Model Equations for Multi–Agent Networks

  • Thomas Meurer
Part of the Communications and Control Engineering book series (CCE)


In the past decades, extensive research has been conducted on the cooperative control of multi–agent systems with possible applications ranging from UAVs and sensor networks over transportation systems to micro–satellite clusters (see, e.g., [19] for a rather recent overview). Thereby, different analysis and design approaches have emerged depending on the available communication topology and the considered formation control task.


Mobile Agent Agent System Communication Graph Consensus Problem Leader Agent 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Alvarez, L., Horowitz, R., Li, P.: Traffic flow control in automated highway systems. Control Eng. Practice 7, 1071–1078 (1999)CrossRefGoogle Scholar
  2. 2.
    Arenas, A., Diaz-Guilera, A., Kurths, J., Moreno, Y., Zhou, C.: Synchronization in complex networks. Physics Reports 469(3), 93–153 (2008)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Balch, T., Arkin, R.: Behavior–Based Formation Control for Multirobot Teams. IEEE Trans. Robotics Automat. 14(6), 926–939 (1998)CrossRefGoogle Scholar
  4. 4.
    Barooah, P., Mehta, P., Hespanha, J.: Mistuning–Based Control Design to Improve Closed–Loop Stability Margin of Vehicular Platoons. IEEE Trans. Automat. Control 54(9), 2100–2113 (2009)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Bullo, F., Cortés, J., Martínez, S.: Distributed Control of Robotic Networks. Applied Mathematics Series. Princeton University Press (2009)Google Scholar
  6. 6.
    Cybenko, G.: Dynamic Load Balancing for Distributed Memory Multiprocessors. J. Parallel Distr. Com. 7, 279–301 (1989)CrossRefGoogle Scholar
  7. 7.
    Dunbar, W., Murray, R.: Distributed Receding Horizon Control for Multi–Vehicle Formation Stabilization. Automatica 42(4), 549–558 (2006)MathSciNetzbMATHCrossRefGoogle Scholar
  8. 8.
    Ferrari-Trecate, G., Buffa, A., Gati, M.: Analysis and Coordination in Multi–Agent Systems Through Partial Difference Equations. IEEE Trans. Automat. Control 51(6), 1058–1063 (2006)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Frihauf, P., Krstic, M.: Rapidly convergent leader-enabled multi-agent deployment into planar curves. In: Proc. American Control Conference, St. Louis (MO), USA, pp. 1994–1999 (2009)Google Scholar
  10. 10.
    Frihauf, P., Krstic, M.: Leader–Enabled Deployment Onto Planar Curves: A PDE-Based Approach. IEEE Trans. Automat. Control 56(8), 1791–1806 (2011)MathSciNetCrossRefGoogle Scholar
  11. 11.
    Helbing, D.: Traffic and related self–driven many-particle systems. Rev. Mod. Phys. 73(4), 1067–1141 (2001)CrossRefGoogle Scholar
  12. 12.
    Jadbabaie, A., Lin, J., Morse, A.: Coordination of groups of mobile autonomous agents using nearest neighbor rules. IEEE Trans. Autom. Control 48(6), 988–1001 (2003)MathSciNetCrossRefGoogle Scholar
  13. 13.
    Ji, M., Ferrari-Trecate, G., Egerstedt, M., Buffa, A.: Containment Control in Mobile Networks. IEEE Trans. Autom. Control 53(8), 1972–1975 (2008)MathSciNetCrossRefGoogle Scholar
  14. 14.
    Kim, J., Kim, K.D., Natarajan, V., Kelly, S., Bentsman, J.: PdE–based model reference adaptive control of uncertain heterogeneous multiagent networks. Nonlinear Analysis: Hybrid Systems 2, 1152–1167 (2008)MathSciNetzbMATHCrossRefGoogle Scholar
  15. 15.
    Krstic, M., Smyshlyaev, A.: Boundary Control of PDEs: A Course on Backstepping Designs. SIAM, Philadelphia (2008)zbMATHGoogle Scholar
  16. 16.
    Mesbahi, M., Egerstedt, M.: Graph Theoretic Methods in Multiagent Networks. Princeton Univeristy Press, Princeton (2010)zbMATHGoogle Scholar
  17. 17.
    Meurer, T., Krstic, M.: Nonlinear PDE–based motion planning for the formation control of mobile agents. In: Proc (CD–ROM) 8th IFAC Symposium Nonlinear Control Systems (NOLCOS 2010), Bologna (I), pp. 599–604 (2010)Google Scholar
  18. 18.
    Meurer, T., Krstic, M.: Finite–time multi–agent deployment: A nonlinear PDE motion planning approach. Automatica 47(11), 2534–2542 (2011)MathSciNetzbMATHCrossRefGoogle Scholar
  19. 19.
    Murray, R.: Recent Research in Cooperative Control of Multivehicle Systems. J. Dyn. Meas. Contr. 129, 571–583 (2007)CrossRefGoogle Scholar
  20. 20.
    Olfati-Saber, R.: Flocking for Multi–Agent Dynamic Systems: Algortihms and Theory. IEEE Trans. Automat. Control 51(3), 401–420 (2006)MathSciNetCrossRefGoogle Scholar
  21. 21.
    Olfati-Saber, R., Murray, R.: Consensus Problems in Networks of Agents With Switching Topology and Time-Delays. IEEE Trans. Automat. Control 49(9), 1520–1533 (2004)MathSciNetCrossRefGoogle Scholar
  22. 22.
    Ren, W., Beard, R.: Formation feedback control for multiple spacecraft via virtual structures. IEE Proceedings 151(3), 357–368 (2004)Google Scholar
  23. 23.
    Ren, W., Beard, R.: Distributed Consensus in Multi–vehicle Cooperative Control. Springer, London (2008)zbMATHGoogle Scholar
  24. 24.
    Sarlette, A., Sepulchre, R.: A PDE viewpoint on basic properties of coordination algorithms with symmetries. In: Proc. IEEE Conference on Decision and Control (CDC), pp. 5139–5144 (2009)Google Scholar
  25. 25.
    Schwarz, H.: Numerische Mathematik. Teubner-Verlag, Stuttgart (1997)zbMATHCrossRefGoogle Scholar
  26. 26.
    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)CrossRefGoogle Scholar
  27. 27.
    Zhang, W., Hu, J.: Optimal multi–agent coordination under tree formation constraints. IEEE Trans. Automat. Control 53(3), 692–705 (2008)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Automation and Control Institute / E376Vienna University of TechnologyViennaAustria

Personalised recommendations