# Stability Bounds for Learning-Based Adaptive Control of Discrete-Time Multi-Dimensional Stochastic Linear Systems with Input Constraints

arXiv: https://arxiv.org/abs/2304.00569 · HTML: https://mlsanity.com/paper/2304.00569/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 18 references that are in the map.
- First posted on arXiv 2 Apr 2023.

## Builds on (most cited first, 7 of 7)

- [Learning Without Mixing: Towards A Sharp Analysis of Linear System Identification](https://mlsanity.com/paper/1802.08334/) (2018)
- [Naive Exploration is Optimal for Online LQR](https://mlsanity.com/paper/2001.09576/) (2020)
- [Statistical Learning Theory for Control: A Finite Sample Perspective](https://mlsanity.com/paper/2209.05423/) (2022)
- [Safe Adaptive Learning-based Control for Constrained Linear Quadratic Regulators with Regret Guarantees](https://mlsanity.com/paper/2111.00411/) (2021)
- [Thompson Sampling Achieves tilde O(√T) Regret in Linear Quadratic Control](https://mlsanity.com/paper/2206.08520/) (2022)
- [Learning-Based Adaptive Control for Stochastic Linear Systems with Input Constraints](https://mlsanity.com/paper/2209.07040/) (2022)
- [Stability and performance of stochastic predictive control](https://mlsanity.com/paper/1304.2581/) (2013)

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

- [Non-Asymptotic Bounds for Closed-Loop Identification of Sub-Exponentially Growing Nonlinear Stochastic Systems](https://mlsanity.com/paper/2412.04157/) (2024)
- [A Framework for Adaptive Stabilisation of Nonlinear Stochastic Systems](https://mlsanity.com/paper/2511.17436/) (2025)

## Abstract (arXiv)

We consider the problem of adaptive stabilization for discrete-time, multi-dimensional linear systems with bounded control input constraints and unbounded stochastic disturbances, where the parameters of the true system are unknown. To address this challenge, we propose a certainty-equivalent control scheme which combines online parameter estimation with saturated linear control. We establish the existence of a high probability stability bound on the closed-loop system, under additional assumptions on the system and noise processes. Finally, numerical examples are presented to illustrate our results.