Posts by Collection

A decentralized algorithm for a mean field control problem of piecewise deterministic Markov processes

Published in ESAIM: Probability and Statistics, Vol. 28, pp. 22–45, 2024

This article proposes a decentralized algorithm to solve a mean field control problem for piecewise deterministic Markov processes (PDMPs), with application to the smart charging of large EV fleets. The authors prove convergence of a stochastic Uzawa algorithm in a non-convex setting with unbounded control intensities. Download Paper

Moment Constrained Optimal Transport for Thermostatically Controlled Loads

Published in Arxiv, 2025

This work addresses the distributed control of large populations of thermostatically controlled loads (TCLs), such as water heaters, balancing global constraints like grid stability with individual physical and service limitations. We propose a framework based on Moment Constrained Optimal Transport (MCOT), which formulates the control problem as an optimal transport problem with moment constraints. This allows incorporating global consumption limits and physical feasibility directly into the control design. The high-dimensional problem is reduced to a tractable finite-dimensional formulation, and gradients are computed via Monte Carlo simulations of TCL trajectories. Unlike previous approaches, our framework allows selecting the sampling law, significantly speeding up computations and avoiding extensive state-space discretization. Numerical experiments show that the method effectively coordinates TCLs under various constraints, and we demonstrate its applicability in an online setting using simulated data from the SMACH platform. Download Paper

Moment Constrained Optimal Transport for Energy Demand Management of Heterogeneous Loads

Published in 12th International Conference of Networks, Games, Control and Optimization (NETGCOOP), 2025

This paper addresses the problem of coordinating a large population of heterogeneous electrical loads, such as electric vehicles (EVs) and water heaters (WHs), under global operational constraints. We extend the Moment Constrained Optimal Transport for Control (MCOT-C) framework to accommodate multiple classes of agents with distinct dynamics and cost structures. Our formulation relies on a mean-field limit that captures agent heterogeneity through class-specific distributions. We propose a scalable gradient descent algorithm and a Model Predictive Control (MPC) scheme that enables online adaptation of this algorithm to uncertain or progressively revealed agent information. The proposed approach is validated through numerical experiments on real datasets for EVs and WHs, demonstrating the effectiveness of this method in enforcing global constraints while preserving agent-level dynamics. Download Paper

Mean-Field Control of Heterogeneous Piecewise Deterministic Markov Processes under Grid Constraints

Published in 2025 IEEE International Conference on Communications, Control, and Computing Technologies for Smart Grids (SmartGridComm), 2025

This paper investigates mean-field control problems for large populations of agents modeled by piecewise deterministic Markov processes. Motivated by the growing need for demand-side management in power systems, we develop a decentralized control framework that accounts for key operational grid constraints such as maximum aggregate power and ramping limits. These constraints are critical to ensure the feasibility and reliability of control strategies in real-world power grids. Furthermore, we address the limitation of classical mean-field approaches that assume agent homogeneity by extending the formulation to heterogeneous populations, where agent-specific characteristics (such as charging power or battery capacity) are encoded through fixed parameters. The resulting framework enables the scalable and feasible coordination of various flexible loads. Theoretical developments are illustrated through applications to electric vehicle charging, demonstrating the impact of the proposed constraints and heterogeneity modeling on the system’s aggregate behavior. Download Paper

Mean Field Control of Thermostatically Controlled Loads as Piecewise Deterministic Markov Processes

Published in ECC 2026 (Accepted), 2025

This paper presents a mean-field control approach for Piecewise Deterministic Markov Processes (PDMPs), specifically designed for controlling a large number of agents. By modeling the interactions of a large number of agents through an aggregate cost function, the proposed method mitigates the high dimensionality of the problem by focusing on a representative agent. The contribution of this work is the application of a PDMP-based mean-field control framework to the coordination of a large population of Thermostatically Controlled Loads (TCLs). Adapting this framework to TCLs requires incorporating a quality-of-service constraint ensuring that each agent’s temperature remains within a specified comfort range. To achieve this, an additional jump intensity is introduced so that agents are very likely to switch between heating and cooling modes when they reach the boundaries of their temperature range. This extension to TCLs is demonstrated through Water Heaters (WHs) control, with a decentralized algorithm based on a dual formulation and stochastic gradient descent. The numerical results obtained illustrate this approach on two examples (signal tracking and taking into account energy price). Download Paper

Moment Constrained Optimal Transport for Control Applications

Published in TMLR, 2026

This paper introduces a one-sided relaxation of optimal transport for distributed control, where the second marginal is constrained to a moment class. The approach, motivated by mean field control problems, includes entropic regularization and enables decentralized coordination without specifying a target distribution. Applications include electric vehicle charging under grid constraints, validated on a large real-world dataset. Download Paper

Online Moment Constrained Optimal Transport applied to Electric Vehicle Charging

Published: November 20, 2024

Mean-Field Control of Heterogeneous Piecewise Deterministic Markov Processes under Grid Constraints

Published: September 30, 2025

Moment Constrained Optimal Transport for Energy Demand Management of Heterogeneous Loads

Published: October 10, 2025

Moment Constrained Optimal Transport for Energy Demand Management of Heterogeneous Loads

Published: November 18, 2025

Mathématiques pour les études scientifiques II

Exercises Lessons for L1 students (Undergraduate), Sorbonne Université, 2022

Algèbre linéaire et bilinéaire

Exercises lessons for L2 students (Undergraduate), Sorbonne Université, 2022

Differential calculus and optimization

Exercises lessons for L3 students (Undergraduate), Sorbonne Université, 2023

Modèles et Algorithmes pour les réseaux

Exercises lessons for M1 students (Graduate), ENS Paris, 2024

Biostatistiques

Lecture for CPES students in 3rd year (Undergraduate), ENS de Lyon, 2025

Modélisation Option A: Probabilités et Statistiques

Lecture and tutorials for ENS students preparing for the agrégation exam (Graduate), ENS de Lyon, 2025

Introduction to Machine Learning

Lecture and tutorials for CPES students in 3rd year (Undergraduate), ENS de Lyon, 2026

Statistiques

Tutorials for M1 ENS students (Graduate), ENS de Lyon, 2026