TL Thibault Liard

Associate Professor in Mathematics

Thibault Liard

My research focuses on the modelling and control of PDE systems, with applications to traffic flow and collective dynamics such as ant foraging.

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Thibault Liard

University of Limoges

XLIM Research Institute
MOD Team — MATHIS Department

Limoges, France

Control of PDEs Conservation Laws Optimisation Machine Learning Traffic Flow Ant dynamics

Research

Research interests

My work lies at the interface of mathematical analysis, control theory, numerical optimisation.

Traffic flow modelling and control

Mathematical modelling, observation, optimisation and control of road traffic using conservation laws and coupled PDE–ODE systems.

Without control

Total fuel consumption
494 L

With Autonomous Vehicle control

Total fuel consumption
480 L

Collective dynamics

Mathematical modelling of collective behaviour, with a particular focus on ant foraging and the interaction between population dynamics and pheromone trails.

Publications

Research Articles

View the complete list on Google Scholar →

Submitted papers in 2026

  1. Strongly coupled second-order hyperbolic ODE-PDE systems with moving flux constraints: analysis and existence of solutions
    A. Hayat, T. Liard, B. Piccoli — submitted (2026).
  2. Imaging the building blocks of ant pheromone communication
    L.A. Poissonnier, E. Amichot, J. Brevier, T. Liard, P. Bon — submitted (2026).

Journal Articles

  1. A PDE-ODE model for traffic control with autonomous vehicles
    T. Liard, R. Stern and M.L. Delle Monache, Networks and Heterogeneous Media, Vol. 18, Issue 3, 1190–1206 (2023).
  2. Analysis and numerical solvability of backward-forward conservation laws
    T. Liard and E. Zuazua, SIAM Journal on Mathematical Analysis, Vol. 55, No. 4, 1949–1968 (2023).
  3. Super-twisting sliding mode control for the stabilization of a linear hyperbolic system
    I. Balogoun, S. Marx, T. Liard, F. Plestan, IEEE Control Systems Letters, Vol. 7, 1–6 (2023).
  4. Boundary sliding mode control of a system of linear hyperbolic equations: a Lyapunov approach
    T. Liard, I. Balogoun, S. Marx, F. Plestan, Automatica, Vol. 135, 109964 (2022).
  5. Initial data identification for the one-dimensional Burgers equation
    T. Liard and E. Zuazua, IEEE Transactions on Automatic Control Vol. 67, No. 6, 3098-3104 (2021).
  6. On entropic solutions to conservation laws coupled with moving bottlenecks
    T. Liard and B. Piccoli, Communications in Mathematical Sciences, Vol. 19, No. 4, 919–945 (2021).
  7. A controlled multiscale model for traffic regulation via autonomous vehicles
    M. Garavello, P. Goatin, T. Liard and B. Piccoli, Journal of Differential Equations Vol. 269, Issue 7, 6088-6124 (2020).
  8. Traffic reconstruction using autonomous vehicles
    M.L. Delle Monache, T. Liard, B. Piccoli, R. Stern, D. Work, SIAM Journal on Applied Mathematics, Vol. 79, No. 5, 1748–1767 (2019).
  9. Well-posedness for scalar conservation laws with moving flux constraints
    T. Liard and B. Piccoli, SIAM Journal on Applied Mathematics, No. 2, 641–667 (2019).
  10. Non-localization of eigenfunctions for Sturm-Liouville operators
    T. Liard, P. Lissy and Y. Privat, Journal of Differential Equations, 264, No. 4, 2449–2494 (2018).
  11. A Kalman rank condition for the indirect controllability of coupled systems of linear operator groups
    T. Liard and P. Lissy, Mathematics of Control, Signals, and Systems, 29:9 (2017).
  12. How to estimate observability constants of one-dimensional wave equations? Propagation versus Spectral methods
    A. Haraux, T. Liard and Y. Privat, Journal of Evolution Equations, 16, 825–856 (2016).

Conference Proceedings

  1. Traffic Flow Reconstruction from Limited Collected Data
    N. Baloul, A. Hayat, T. Liard and P. Lissy, 2025 IEEE 64th Conference on Decision and Control (CDC), 7981–7986 (2025).
  2. Optimal driving strategies for traffic control with autonomous vehicles
    T. Liard, R. Stern and M.L. Delle Monache, IFAC World Congress, Berlin, Germany, IFAC-PapersOnLine 53(2), 5322–5329 (2020).
  3. The Riemann Problem for the GARZ Model with a moving constraint
    T. Liard, F. Marcellini, B. Piccoli, XVII International Conference on Hyperbolic Problems (HYP2018), Vol. 10, 524–530 (2018).

Book Chapters

  1. Feedback Control Algorithms for the Dissipation of Traffic Waves with Autonomous Vehicles
    M.L. Delle Monache et al., Computational Intelligence and Optimization Methods for Control Engineering, Springer Optimization and Its Applications, Vol. 150, Springer, Cham (2019).

Projects

Research Projects and Funding

ANR JCJC · 2024–2028

CDDTM

Connecting Deep Learning with Dynamic Models for Traffic Flow Management

Systematic and robust feedback controllers for traffic monitoring and management are developed by combining dynamical systems with machine learning and reinforcement learning.

Principal Investigator
Funding awarded: €242,247

Sci-ty · 2026–2027

CORTEX

Coordination des Réseaux de Trafic à grande Échelle

Development of methods and software for the observation, prediction and control of large-scale urban traffic networks. The CORTEX software prototype is currently being registered with the APP (French Software Protection Agency).

Principal Investigator
Funding awarded: €50,000

Exploratory Call for Projects·2024

MCF

Modeling the Impact of Individual and Collective Cognition on Ant Foraging

Mathematical and experimental study of the role of individual and collective cognition in ant foraging dynamics.

Principal Investigator
Funding awarded: €12,500

University of Limoges · AOI 2025

RLPS

Reinforcement learning for polynomial system solving

Development of reinforcement learning approaches combined with homotopy continuation for solving polynomial systems

Principal Investigator
Funding awarded: €4,500

Supervision

Supervision

PhD Student

Nail Baloul, since October 2024 — 45% co-supervision with Amaury Hayat and Pierre Lissy.

Postdoctoral Researchers

Laure Anne Poissonnier, June 2025 – August 2026.
Kala Agbo bidi, October 2025 – September 2026.

Internships and Master's Students

Shun Arakawa, 2025–2026, 6 months — co-advised with Olivier Ruatta and Tristan Vaccon.
Kein Ebindja, 2025, 3 months.
Alexandre Paulin, 2024, 2 months — co-advised with Francisco Silva.
Anais Rat, 2017, 2 months — co-advised with Benedetto Piccoli.

Academic Service

Academic Service

Administrative Responsibilities

Coordinator for Master 2 internships; organizer of the MOD team seminar; communication coordinator for the MATHIS research axis; member of the Master 1 examination board.

Reviewing Activities

Reviewer for journals and international conferences including Automatica, IEEE Transactions on Automatic Control, IEEE Control Systems Letters, IEEE Transactions on Control Systems Technology, Journal of Differential Equations, Transportation Research Part B, Journal of Mathematical Analysis and Applications, and IFAC and ACC conferences.

Teaching

Approximately 250–300 hours of teaching per year at undergraduate and Master's levels.

Courses taught include Fundamentals of Mathematics; Mathematics Reinforcement; Introduction to Machine Learning; Linear and Quadratic Optimization; Convex Analysis; Splitting Methods for Convex Analysis; and Numerical Analysis.

Contact

Get in touch

For scientific questions, collaboration proposals, supervision enquiries or invitations, please feel free to contact me by email.

Thibault Liard
Associate Professor in Mathematics

University of Limoges — XLIM
Limoges, France

thibault.liard@unilim.fr