# System Identification under Noise and Attack Regimes: Agnostic and Composite Robustness

arXiv: https://arxiv.org/abs/2602.07288 · HTML: https://mlsanity.com/paper/2602.07288/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Feb 2026.

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

- [RobustLDS: Learning linear dynamical systems under adversarial corruptions](https://mlsanity.com/paper/2610.11906/) (2026)

## Abstract (arXiv)

Dynamical systems often confront persistent zero-mean independent noise and/or sparse nonzero-mean adversarial attacks. While mean-based estimators like least-squares handle the former, the median-based ℓ1-norm estimator is effective for the latter. In this paper, we develop robust system identification frameworks to identify a linearly-parametrized nonlinear system from a single trajectory of length T. We tackle two types of robustness: (1) textitagnostic robustness under either pure noise or pure attacks without knowing which regime is active; and (2) textitcomposite robustness under concurrent noise and attacks. We first show that the Huber estimator attains agnostic robustness by achieving an O(1/√T) error rate for the noise regime and a bounded error for the attack regime, serving as a one-stage estimator interpolating between mean- and median-based methods. We then prove that no convex one-stage estimator is consistent under both noise and attacks, which motivates a two-stage estimation that sequentially applies median- and mean-based estimators for composite robustness. These dual notions of robustness require a corresponding duality in estimator design, providing a solid foundation for robust control in safety-critical systems.