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Feedback Control for Dynamic Traffic Routing in Lumped Parameter Setting

  • Pushkin Kachroo
  • Kaan M. A. Özbay
Chapter
Part of the Advances in Industrial Control book series (AIC)

Abstract

The aim of this chapter is to solve the point diversion problem between two nodes using feedback control where the dynamics of the system are written in the lumped parameter form, i.e., in terms of Ordinary Differential Equations (ODE). Chapter presents the system dynamics model for the routing problem as a space discretized version of the LWR traffic model. This model is also a direct consequence of the conservation law in the space discretized setting. The nonlinear control method of feedback linearization is presented and it is shown how that can be utilized to develop feedback traffic routing controllers. Two routes with one section each, followed by multiple sections, as well as multiple routes each with multiple sections are studied for the routing control design, and simulations are performed to show the results of the controller. Sliding mode control is used for the model with uncertainties.

References

  1. 1.
    Papgeorgiou M, Messmer A (1991) Dynamic network traffic assignment and route guidance via feedback regulation. Transp Res Record 1306:49–58Google Scholar
  2. 2.
    Kachroo P, Sastry S (2016a) Travel time dynamics for intelligent transportation systems: theory and applications. IEEE Trans Intell Transp Syst 17(2):385–394CrossRefGoogle Scholar
  3. 3.
    Kachroo P, Sastry S (2016b) Traffic assignment using a density-based travel-time function for intelligent transportation systems. IEEE Trans Intell Transp Syst 17(5):1438–1447CrossRefGoogle Scholar
  4. 4.
    Isidori A (2013) Nonlinear control systems. Springer Science & Business MediaGoogle Scholar
  5. 5.
    Slotine JJE, Li W (1991) Applied nonlinear control. Prentice HallGoogle Scholar
  6. 6.
    Godbole DN, Sastry S (1995) Approximate decoupling and asymptotic tracking for MIMO systems. IEEE Trans Autom Control 40(3):441–450MathSciNetCrossRefGoogle Scholar
  7. 7.
    Elmqvist H (1975) An interactive simulation program for nonlinear systems: user’s manualGoogle Scholar
  8. 8.
    Kachroo P, Tomizuka M (1996) Chattering reduction and error convergence in the sliding-mode control of a class of nonlinear systems. IEEE Trans Autom Control 41(7):1063–1068MathSciNetCrossRefGoogle Scholar
  9. 9.
    Kachroo P (1999) Existence of solutions to a class of nonlinear convergent chattering-free sliding mode control systems. IEEE Trans Autom Control 44(8):1620–1624MathSciNetCrossRefGoogle Scholar
  10. 10.
    Kachroo P, Tomizuka M (1992) Integral action for chattering reduction and error convergence in sliding mode control. In: American control conference, 1992. IEEE, pp 867–870Google Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Electrical and Computer EngineeringUniversity of NevadaLas VegasUSA
  2. 2.Department of Civil and Urban EngineeringNew York UniversityBrooklynUSA

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