Feedback Control for Dynamic Traffic Routing in Lumped Parameter Setting

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.

This chapter is adapted from the paper by Pushkin Kachroo and Kaan Özbay, “Solution to the User Equilibrium Dynamic Traffic Routing Problem using Feedback Linearization,” Transportation Research: Part B, Vol. 32, No. 5, pp. 343–360, DOI: https://doi.org/10.1016/S0191-2615(97)00031-3, ©1998, with permission from Elsevier.