Dario Prandi - Teaching

Teaching

This page collects some material concerning my teaching activities.

Lecture notes for old courses:

Analyse et Topologie (in french, teached from 2015 to 2021 at CPES, PSL University, Paris, France)

Spectral geometry (PhD course, teached in 2022 at IMSP, Porto-Novo, Benin)

Ongoing courses

Geometric control theory

Graduate course (niveau M2/PhD)

Course on control theory from a geometric perspective.

Lecture notes (in collaboration with U. Boscain and M. Sigalotti)

Teached in various iterations since 2019 at Université Paris-Sud, ENSTA Paris, and SISSA (Trieste, Italy).

Outline of the course

Basic questions in the control formalism, some examples of control systems.

Controllability of linear systems. Lie brackets and their relation with controlled motions.

Krener's theorem, Rashevskii-Chow's theorem, and the orbit theorem.

Compatible vector fields, the strong bracket generating condition, recurrence and controllability.

Existence of minimizer in optimal control problems: Filippov's theorem.

First-order necessary conditions for optimality: Pontryagin's maximum principle.

Minimum time problems with bounded controls.

Sub-Riemannian geometry and geodesics.

Old assignments

Optimization, Control, and Data

Graduate course (niveau M2)

This course studies the relationship between data, deep neural networks, optimization, and control theory. Its goal is to present a unified perspective and show how optimization and control naturally apply to modern artificial intelligence.

Lecture notes

Teached since 2025 at Sorbonne Université.

Outline of the course

Optimization

Convex analysis: convex conjugation, subdifferentials, convex optimization.
Lagrange multipliers.
Numerical optimization methods: gradient descent, stochastic gradient, primal and dual methods.

Control

Introduction to control theory.
Linear systems: Kalman criterion, pole placement, Luenberger observer.
Optimal control.
Linear-quadratic systems: Riccati equation, Kalman filter.

Data

Linear and nonlinear neural networks, backpropagation, residual networks.
Neural ODEs and the link between backpropagation and Pontryagin's maximum principle.
Control-theoretic formulations: ensemble control and flow-matching generative models via control of the transport equation.

Old assignments

See the TA (Kevin Le Bal'ch) website for the exercises.

First session exam 2025 (corrected version)