# Finite Time Adaptive Stabilization of LQ Systems

arXiv: https://arxiv.org/abs/1807.09120 · HTML: https://mlsanity.com/paper/1807.09120/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Jul 2018.

## Built on by (most cited first, 7 of 7)

- [Stabilizing Dynamical Systems via Policy Gradient Methods](https://mlsanity.com/paper/2110.06418/) (2021)
- [Robust Online Control with Model Misspecification](https://mlsanity.com/paper/2107.07732/) (2021)
- [Joint Learning-Based Stabilization of Multiple Unknown Linear Systems](https://mlsanity.com/paper/2201.01387/) (2022)
- [Scalable regret for learning to control network-coupled subsystems with unknown dynamics](https://mlsanity.com/paper/2108.07970/) (2021)
- [Bayesian Algorithms Learn to Stabilize Unknown Continuous-Time Systems](https://mlsanity.com/paper/2112.15094/) (2021)
- [Safe Linear-Quadratic Dual Control with Almost Sure Performance Guarantee](https://mlsanity.com/paper/2103.13278/) (2021)
- [Reinforcement Learning Policies in Continuous-Time Linear Systems](https://mlsanity.com/paper/2109.07630/) (2021)

## Abstract (arXiv)

Stabilization of linear systems with unknown dynamics is a canonical problem in adaptive control. Since the lack of knowledge of system parameters can cause it to become destabilized, an adaptive stabilization procedure is needed prior to regulation. Therefore, the adaptive stabilization needs to be completed in finite time. In order to achieve this goal, asymptotic approaches are not very helpful. There are only a few existing non-asymptotic results and a full treatment of the problem is not currently available. In this work, leveraging the novel method of random linear feedbacks, we establish high probability guarantees for finite time stabilization. Our results hold for remarkably general settings because we carefully choose a minimal set of assumptions. These include stabilizability of the underlying system and restricting the degree of heaviness of the noise distribution. To derive our results, we also introduce a number of new concepts and technical tools to address regularity and instability of the closed-loop matrix.