On Stochastic Continuous-Time Linear System Identification for Adaptive Stabilization
Abstract
Learning to stabilize an unknown continuous-time stochastic linear system is a central problem in control theory and reinforcement learning. This paper numerically studies data-driven identification of such systems with possibly unstable dynamics for the purpose of stabilization. We present a method that learns a stabilizing gain from observed trajectories, and examine how the failure probability, namely the probability that the learned gain does not stabilize the system, depends on the amount of data, dimension, noise intensity, excitation, and controllability. Numerical experiments on an unstable batch-reactor benchmark show that the squared identification error decays inversely with the aggregate observation time, that is, the combined length of all trajectories, while the failure probability decays exponentially in the same quantity. Hence, despite instability, a single long trajectory can achieve similar stabilization performance to that of many short trajectories of the same total length. We also observe \emph{signal saturation}: stronger excitation improves stabilization only logarithmically with the excitation strength. Finally, we show experimentally that accurate identification of the full dynamics is \emph{not} necessary for successful stabilization.
Related
- Necessary and Sufficient Conditions for Adaptive Stabilizability of Continuous-Time Markov Jump Linear Stochastic Systems
- Critical Growth for Stochastic Adaptive Stabilization with an Unknown Input Gain
- Reinforcement learning for constrained stochastic linear--quadratic control in continuous time
- Resource-Adaptive Stochastic Gradient Descent for Online Linear Programming without Re-solving
- High-Probability Sampled-Data Stabilization of General Nonlinear Stochastic Systems
BibTeX
@misc{hafshejani2026stochastic,
title = {{On Stochastic Continuous-Time Linear System Identification for Adaptive Stabilization}},
author = {Reza Sadeghi Hafshejani and Mohamad Kazem Shirani Faradonbeh},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.02340},
eprint = {2611.02340},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.02340},
}
RIS
TY - UNPB
TI - On Stochastic Continuous-Time Linear System Identification for Adaptive Stabilization
AU - Reza Sadeghi Hafshejani
AU - Mohamad Kazem Shirani Faradonbeh
PY - 2026
DA - 2026/11/02
PB - arXiv
DO - 10.48550/arxiv.2611.02340
UR - https://arxiv.org/abs/2611.02340
AB - Learning to stabilize an unknown continuous-time stochastic linear system is a central problem in control theory and reinforcement learning. This paper numerically studies data-driven identification of such systems with possibly unstable dynamics for the purpose of stabilization. We present a method that learns a stabilizing gain from observed trajectories, and examine how the failure probability, namely the probability that the learned gain does not stabilize the system, depends on the amount of data, dimension, noise intensity, excitation, and controllability. Numerical experiments on an unstable batch-reactor benchmark show that the squared identification error decays inversely with the aggregate observation time, that is, the combined length of all trajectories, while the failure probability decays exponentially in the same quantity. Hence, despite instability, a single long trajectory can achieve similar stabilization performance to that of many short trajectories of the same total length. We also observe \emph{signal saturation}: stronger excitation improves stabilization only logarithmically with the excitation strength. Finally, we show experimentally that accurate identification of the full dynamics is \emph{not} necessary for successful stabilization.
ER -