Stage « Development of a mesoscopic model for traffic control systems »

Date limite de candidature : 28/02/2022
Date de début : 01/04/2022
Date de fin : 30/09/2022

Pôle : Automatique et systèmes
Type de poste : Stage
Contact : AURIOL Jean (

la fiche

Internship position
Development of a mesoscopic model for traffic control systems

Subject: Development and implementation of PDE-ODE traffic models for control purposes.

Student profile: master student (bac+5), possibly with experience in traffic control or automatics.
Duration: internship of 5-6 months, possibly starting mid February-March 2022.
Salary: 500-600 €, according to the working days of the month.
Work place: L2S, CentraleSupélec, 3, rue Joliot Curie, 91190 Gif-sur-Yvette, France.
Keywords: nonlinear control, PDE models, machine learning, parameter estimation, coding.


Jean Auriol,
(CV Hal

Alessio Iovine,

Internship description
Disruptive technologies have paved the road for new types of traffic control systems. Two main approaches have been proposed in the literature:
• traffic management through intelligent infrastructures imposing speed limitations according to traffic conditions, based on a Partial Differential Equation (PDE) modeling describing the traffic flow from a macroscopic point of view (mainly flow and density of the whole set of vehicles);
• displacement of autonomous vehicles to reduce stop-and-go waves propagation and traffic oscillations via the concepts of String Stability, based on an Ordinary Differential Equations (ODEs) modeling describing the traffic flow from a microscopic point of view (every single vehicle-driver unit and the interactions with the others).

Recently, new methods targeting to exploit the interaction between the controlled vehicles and the surrounding flow can be used to modify the traffic density to improve congestion and reduce emissions.These methods are based on a mesoscopic approach, introducing macroscopic information in a microscopic framework for improving local control strategies. A state variable describing the macroscopic information in an aggregate formalism is defined. The necessity to investigate the matching between the macroscopic vision and the microscopic one rises to verify the mixed approach’s compatibility.

The goal is to consider a vehicular platoon both from the macroscopic and microscopic points of view and to investigate and quantify the relations between the two models. To this purpose, a coupled PDEODE model is of interest. The coupling of the ODE model with the PDE is generated by taking into account the impact of macroscopic variables for the microscopic model in the vehicles’ control laws. Consequently, the PDE will depend on the speed average value of the set of vehicles generated by the ODEs. Such a mixed model could allow more accurate estimations of the system’s global (macroscopic and microscopic) state. Such reliable estimations could be used to design more efficient control algorithms that eliminate the stop-and-go oscillations.

The stage’s first target is to numerically analyze the differences between the PDE and ODE models in a similar scenario. The hired person will study already existing macroscopic and microscopic traffic models and implement them in MATLAB or Python. In the next step, she/he is expected to compare the two models. Given a set of parameters for the microscopic model, the objective is to tune the different physical parameters of the macroscopic model such that the two models present similar behaviors. This will be done using parameter identification and machine learning techniques. Then, the resulting ODEPDE model will be used to control prospects. The intern should first define a suitable definition of stability for the resulting mesoscopic system (combining global stability and string stability) before focusing on the design of a stabilizing control law. Thus this internship spans the full range from theoretical research to
simulations and data analysis. The desired steps are described as follows:

1. Literature investigation;
2. Implementation and comparison of the PDE and ODE approach for traffic control purposes;
3. Mismatch quantification by machine learning;
4. Compatibility investigation of the ODE modeling with PDE characteristics;
5. Proposition of a stability concept for the PDE-ODE model.

The stage is part on a research line on traffic control, that is carried out at L2S, CentraleSupélec.
Remark: an interested student could follow up the project with a PhD on the same subject.
Desired experience
(a) notions of dynamical systems (ODE and PDE);
(b) parameter identification by machine learning;
(c) notions of control theory, controller design, stability;
(d) interest in traffic control problem;
(e) MATLAB, python;
(f) LaTeX.

[1] H. Yu, J. Auriol, M. Krstic, « Simultaneous Downstream and Upstream Output-Feedback Stabilization of Cascaded Freeway Traffic », Automatica, 2021.
[2] M. Mirabilio, A. Iovine, E. De Santis, M. D. Di Benedetto and G. Pola, « String Stability of a Vehicular Platoon With the Use of Macroscopic Information, » in IEEE Transactions on Intelligent Transportation Systems, vol. 22, no. 9, pp. 5861-5873, Sept. 2021.
[3] S. Feng, Y. Zhang, S. E. Li, Z. Cao, H. X. Liu, andL. Li, “String stability for vehicular platoon control: Definitions and analysis methods,” Annual Reviews in Control, vol. 47, pp. 81–97, March 2019.
[4] S. Siri, C. Pasquale, S. Sacone, A. Ferrara, « Freeway traffic control: A survey », Automatica, Volume 130, 2021, 109655, ISSN 0005-1098.

Please send a CV and a motivation letter with object [stage traffic]