Close

‹ Back to the directory

Delphine Bresch-Pietri

Delphine Bresch-Pietri

Lecturer

Center · CAS

Keywords

Awards & distinctions

  • 2014 Award for Best European Thesis
  • 2013 ParisTech Thesis Prize

Team

CAS

Biography

Delphine Bresch-Pietri is a researcher specializing in the analysis and control of dynamic systems with delays, with particular expertise in control theory and system stability. Her work focuses primarily on the study of delay differential and integral equations, particularly through approaches based on Lyapunov functionals, backstepping methods, and representations using partial differential equations (PDEs). She is particularly interested in linear and nonlinear systems subject to variable or state-dependent delays, as well as delay compensation in industrial and microfluidic applications. Her research also includes the development of predictive control laws for hybrid or stochastic systems, as well as the application of these methods to real-world problems, such as energy management and microfluidic processes under the Zweifach-Fung effect.

Publication(s)

Teaching

Differential, Integral, and Stochastic Calculus I (Math1)

Lecturer

This first module of UE11 will begin with an introduction to the topology of metric spaces: open sets, closed sets, density, completeness, compactness, and the space of continuous maps between metric spaces. We will then cover the essential elements of measure theory (without doing all the proofs in lecture), which allows us to define the Lebesgue integral; we will clarify how it differs from the Riemann integral covered in preparatory classes. This integral will allow us to define the main functional spaces used in the mathematical study of equations in physics—the Lp spaces—and in particular the L2 space. We will then study Hilbert spaces (of which L2 is an archetypal example), which are generalizations of Euclidean spaces to infinite dimensions, and we will examine their main properties, in particular the existence of so-called Hilbert bases. The final part of the course will be devoted to differential calculus for mappings from R^n to R^m: the concept of a partial derivative, the differential of a mapping, the finite increase theorem in R^d, the implicit function theorem, and the local inversion theorem. Advanced tutorial sessions will allow motivated students to go beyond the concepts required for the exam: more in-depth analysis of measure and integration theory, functional analysis, Banach spaces, the Hahn-Banach theorem, operators in infinite-dimensional spaces, Sobolev spaces… This theoretical course aims to provide the foundations that will enable students to tackle the major challenges of applied mathematics, in particular the study and numerical solution of differential equations, partial differential equations, and optimization.

Differential, Integral, and Stochastic Calculus II (Math2)

Lecturer

EC2 consists of two modules: Differential Equations and Probability. The differential equations course aims to introduce students to the study of dynamical systems: existence, uniqueness, and regularity of solutions to a differential equation (Peano–Arzela, Cauchy-Lipschitz, regularity with respect to initial conditions in finite time, chaotic systems), as well as an introduction to the study of the asymptotic behavior of solutions (periodic cycles, asymptotic stability of equilibrium points, etc.) An introduction to the simulation and numerical analysis of differential equations is also provided (discretization schemes, consistency/convergence analysis, differences between explicit and implicit schemes for stiff systems, the role of symplectic schemes for Hamiltonian systems, etc.) The probability course aims to consolidate and supplement the knowledge of probability theory acquired in CPGE, but above all to develop probabilistic reasoning. In CPGE, probability was studied in the context of random phenomena with at most a countable number of possible outcomes. Probabilities defined on the real line, as well as real random variables and vectors, are first introduced within the general formalism of measure theory—covered in EC1—which allows for the inclusion of the discrete case. The concepts of independence and conditioning of random variables, sequences of random variables, and finally stochastic simulation methods are addressed in succession to cover all the prerequisites necessary for the various engineering specializations offered at the school, particularly data science.

Optimization

Course Director

This optimization course covers finite-dimensional convex nonlinear optimization. It begins by presenting the fundamentals of convex analysis and the sufficient and necessary conditions for optimality. Next, optimization algorithms—first for unconstrained problems and then for constrained problems—are discussed in detail, along with detailed proofs of convergence guarantees. Finally, elements of advanced convex analysis are covered to provide an introduction to non-smooth optimization methods. This course includes lectures (10 hours), tutorials (8 hours), and practical sessions conducted in Python (6 hours). Detailed ContentChapter 1: Optimality Conditions and Convex Analysis (3 hours)Definitions, optimality conditions, convex analysis (convex function, subdifferential, optimality conditions, strong convexity)Chapter 2: Numerical Methods for Differentiable Optimization (15 hours)2.1 Unconstrained Optimization: Gradient Methods (non-optimal step, linear search, stochastic gradient)Newton and quasi-Newton (BFGS)2.2 Constrained OptimizationLagrange multipliers, stationarity conditionsKKT conditions, active constraint algorithmsDuality and saddle points, Uzawa’s algorithmChapter 3: Introduction to Non-Smooth Optimization (6 hours) Advanced convex analysis: Fechner transform, proximal operator; subgradient methods, proximal gradient method, bundle methods

Project (PI MECATRO)

Lecturer

PhD supervision

  • 2025 Command of the Cold Spray process using reinforcement learning LAMARQUE Maxence
  • 2024 State-of-the-art observers for hydrogen fuel cells for performance and durability optimization FONTAINE Anne-Flor
  • 2023 Wind farm control strategies based on dynamic wake modeling for balancing energy production and fatigue. FALL Ousmane
  • 2020 Wind speed estimation in a wind farm BEZERRA RUFINO FERREIRA PAIVA Eduardo
  • 2019 Control based on the prediction of dynamic systems with stochastic input delay KONG Sijia
  • 2018 Design of residential photovoltaic self-consumption facility managers AMABILE Loris