Online learning of neural state-space models

2026-07-20

AI Summary

This work addresses the challenge of online learning and real-time adaptation in existing deep neural state-space models by proposing a unified framework that integrates recursive identification with batch online learning, tailored to subspace-structured encoders. It introduces, for the first time, a provably convergent recursive online learning mechanism specifically designed for encoder-based neural state-space models, accompanied by rigorous theoretical convergence guarantees. By jointly leveraging subspace encoding, recursive system identification, and an efficient batch update strategy, the proposed approach enables simultaneous real-time optimization of both latent states and model parameters directly from input-output data. Simulation results demonstrate that the method achieves high modeling accuracy while significantly enhancing online computational efficiency and dynamic adaptability.

Abstract

Recent advances in deep-learning-based nonlinear system identification have led to encoder-based estimation of neural state-space (ANN-SS) models that achieve state-of-the-art performance in offline settings by estimating initial model states from past input-output data. These methods are typically used in multiple-shooting-based offline identification, and online learning of these models remains largely unexplored. This paper presents a batch-wise learning pipeline and a direct recursive identification algorithm for subspace encoder-based ANN-SS models. We provide convergence analysis of the recursive formulation and validate its performance through extensive simulation studies. The results demonstrate that the proposed approach enables computationally efficient online adaptation with high model accuracy.

Problem

• online learning
• neural state-space models
• system identification
• recursive identification
• subspace encoder

Innovation

• online learning
• neural state-space models
• recursive identification
• subspace encoder
• convergence analysis