Hierarchical Coordinated Freeway On-Ramp Metering Using Switching System Theory

Abstract

This paper deals with the problem of freeway traffic control through ramp metering to enhance their efficiency. The traffic is often modeled by a nonlinear hyperbolic conservation laws that may develop and propagate shock waves. The Cell Transmission model (CTM) developed in (Daganzo [1994]),(C. F. Daganzo [1995]) is taken in this work since linear control tools can be used for analysis and control design. This model is extended with parametric uncertainties. A hierarchical control scheme with two levels is considered. The first level gives the optimal densities to apply on the freeway. The second level is charged for compensating local parametric uncertainties and disturbances (on-ramp demands, boundary conditions). These controllers are designed using switching control theory. A real-data based simulation is used to validate the effectiveness of the proposed control approach.

Robust design of a switched PI controller for an uncertain traffic model

“…We obtain the following state feedback gain: The sensitivity functions between disturbances and ρ 3 are given in Figure 7, we can see only 6 sensitivity function because the matrix E a4 has several columns of zeros. The attenuation is good in low frequency, where disturbances occurs [10]. In the scenario we have chosen, the system has to track a congestion front which propagates backward then forward.…”

Distributed identification of the Cell Transmission traffic model: A case study

“…For the region j = 100, δ 100 = [1, 1, 0, 0, 1, 0, 0, 0] T , so the cells 1, 2 and 5 are in free flow state, while the rest are under congestion. In the notation used in [11], δ 100 = [F, F,C,C, F,C,C,C] T where F stands for free flow and C for congested flow.…”

“…the Cell Transmission Model (CTM), developed in [5], [6]. This model is a linear switching system [11], and the parameters to be identified characterize the dynamics of different cells. Those parameters are: the free velocity, the maximum density, and the backward congestion propagation speed.…”

Smooth Switching H∞ PI Controller for Local Traffic On-ramp Metering, an LMI Approach

“…The aim of local controllers is to ensure that the system really tracks optimal references. The Cell Transmission Model (CTM) proposed in Daganzo [1994] has been extended with parametric uncertainties in Lemarchand et al [2010b]. Using this model, a bank of robust switched PI controller can be designed as proposed in Lemarchand et al [2010a].…”