Modeling and Control of Large-Scale Traffic Urban Networks

Carlos Canudas de Wit

In this talk we presents some results from the ERC Scale-FreeBAck [Ref.1] The presentation deals with the problems of model and control of large-scale traffic urban networks. For that we first device a traffic model that aggregates traffic flow in the plane and is described as a 2-D PDE’s. The density variable turns out to be a continuous function of the positon in the plane. Then, based on that model, we present various control strategies, including the computation of optimal operation points, Boundary flow control, and some recent results on Variable Speed control.
This talk will be structured in two parts.
In the first part, we present a new two-dimensional traffic model based on the PDEs of the type LWR. These models are macroscopic and based on a two dimensional conservation laws. We present a method to estimate the flow direction in the case where a preferred direction of flow exists. A numerical method and some simulations will be shown. We also present a validation of two-dimensional, which includes a methodology to reconstruct two-dimensional quantities from synthetic data, the estimation of the model parameters, and a comparison of the simulation results between the proposed two-dimensional model and a microscopic model (AIMSUN) [Ref.2].
In the second part, we propose an innovative control design based on the 2-D model that considerably simplifies control design for traffic systems evolving in large-scale networks. The idea consist in projecting the flow evolution into a new space where the control problem can be de-composed in a finite number of one-dimensional problems. In particular, we introduce a new coordinate transformation that transforms a 2D continuous traffic model, based on a conservation law, into a continuous set of equations with a structure similar to the classical LWR equation. Then for this system, we explicitly design a boundary controller that drives the state to any space- and time-dependent desired trajectory. Then we pose a variable speed limit (VSL) controller elaborating intrinsic properties of the model. We validate the results numerically using the network of Grenoble [Ref.3]

The talk is based on the following material:
1. ERC Scale-FreeBAck. (This project has received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation program (grant agreement N° 694209)"), see details at:
2. S. Mollier, M.-L. Delle Monache, C. Canudas-de-Wit and B. Seibold (2019). “Two-dimensional macroscopic model for large scale traffic networks.” Transportation Research Part B : Methodological, Elsevier, 2019, 122, pp.309-326.
3. Liudmila Tumash, Carlos Canudas-de-Wit, and Maria Laura Delle Monache. “Control Design for Traffic with Nonlinear Dynamics in Large Urban Networks”. Submitted to IEEE-TAC, Oct. 2020

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