7 papers
Learning Neural Maximal Lyapunov Functions on
Adeel Akhtar, Matthieu Barreau
Establishing stability guarantees for dynamical systems on Lie groups is a fundamental challenge, as classical Lyapunov methods developed for Euclidean spaces do not directly trans…
Locally Stable Neural ODEs with Characterized Region of Attraction
Alice Harting, Karl Henrik Johansson, Sophie Tarbouriech +1
We propose a class of neural ODEs that universally approximates locally exponentially stable dynamics and the region of attraction from trajectory data. The model dynamics are cons…
Region of Attraction Estimation for Linear Quadratic Regulator, Linear and Robust Model Predictive Control on a Two-Wheeled Inverted Pendulum
Lorenzo Fici, Dalim Wahby, Alvaro Detailleur +2
Nonlinear underactuated systems such as two-wheeled inverted pendulums (TWIPs) exhibit a limited region of attraction (RoA), which defines the set of initial conditions from which…
KKL Observer Synthesis for Nonlinear Systems via Physics-Informed Learning
M. Umar B. Niazi, John Cao, Matthieu Barreau +1
This paper proposes a novel learning approach for designing Kazantzis-Kravaris or nonlinear Luenberger (KKL) observers for autonomous nonlinear systems. The design of a KKL observe…
Vanishing Stacked-Residual PINN for State Reconstruction of Hyperbolic Systems
Katayoun Eshkofti, Matthieu Barreau
In a more connected world, modeling multi-agent systems with hyperbolic partial differential equations (PDEs) offers a compact, physics-consistent description of collective dynamic…
(Un)supervised Learning of Maximal Lyapunov Functions
Matthieu Barreau, Nicola Bastianello
In this paper, we address the problem of discovering maximal Lyapunov functions, as a means of determining the region of attraction of a dynamical system. To this end, we design a…