The paper presents an in-context learning framework for system identification that replaces traditional two-step model estimation with a meta model mapping training data and query inputs directly to outputs. It introduces a probabilistic Transformer-based architecture capable of handling long training sequences and producing calibrated predictions over extended horizons. Additionally, the authors demonstrate that a pre-trained meta model can generate uncertainty-aware synthetic data to aid classical identification methods and validate their approach on standard nonlinear benchmarks and challenging out-of-distribution scenarios, achieving competitive accuracy and strong generalization.
By Matteo Rufolo, Dario Piga, Filippo Pura, Marco Forgione
arXiv:2505. 15497v3 Announce Type: replace Abstract: Neural networks hold great potential to act as approximate models of nonlinear dynamical systems, with the resulting neural approximations enabling verification and control of such systems.
By Frederik Baymler Mathiesen, Nikolaus Vertovec, Francesco Fabiano, Luca Laurenti, Alessandro Abate
The paper studies least squares parameter estimation for discrete‑time, unstable, closed‑loop nonlinear stochastic systems with linearly parametrised uncertainty and additive i.i.d. process noise. By perturbing the control policy with exploratory input and assuming a sub‑exponential input‑to‑state growth property, the authors derive non‑asymptotic bounds on the estimation error whenever the state trajectory remains in an informative region of the state space. When the entire state space is informative, the bounds hold with high probability for all time steps, and the authors illustrate the applicability of their results with examples that extend beyond existing work.
By Seth Siriya, Jingge Zhu, Dragan Ne\v{s}i\'c, Ye Pu
arXiv:2602. 12756v2 Announce Type: replace Abstract: Large Language Models (LLMs) have recently shown exceptional potential in time series forecasting (TSF), leveraging their inherent sequential reasoning capabilities to model complex temporal dynamics.
By Xingyu Zhang, Jingyao Wang, Zeen Song, Changwen Zheng, Wenwen Qiang
The paper discusses how offline-trained neural networks, when used in closed-loop control systems, can change the state distribution they were trained on, leading to performance degradation. It introduces a taxonomy of failure modes—Closed-Loop Identification Error, deployment-induced Action Error, and continuous Tracking Error—and uses discrete-time sensitivity analysis to explain how these errors arise. The authors propose time-scale separated online adaptation policies to mitigate distribution shift, validated on a nonlinear Duffing oscillator, showing that bounded continuous learning can prevent trajectory divergence while static deployments cannot.
By Vittorio Lippi
arXiv:2506. 01226v3 Announce Type: replace-cross Abstract: We study parameterizations of stabilizing nonlinear policies for learning-based control.
By Nicholas H. Barbara, Ruigang Wang, Alexandre Megretski, Ian R. Manchester
arXiv:2607. 14185v1 Announce Type: cross Abstract: Feedback-driven loops support iterative improvement in large language models, reinforcement learning, and autonomous discovery, yet their gains often diminish under repeated internal feedback.
By Xuening Wu, Shan Yu, Shenqin Yin
arXiv:2608. 04471v1 Announce Type: cross Abstract: Time series in real-world applications are often generated by nonlinear dynamical systems, making accurate forecasting challenging.
By Mengzhou Gao, Huangqian Yu, Pengfei Jiao
arXiv:2608.30431v1 Announce Type: cross
Abstract: By focusing on algorithmic stability as a means of establishing out-of-sample bounds, we provide a system-theoretic interpretation of generalization...
By Filippo Fabiani
arXiv:2607. 19628v1 Announce Type: new Abstract: In this work we investigate reinforcement learning (RL) as a framework for the robust control of parametrized dynamical systems in presence of measurements and model uncertainties.
By Nicol\`o Botteghi, Gabriele Pascali, Urban Fasel, Andrea Manzoni
arXiv:2412. 12036v2 Announce Type: replace Abstract: System identification, the process of deriving mathematical models of dynamical systems from observed input-output data, has undergone a paradigm shift with the advent of learning-based methods.
By Arunabh Singh, Joyjit Mukherjee
The paper presents a framework for creating neural network controllers that inherit the safety and stability guarantees of a robust model predictive control (MPC) policy. By treating the neural network’s approximation error as a bounded input disturbance and incorporating it into the MPC design, the method ensures recursive feasibility and stability before deployment. The approach is offline and constructive, requiring only Lipschitz bounds, and simulations show the learned controller matches the original MPC’s closed‑loop behavior while reducing online computation.
By Hendrik Alsmeier, Maik Pfefferkorn, Rolf Findeisen