. Ren, R. W. Beard, and E. M. Atkins, “Information consensus in multivehicle cooperative control,” IEEE Control Systems Magazine, vol. 27, no. 2, pp. 71–82, 2007.CrossRefGoogle Scholar
  8. [8]
    J. H. Seo, H. Shim, and J. Back, “Consensus of high-order linear systems using dynamic output feedback compensator: low gain approach,” Automatica, vol. 11, pp. 2659–2664, 2009.CrossRefGoogle Scholar
  9. [9]
    J. H. Seo, H. Shim, and J. Back, “Reduced-order consensus controllers for output-coupled SISO linear systems,” International Journal of Control, Automation, and Systems, vol. 8, no. 6, pp. 1356–1363, 2010.CrossRefGoogle Scholar
  10. [10]
    S. E. Tuna, “LQR-based coupling gain for synchronization of linear systems,” Arxiv:0801.3390 [math.OC], February 2008.Google Scholar
  11. [11]
    J. Wang, D. Cheng, and X. Hu, “Consensus of multi-agent linear dynamic systems,” Asian Journal of Control, vol. 10, pp. 144–155, 2008.MathSciNetCrossRefGoogle Scholar
  12. [12]
    P. Wieland, J.-S. Kim, and F. Allgöwer, “On topology and dynamics of consensus among linear highorder agents,” International Journal of Systems Science, vol. 42, no. 10, pp. 1831–1842, 2011.CrossRefGoogle Scholar

Copyright information

© Institute of Control, Robotics and Systems and The Korean Institute of Electrical Engineers and Springer-Verlag Berlin Heidelberg  2011

Authors and Affiliations

  • Jinyoung Lee
    • 1
  • Jung-Su Kim
    • 2
  • Hwachang Song
    • 2
  • Hyungbo Shim
    • 1
  1. 1.ASRI, School of Electrical Engineering and Computer ScienceSeoul National University, KwanakSeoulKorea
  2. 2.Dept. of Control and Instrumentation Eng. and Dept. of Electrical Eng., respectivelySeoul National University of Science and TechnologySeoulKorea

Personalised recommendations