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

• Published in: International Conference on Control, Decision and Information Technologies (Online) pp. 284 - 288
• Main Authors: Mele, Adriano, Pironti, Alfredo
• Format: Conference Proceeding
• Language: English
• 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
• DOI: 10.1109/CoDIT62066.2024.10708322

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.