Learning Dynamical Systems using Local Stability Priors

TL;DR

This paper introduces a novel method for learning dynamical systems by integrating local stability priors and region of attraction information, improving the accuracy and efficiency of system identification from trajectory data.

Contribution

It presents a coupled approach that simultaneously learns the vector field and the region of attraction, utilizing stability priors and Lyapunov functions for regularization.

Findings

Efficient sampling of trajectories within the estimated region of attraction.

Accurate inner approximation of the system's dynamics.

Enhanced system identification leveraging stability information.

Abstract

A coupled computational approach to simultaneously learn a vector field and the region of attraction of an equilibrium point from generated trajectories of the system is proposed. The nonlinear identification leverages the local stability information as a prior on the system, effectively endowing the estimate with this important structural property. In addition, the knowledge of the region of attraction plays an experiment design role by informing the selection of initial conditions from which trajectories are generated and by enabling the use of a Lyapunov function of the system as a regularization term. Numerical results show that the proposed method allows efficient sampling and provides an accurate estimate of the dynamics in an inner approximation of its region of attraction.