Stabilization of nonlinear systems by neural Lyapunov approximators and Sontag's formula

This note describes a method to train a Neural Network so that it approximates a control Lyapunov function for a nonlinear system in affine form. The network is trained in a physics-informed fashion, as the training data are generated by enforcing the negativity of the orbital derivative of the clf...

Full description

Saved in:
Bibliographic Details
Published inInternational Conference on Control, Decision and Information Technologies (Online) pp. 284 - 288
Main Authors Mele, Adriano, Pironti, Alfredo
Format Conference Proceeding
LanguageEnglish
Published IEEE 01.07.2024
Subjects
Convergence
Information technology
Knowledge engineering
Lyapunov
Lyapunov methods
neural control
Neural networks
Nonlinear systems
Orbits
Robustness
Sontag's formula
stabilization
Training data
Trajectory
universal approximation
Online AccessGet full text

Cover

More Information
Summary:This note describes a method to train a Neural Network so that it approximates a control Lyapunov function for a nonlinear system in affine form. The network is trained in a physics-informed fashion, as the training data are generated by enforcing the negativity of the orbital derivative of the clf along the system trajectories in a large set of collocation points. Positive-definiteness of the clf is guaranteed by the choice of the network structure. The network is then used to derive a stabilizing control law based on the well-known Sontag's formula. The validity of the proposed approach is illustrated through numerical examples.
ISSN:2576-3555
DOI:10.1109/CoDIT62066.2024.10708322