# Learning Stabilizing Controllers for Unstable Linear Quadratic Regulators from a Single Trajectory

arXiv: https://arxiv.org/abs/2006.11022 · HTML: https://mlsanity.com/paper/2006.11022/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Jun 2020.

## Built on by (most cited first, 1 of 1)

- [Direct Data-Driven Discounted Infinite Horizon Linear Quadratic Regulator with Robustness Guarantees](https://mlsanity.com/paper/2409.10703/) (2024)

## Abstract (arXiv)

The principal task to control dynamical systems is to ensure their stability. When the system is unknown, robust approaches are promising since they aim to stabilize a large set of plausible systems simultaneously. We study linear controllers under quadratic costs model also known as linear quadratic regulators (LQR). We present two different semi-definite programs (SDP) which results in a controller that stabilizes all systems within an ellipsoid uncertainty set. We further show that the feasibility conditions of the proposed SDPs are equivalent. Using the derived robust controller syntheses, we propose an efficient data dependent algorithm -- textsceXploration -- that with high probability quickly identifies a stabilizing controller. Our approach can be used to initialize existing algorithms that require a stabilizing controller as an input while adding constant to the regret. We further propose different heuristics which empirically reduce the number of steps taken by textsceXploration and reduce the suffered cost while searching for a stabilizing controller.