# A New Approach to Controlling Linear Dynamical Systems

arXiv: https://arxiv.org/abs/2504.03952 · HTML: https://mlsanity.com/paper/2504.03952/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 37 references that are in the map.
- First posted on arXiv 4 Apr 2025.

## Builds on (most cited first, 21 of 21)

- [Introduction to Online Convex Optimization](https://mlsanity.com/paper/1909.05207/) (2019)
- [Online Control with Adversarial Disturbances](https://mlsanity.com/paper/1902.08721/) (2019)
- [Near optimal finite time identification of arbitrary linear dynamical systems](https://mlsanity.com/paper/1812.01251/) (2018)
- [Regret Bounds for Robust Adaptive Control of the Linear Quadratic Regulator](https://mlsanity.com/paper/1805.09388/) (2018)
- [Improper Learning for Non-Stochastic Control](https://mlsanity.com/paper/2001.09254/) (2020)
- [Gradient Descent Learns Linear Dynamical Systems](https://mlsanity.com/paper/1609.05191/) (2016)
- [Learning Linear-Quadratic Regulators Efficiently with only √T Regret](https://mlsanity.com/paper/1902.06223/) (2019)
- [Online Linear Quadratic Control](https://mlsanity.com/paper/1806.07104/) (2018)
- [Learning Linear Dynamical Systems via Spectral Filtering](https://mlsanity.com/paper/1711.00946/) (2017)
- [Logarithmic Regret for Adversarial Online Control](https://mlsanity.com/paper/2003.00189/) (2020)
- [Logarithmic Regret for Online Control](https://mlsanity.com/paper/1909.05062/) (2019)
- [Spectral Filtering for General Linear Dynamical Systems](https://mlsanity.com/paper/1802.03981/) (2018)
- [A New Approach to Learning Linear Dynamical Systems](https://mlsanity.com/paper/2301.09519/) (2023)
- [Introduction to Online Control](https://mlsanity.com/paper/2211.09619/) (2022)
- [Learning Mixtures of Linear Dynamical Systems](https://mlsanity.com/paper/2201.11211/) (2022)
- [Online Control of Unknown Time-Varying Dynamical Systems](https://mlsanity.com/paper/2202.07890/) (2022)
- [Tensor Decompositions Meet Control Theory: Learning General Mixtures of Linear Dynamical Systems](https://mlsanity.com/paper/2307.06538/) (2023)
- [Optimal Rates for Bandit Nonstochastic Control](https://mlsanity.com/paper/2305.15352/) (2023)
- [FutureFill: Fast Generation from Convolutional Sequence Models](https://mlsanity.com/paper/2410.03766/) (2024)
- [Universal Sequence Preconditioning](https://mlsanity.com/paper/2502.06545/) (2025)
- [Population Dynamics Control with Partial Observations](https://mlsanity.com/paper/2502.14079/) (2025)

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

- [Efficient Spectral Control of Partially Observed Linear Dynamical Systems](https://mlsanity.com/paper/2505.20943/) (2025)
- [A Spectral Filtering Approach to Regret Analysis of Distributed Online Control for Linear Dynamical Systems](https://mlsanity.com/paper/2608.02375/) (2026)

## Abstract (arXiv)

We propose a new method for controlling linear dynamical systems under adversarial disturbances and cost functions. Our algorithm achieves a running time that scales polylogarithmically with the inverse of the stability margin, improving upon prior methods with polynomial dependence maintaining the same regret guarantees. The technique, which may be of independent interest, is based on a novel convex relaxation that approximates linear control policies using spectral filters constructed from the eigenvectors of a specific Hankel matrix.