Encyclopedia of Systems and Control

2015 Edition
| Editors: John Baillieul, Tariq Samad

Vehicular Chains

  • Mihailo R. Jovanović
Reference work entry
DOI: https://doi.org/10.1007/978-1-4471-5058-9_221


Even since the pioneering work of Levine and Athans and Melzer and Kuo, control of vehicular formations has been a topic of active research. In spite of its apparent simplicity, this problem poses significant engineering challenges, and it has often inspired theoretical developments. In this article, we view vehicular formations as a particular instance of dynamical systems over networks and summarize fundamental performance limitations arising from the use of local feedback in formations subject to stochastic disturbances. In topology of regular lattices, it is impossible to have coherent large formations, which behave like rigid lattices, in one and two spatial dimensions; yet this is achievable in 3D. This is a consequence of the fact that, in 1D and 2D, local feedback laws with relative position measurements are ineffective in guarding against disturbances with slow temporal variations and large spatial wavelength.


Fundamental performance limitations Localized control Optimal control Relative information exchange Spatially invariant systems Toeplitz and circulant matrices Vehicular formations 
This is a preview of subscription content, log in to check access.


  1. Bamieh B, Paganini F, Dahleh MA (2002) Distributed control of spatially invariant systems. IEEE Trans Autom Control 47(7):1091–1107MathSciNetCrossRefGoogle Scholar
  2. Bamieh B, Jovanović MR, Mitra P, Patterson S (2012) Coherence in large-scale networks: dimension dependent limitations of local feedback. IEEE Trans Autom Control 57(9): 2235–2249CrossRefGoogle Scholar
  3. Bullo F, Cortés J, Martínez S (2009) Distributed control of robotic networks. Princeton University Press, PrincetonCrossRefGoogle Scholar
  4. Jovanović MR, Bamieh B (2005) On the ill-posedness of certain vehicular platoon control problems. IEEE Trans Autom Control 50(9):1307–1321CrossRefGoogle Scholar
  5. Levine WS, Athans M (1966) On the optimal error regulation of a string of moving vehicles. IEEE Trans Autom Control AC-11(3):355–361CrossRefGoogle Scholar
  6. Lin F, Fardad M, Jovanović MR (2012) Optimal control of vehicular formations with nearest neighbor interactions. IEEE Trans Autom Control 57(9):2203–2218CrossRefGoogle Scholar
  7. Melzer SM, Kuo BC (1971a) Optimal regulation of systems described by a countably infinite number of objects. Automatica 7:359–366MathSciNetCrossRefGoogle Scholar
  8. Melzer SM, Kuo BC (1971b) A closed-form solution for the optimal error regulation of a string of moving vehicles. IEEE Trans Autom Control AC-16(1):50–52CrossRefGoogle Scholar
  9. Mesbahi M, Egerstedt M (2010) Graph theoretic methods in multiagent networks. Princeton University Press, PrincetonGoogle Scholar
  10. Middleton RH, Braslavsky JH (2010) String instability in classes of linear time invariant formation control with limited communication range. IEEE Trans Autom Control 55(7):1519–1530MathSciNetCrossRefGoogle Scholar
  11. Seiler P, Pant A, Hedrick K (2004) Disturbance propagation in vehicle strings. IEEE Trans Autom Control 49(10):1835–1842MathSciNetCrossRefGoogle Scholar
  12. Swaroop D, Hedrick JK (1996) String stability of interconnected systems. IEEE Trans Autom Control 41(2):349–357MathSciNetCrossRefGoogle Scholar
  13. Swaroop D, Hedrick JK (1999) Constant spacing strategies for platooning in automated highway systems. J Dyn Syst Meas Control 121(3):462–470CrossRefGoogle Scholar
  14. Varaiya P (1993) Smart cars on smart roads: problems of control. IEEE Trans Autom Control 38(2):195–207MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer-Verlag London 2015

Authors and Affiliations

  • Mihailo R. Jovanović
    • 1
  1. 1.Department of Electrical and Computer EngineeringUniversity of MinnesotaMinneapolisUSA