Data-driven adversarial online control for unknown linear systems

Zishun Liu

doi:10.1016/j.sysconle.2025.106224

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Data-driven adversarial online control for unknown linear systems

2025-09-01

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Zishun Liu *

Yongxin Chen

DOI：10.1016/j.sysconle.2025.106224

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Abstract

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We consider the online control problem with an unknown linear dynamical system in the presence of adversarial perturbations and adversarial convex loss functions. Although the problem is widely studied in model-based control, it remains unclear whether data-driven approaches, which bypass the system identification step, can solve the problem. In this work, we present a novel data-driven online adaptive control algorithm to address this online control problem. Our algorithm leverages the behavioral systems theory to learn a non-parametric system representation and then adopts a perturbation-based controller updated by online gradient descent. We prove that our algorithm guarantees an O(T2/3) regret bound with high probability, which matches the best-known regret bound for this problem. Furthermore, we extend our algorithm and performance guarantee to the cases with output feedback. A numerical experiment is conducted to validate our theoretical results.

Keywords:

Data-driven control

Behavioral systems theory

Online learning

Adaptive control