Perimeter flow control of bi-modal urban road networks: A robust feedback control approach

In this paper, we integrate a three-dimensional Macroscopic Fundamental Diagram (3D-MFD) modelling for mixed bi-modal urban traffic in a control framework for congested urban regions. The 3D-MFD relates the accumulation of cars and buses and the outflow (or circulating flow) in a traffic network with two modes of transport, cars and buses. We introduce the composition of traffic in the network as a parameter that affects the shape of the 3D-MFD. A linear system subject to uncertain time-varying vehicle composition is employed to describe the aggregated bi-modal traffic dynamics. This model aims at designing a proportional perimeter flow controller that guarantees robust regulation and stability, given that vehicle composition is a slow time-varying parameter. The control gain of the proposed regulator is calculated offline using semi-definite programming. In order to evaluate the proposed scheme, a simulation-based comparison of the robust perimeter flow controller with a pre-timed control plan for an area of Downtown San Francisco is carried out.