# Bayesian Algorithms Learn to Stabilize Unknown Continuous-Time Systems

arXiv: https://arxiv.org/abs/2112.15094 · HTML: https://mlsanity.com/paper/2112.15094/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 25 references that are in the map.
- First posted on arXiv 30 Dec 2021.

## Builds on (most cited first, 9 of 9)

- [Finite Time Identification in Unstable Linear Systems](https://mlsanity.com/paper/1710.01852/) (2017)
- [Black-Box Control for Linear Dynamical Systems](https://mlsanity.com/paper/2007.06650/) (2020)
- [Logarithmic regret for episodic continuous-time linear-quadratic reinforcement learning over a finite-time horizon](https://mlsanity.com/paper/2006.15316/) (2020)
- [On Adaptive Linear-Quadratic Regulators](https://mlsanity.com/paper/1806.10749/) (2018)
- [Input Perturbations for Adaptive Control and Learning](https://mlsanity.com/paper/1811.04258/) (2018)
- [Optimism-Based Adaptive Regulation of Linear-Quadratic Systems](https://mlsanity.com/paper/1711.07230/) (2017)
- [On Applications of Bootstrap in Continuous Space Reinforcement Learning](https://mlsanity.com/paper/1903.05803/) (2019)
- [Finite Time Adaptive Stabilization of LQ Systems](https://mlsanity.com/paper/1807.09120/) (2018)
- [Randomized Algorithms for Data-Driven Stabilization of Stochastic Linear Systems](https://mlsanity.com/paper/1905.06978/) (2019)

## Built on by (most cited first, 2 of 2)

- [Regret Analysis of Certainty Equivalence Policies in Continuous-Time Linear-Quadratic Systems](https://mlsanity.com/paper/2206.04434/) (2022)
- [On the Effect of Instability on Learning Continuous-Time Linear Control Systems](https://mlsanity.com/paper/2409.11327/) (2024)

## Abstract (arXiv)

Linear dynamical systems are canonical models for learning-based control of plants with uncertain dynamics. The setting consists of a stochastic differential equation that captures the state evolution of the plant understudy, while the true dynamics matrices are unknown and need to be learned from the observed data of state trajectory. An important issue is to ensure that the system is stabilized and destabilizing control actions due to model uncertainties are precluded as soon as possible. A reliable stabilization procedure for this purpose that can effectively learn from unstable data to stabilize the system in a finite time is not currently available. In this work, we propose a novel Bayesian learning algorithm that stabilizes unknown continuous-time stochastic linear systems. The presented algorithm is flexible and exposes effective stabilization performance after a remarkably short time period of interacting with the system.