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arXiv · 2507.03630

On the Limits of Robust Control Under Adversarial Disturbances

Paul Trodden·José M. Maestre·Hideaki Ishii
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Abstract

This paper addresses a fundamental and important question in control: under what conditions does there fail to exist a robust control policy that keeps the state of a constrained linear system within a target set, despite bounded disturbances? This question has practical implications for actuator and sensor specification, feasibility analysis for reference tracking, and the design of adversarial attacks in cyber-physical systems. While prior research has predominantly focused on using optimization to compute control-invariant sets to ensure feasible operation, our work complements these approaches by characterizing explicit sufficient conditions under which robust control is fundamentally infeasible. Specifically, we derive novel closed-form, algebraic expressions that relate the size of a disturbance set -- modelled as a scaled version of a basic shape -- to the system's spectral properties and the geometry of the constraint sets.

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Paul Trodden, José M. Maestre, Hideaki Ishii. 2025-07-04. On the Limits of Robust Control Under Adversarial Disturbances. https://arxiv.org/abs/2507.03630

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