Learning Stable Deep Dynamics Models for Partially Observed or Delayed Dynamical Systems

TL;DR

This paper introduces a neural delay differential equation framework with stability guarantees for modeling partially observed dynamical systems, enhancing safety and reliability in system identification and control.

Contribution

It proposes augmenting system states with history to improve neural ODE stability under partial observations, backed by theoretical analysis and practical experiments.

Findings

Effective stability guarantees for neural delay differential equations.

Successful system identification with partial observations.

Learning stabilizing feedback policies in delayed control scenarios.

Abstract

Learning how complex dynamical systems evolve over time is a key challenge in system identification. For safety critical systems, it is often crucial that the learned model is guaranteed to converge to some equilibrium point. To this end, neural ODEs regularized with neural Lyapunov functions are a promising approach when states are fully observed. For practical applications however, partial observations are the norm. As we will demonstrate, initialization of unobserved augmented states can become a key problem for neural ODEs. To alleviate this issue, we propose to augment the system's state with its history. Inspired by state augmentation in discrete-time systems, we thus obtain neural delay differential equations. Based on classical time delay stability analysis, we then show how to ensure stability of the learned models, and theoretically analyze our approach. Our experiments demonstrate its applicability to stable system identification of partially observed systems and learning a stabilizing feedback policy in delayed feedback control.