# Randomized Algorithms for Data-Driven Stabilization of Stochastic Linear Systems

## TL;DR

This paper introduces two randomized algorithms for stabilizing stochastic linear systems with unknown parameters, analyzing their performance and showing that sufficient randomizations ensure fast stabilization.

## Contribution

It provides a detailed analysis of the stabilization speed and failure probability of two novel data-driven randomized control algorithms.

## Key findings

- Fast stabilization is guaranteed with enough independent randomizations.
- Performance depends on the magnitude and frequency of randomizations.
- Numerical analysis supports the effectiveness of the proposed methods.

## Abstract

Data-driven control strategies for dynamical systems with unknown parameters are popular in theory and applications. An essential problem is to prevent stochastic linear systems becoming destabilized, due to the uncertainty of the decision-maker about the dynamical parameter. Two randomized algorithms are proposed for this problem, but the performance is not sufficiently investigated. Further, the effect of key parameters of the algorithms such as the magnitude and the frequency of applying the randomizations is not currently available. This work studies the stabilization speed and the failure probability of data-driven procedures. We provide numerical analyses for the performance of two methods: stochastic feedback, and stochastic parameter. The presented results imply that as long as the number of statistically independent randomizations is not too small, fast stabilization is guaranteed.