# Distribution Modeling and Stabilization Control for Discrete-Time Linear Random Dynamical Systems Using Ensemble Kalman Filter

## TL;DR

This paper develops a stabilization control framework for discrete-time linear stochastic systems using an ensemble Kalman filter for distribution modeling and feedback gain design, demonstrated through numerical experiments.

## Contribution

It introduces a novel output feedback stabilization method combining EnKF-based distribution modeling with feedback control for stochastic systems.

## Key findings

- Effective stabilization demonstrated through numerical experiments
- EnKF successfully models system distribution for control synthesis
- Framework advances learning-based control for stochastic systems

## Abstract

This paper studies an output feedback stabilization control framework for discrete-time linear systems with stochastic dynamics determined by an independent and identically distributed (i.i.d.) process. The controller is constructed with an ensemble Kalman filter (EnKF) and a feedback gain designed with our earlier result about state feedback control. The EnKF is also used for modeling the distribution behind the system, which is required in the feedback gain synthesis. The effectiveness of our control framework is demonstrated with numerical experiments. This study will become the first step toward the realization of learning type control using our stochastic systems control theory.