Paper Overview
Online Learning for Nonlinear Dynamical Systems without the I.I.D. Condition
Takeaway: The paper develops online identification and prediction algorithms for nonlinear stochastic dynamical systems using data from a single, dependent trajectory rather than i.i.d. samples.
Why It Matters
Learning dynamical systems online is difficult because the data are generated by the system itself, often under feedback. This means samples are generally not independent, and standard persistent-excitation assumptions can be unrealistic in adaptive control and closed-loop operation.
Technical Contribution
- Proposes an online projected Newton-type algorithm for parameter estimation in nonlinear stochastic dynamical systems.
- Builds an online predictor using the current parameter estimate and analyzes prediction performance along a single trajectory.
- Uses stochastic Lyapunov and martingale estimation methods to prove that average regret converges to zero without traditional persistent excitation.
- Introduces an excitation condition for global convergence of parameter estimates that applies beyond standard PE-type trajectories.
Who Should Read This
Researchers in online learning, nonlinear system identification, stochastic dynamical systems, adaptive control, prediction, and learning-based control.
Links
@misc{zhang2025online,
title = {{Online learning for nonlinear dynamical systems without the iid condition}},
author = {Zhang, L. and Zhang, S.},
year = {2025},
eprint = {2504.02995},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2504.02995}
}