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

TL;DR

This paper investigates the recovery of linear dynamical systems under adversarial attacks using null space property-based conditions, providing theoretical guarantees and numerical validation for system identification amidst large sparse disturbances.

Contribution

It introduces necessary and sufficient null space property conditions for system matrix recovery under adversarial attacks, extending lasso theory to dynamical systems.

Findings

Null space property conditions enable accurate system recovery.

Upper bounds on estimation error are derived.

Numerical experiments validate theoretical results.

Abstract

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.