Stochastic Decentralized Control of a Platoon of Vehicles Based on the Inclusion Principle

  • Srdjan S. StankovićEmail author
  • Milorad J. Stanojević
  • Dragoslav D. Šiljak
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 31)


In this paper the Stochastic Inclusion Principle is applied to decentralized Linear Quadratic Gaussian (LQG) suboptimal longitudinal control design of a platoon of automotive vehicles. Starting from a stochastic linearized platoon state model, input/state overlapping subsystems are identified and extracted after an adequate expansion. An algorithm for approximate LQG optimization of these subsystems is developed in accordance with their hierarchical lower-block-triangular (LBT) structure. Vehicle controllers obtained after contraction, which leaves the local Kalman filters uncontracted, provide high performance tracking and noise immunity. Simulation results illustrate characteristic properties of the proposed algorithm.


Original Space Linear Quadratic Linear Quadratic Gaussian Preceding Vehicle State Feedback Gain 
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.



We are grateful to the staff of the PATH Program from the University of Berkeley for real measurement data.

This work is supported by Project Grant III44004 (2011–2014) financed by the Ministry of Education and Science, Republic of Serbia.


  1. 1.
    Anderson, B.D.O., Moore, J.B.: Optimal Control: Linear Quadratic Methods. Prentice Hall, NJ (1990)zbMATHGoogle Scholar
  2. 2.
    Godbole, D.N., Eskafi, F.H., Varaiya, P.P, In: Proceedings of 13th IFAC Congress, San Francisco, CA, L, 121–126 (1996)Google Scholar
  3. 3.
    Iftar, A., Özgüner, Ü.: Contractible controller design and optimal control with state and input inclusion. Automatica 26, 593–597 (1990)zbMATHCrossRefGoogle Scholar
  4. 4.
    Kwakernaak, H., Sivan, R.: Linear Optimal Control Systems. Wiley, New York (1972)zbMATHGoogle Scholar
  5. 5.
    Levine, W.S., Athans, M.: On the optimal error regulation of a string of moving vehicles. IEEE Trans. Autom. Contr. 11, 355–361 (1966)CrossRefGoogle Scholar
  6. 6.
    Özgüner, Ü., Perkins, W.R.: Optimal control of multilevel large-scale systems. Int. J. Contr. 28, 967–980 (1978)zbMATHCrossRefGoogle Scholar
  7. 7.
    Sheikholeslam, S., Desoer, C.A.: Control of interconnected nonlinear dynamic systems, the platoon problem. IEEE Trans. Autom. Contr. 37, 806–810 (1992)MathSciNetzbMATHCrossRefGoogle Scholar
  8. 8.
    Shladover, S.E.: Longitudinal control of automotive vehicles in close formation platoons. J. Dyn. Syst. Meas. Contr. 113, 231–241 (1991)CrossRefGoogle Scholar
  9. 9.
    Stanković, S.S., Šiljak, D.D.: Sequential LQG optimization of hiererchically structured systems. Automatica 25, 545–559 (1989)zbMATHCrossRefGoogle Scholar
  10. 10.
    Stanković, S.S., Šiljak, D.D.: Contractibility of overlapping decentralized control. Syst. Contr. Lett. 44, 189–199 (2001)zbMATHCrossRefGoogle Scholar
  11. 11.
    Stanković S.S., Stanojević, M.J.: Decentralized control of a platoon of vehicles based on a reduced measurement set. In: Proceedings of the 1st International Symposium and 10th Balkan Conference on Operations Research, (BALCOR 2011), Thessaloniki, 22–25 September, Greece, vol. 2, pp. 417–424 (2011)Google Scholar
  12. 12.
    Shladover, S.E., et al.: Automatic vehicle control developments in the PATH program. IEEE Trans. Veh. Tech. 40, 114–130 (1991)CrossRefGoogle Scholar
  13. 13.
    Šiljak, D.D.: Decentralized Control of Complex Systems. Academic, London (1991)Google Scholar
  14. 14.
    Stanković, S.S., Chen, X.B., Šiljak, D.D.: Stochastic inclusion principle applied to decentralized overlapping suboptimal LQG control. In: Proceedings of the 13th IFAC Congress, San Francisco, vol. L, pp. 12–18 (1996)Google Scholar
  15. 15.
    Stanković, S. S., M. J. Stanojević, Šiljak, D.D.: Decentralized suboptimal LQ control of a platoon of vehicles. In: Proceedings of the 8th IFAC/IFIP/IFORS Symp. Trans. Syst., Chania, Greece, vol. 1, pp. 81–86 (1997)Google Scholar
  16. 16.
    Stanković, S.S., Chen, X.B., Mataušek, M.R., Šiljak, D.D.: Stochastic inclusion principle applied to decentralized automatic generation control. Int. J. Contr. 72, 276–288 (1999)zbMATHCrossRefGoogle Scholar
  17. 17.
    Stanković, S.S., Stanojević M.J., Šiljak, D.D.: Decentralized overlapping control of a platoon of vehicles. IEEE Trans. Contr. Syst. Tech. 8(5), 816–832 (2000)CrossRefGoogle Scholar
  18. 18.
    Swaroop, D., Hedrick, J.K.: String stability of interconnected systems. IEEE Trans. Autom. Contr. 41, 349–357 (1996)MathSciNetzbMATHCrossRefGoogle Scholar
  19. 19.
    Varaiya, P.: Smart cars on smart roads: problems of control. IEEE Trans. Autom. Contr. 38, 195–207 (1993)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Srdjan S. Stanković
    • 1
    Email author
  • Milorad J. Stanojević
    • 2
  • Dragoslav D. Šiljak
    • 3
  1. 1.Faculty of Electrical EngineeringUniversity of BelgradeBelgradeSerbia
  2. 2.Faculty of Transport and Traffic EngineeringUniversity of BelgradeBelgradeSerbia
  3. 3.School of EngineeringSanta Clara UniversitySanta ClaraUSA

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