# Analysis and Detectability of Offline Data Poisoning Attacks on Linear Dynamical Systems

arXiv: https://arxiv.org/abs/2211.08804 · HTML: https://mlsanity.com/paper/2211.08804/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Backdoor and data poisoning attacks, one of 12 directions in LLM safety and security.
- Builds on 11 of its 43 references that are in the map.
- First posted on arXiv 16 Nov 2022.

## Placed in

- LLM safety and security / [Backdoor and data poisoning attacks](https://mlsanity.com/safety/backdoor-and-data-poisoning-attacks/)

## Builds on (most cited first, 11 of 11)

- [Poison Frogs! Targeted Clean-Label Poisoning Attacks on Neural Networks](https://mlsanity.com/paper/1804.00792/) (2018)
- [Manipulating Machine Learning: Poisoning Attacks and Countermeasures for Regression Learning](https://mlsanity.com/paper/1804.00308/) (2018)
- [Is feature selection secure against training data poisoning?](https://mlsanity.com/paper/1804.07933/) (2018)
- [Formulas for Data-driven Control: Stabilization, Optimality and Robustness](https://mlsanity.com/paper/1903.06842/) (2019)
- [Robust Regression via Hard Thresholding](https://mlsanity.com/paper/1506.02428/) (2015)
- [Data-Enabled Predictive Control: In the Shallows of the DeePC](https://mlsanity.com/paper/1811.05890/) (2018)
- [Disciplined Convex-Concave Programming](https://mlsanity.com/paper/1604.02639/) (2016)
- [Verifying dissipativity properties from noise-corrupted input-state data](https://mlsanity.com/paper/2004.07270/) (2020)
- [Regret Bounds for LQ Adaptive Control Under Database Attacks (Extended Version)](https://mlsanity.com/paper/2004.00241/) (2020)
- [Poisoning Attacks against Data-Driven Control Methods](https://mlsanity.com/paper/2103.06199/) (2021)
- [Data-Driven Control and Data-Poisoning attacks in Buildings: the KTH Live-In Lab case study](https://mlsanity.com/paper/2103.06208/) (2021)

## Built on by (most cited first, 1 of 1)

- [Empirical Perturbation Analysis of Linear System Solvers from a Data Poisoning Perspective](https://mlsanity.com/paper/2410.00878/) (2024)

## Abstract (arXiv)

In recent years, there has been a growing interest in the effects of data poisoning attacks on data-driven control methods. Poisoning attacks are well-known to the Machine Learning community, which, however, make use of assumptions, such as cross-sample independence, that in general do not hold for linear dynamical systems. Consequently, these systems require different attack and detection methods than those developed for supervised learning problems in the i.i.d. setting. Since most data-driven control algorithms make use of the least-squares estimator, we study how poisoning impacts the least-squares estimate through the lens of statistical testing, and question in what way data poisoning attacks can be detected. We establish under which conditions the set of models compatible with the data includes the true model of the system, and we analyze different poisoning strategies for the attacker. On the basis of the arguments hereby presented, we propose a stealthy data poisoning attack on the least-squares estimator that can escape classical statistical tests, and conclude by showing the efficiency of the proposed attack.