# Joint Learning-Based Stabilization of Multiple Unknown Linear Systems

arXiv: https://arxiv.org/abs/2201.01387 · HTML: https://mlsanity.com/paper/2201.01387/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 30 references that are in the map.
- First posted on arXiv 1 Jan 2022.

## Builds on (most cited first, 20 of 20)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Few-Shot Learning via Learning the Representation, Provably](https://mlsanity.com/paper/2002.09434/) (2020)
- [The Benefit of Multitask Representation Learning](https://mlsanity.com/paper/1505.06279/) (2015)
- [Provable Meta-Learning of Linear Representations](https://mlsanity.com/paper/2002.11684/) (2020)
- [Learning Without Mixing: Towards A Sharp Analysis of Linear System Identification](https://mlsanity.com/paper/1802.08334/) (2018)
- [Non-convex Optimization for Machine Learning](https://mlsanity.com/paper/1712.07897/) (2017)
- [No Spurious Local Minima in Nonconvex Low Rank Problems: A Unified Geometric Analysis](https://mlsanity.com/paper/1704.00708/) (2017)
- [Near optimal finite time identification of arbitrary linear dynamical systems](https://mlsanity.com/paper/1812.01251/) (2018)
- [Global Optimality of Local Search for Low Rank Matrix Recovery](https://mlsanity.com/paper/1605.07221/) (2016)
- [Finite Time Identification in Unstable Linear Systems](https://mlsanity.com/paper/1710.01852/) (2017)
- [Black-Box Control for Linear Dynamical Systems](https://mlsanity.com/paper/2007.06650/) (2020)
- [On Adaptive Linear-Quadratic Regulators](https://mlsanity.com/paper/1806.10749/) (2018)
- [Input Perturbations for Adaptive Control and Learning](https://mlsanity.com/paper/1811.04258/) (2018)
- [Joint Learning of Linear Time-Invariant Dynamical Systems](https://mlsanity.com/paper/2112.10955/) (2021)
- [Optimism-Based Adaptive Regulation of Linear-Quadratic Systems](https://mlsanity.com/paper/1711.07230/) (2017)
- [On Applications of Bootstrap in Continuous Space Reinforcement Learning](https://mlsanity.com/paper/1903.05803/) (2019)
- [Finite Time Adaptive Stabilization of LQ Systems](https://mlsanity.com/paper/1807.09120/) (2018)
- [Randomized Algorithms for Data-Driven Stabilization of Stochastic Linear Systems](https://mlsanity.com/paper/1905.06978/) (2019)
- [Continuous Control with Contexts, Provably](https://mlsanity.com/paper/1910.13614/) (2019)
- [Scalable regret for learning to control network-coupled subsystems with unknown dynamics](https://mlsanity.com/paper/2108.07970/) (2021)

## Built on by (most cited first, 3 of 3)

- [Transformers as Algorithms: Generalization and Stability in In-context Learning](https://mlsanity.com/paper/2301.07067/) (2023)
- [Sample-Efficient Linear Representation Learning from Non-IID Non-Isotropic Data](https://mlsanity.com/paper/2308.04428/) (2023)
- [Learning Dynamical Systems by Leveraging Data from Similar Systems](https://mlsanity.com/paper/2302.04344/) (2023)

## Abstract (arXiv)

Learning-based control of linear systems received a lot of attentions recently. In popular settings, the true dynamical models are unknown to the decision-maker and need to be interactively learned by applying control inputs to the systems. Unlike the matured literature of efficient reinforcement learning policies for adaptive control of a single system, results on joint learning of multiple systems are not currently available. Especially, the important problem of fast and reliable joint-stabilization remains unaddressed and so is the focus of this work. We propose a novel joint learning-based stabilization algorithm for quickly learning stabilizing policies for all systems understudy, from the data of unstable state trajectories. The presented procedure is shown to be notably effective such that it stabilizes the family of dynamical systems in an extremely short time period.