# Learning of Dynamical Systems under Adversarial Attacks -- Null Space Property Perspective

arXiv: https://arxiv.org/abs/2210.01421 · HTML: https://mlsanity.com/paper/2210.01421/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Oct 2022.

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

- [Exact Recovery for System Identification with More Corrupt Data than Clean Data](https://mlsanity.com/paper/2305.10506/) (2023)
- [Exact Recovery Guarantees for Parameterized Nonlinear System Identification Problem under Sparse Disturbances or Semi-Oblivious Attacks](https://mlsanity.com/paper/2409.00276/) (2024)
- [Subgradient Method for System Identification with Non-Smooth Objectives](https://mlsanity.com/paper/2503.16673/) (2025)

## Abstract (arXiv)

We study the identification of a linear time-invariant dynamical system affected by large-and-sparse disturbances modeling adversarial attacks or faults. Under the assumption that the states are measurable, we develop necessary and sufficient conditions for the recovery of the system matrices by solving a constrained lasso-type optimization problem. In addition, we provide an upper bound on the estimation error whenever the disturbance sequence is a combination of small noise values and large adversarial values. Our results depend on the null space property that has been widely used in the lasso literature, and we investigate under what conditions this property holds for linear time-invariant dynamical systems. Lastly, we further study the conditions for a specific probabilistic model and support the results with numerical experiments.