Online Optimization of LTI Systems Under Persistent Attacks: Stability, Tracking, and Robustness
Felipe Galarza-Jimenez, Gianluca Bianchin, Jorge I. Poveda, Emiliano, Dall'Anese

TL;DR
This paper analyzes the stability of control systems with potential malicious attacks on control signals, demonstrating conditions under which stability can be maintained despite persistent switching attacks, using hybrid system theory.
Contribution
It introduces a stability analysis framework for LTI systems under persistent attacks, considering both static and gradient-flow controllers, with conditions for stability preservation.
Findings
Stability is maintained if attack frequency is sufficiently low.
A time-scale separation between plant and controllers is crucial.
Simulation confirms theoretical stability conditions.
Abstract
We study the stability properties of a control system composed of a dynamical plant and a feedback controller, the latter generating control signals that can be compromised by a malicious attacker. We consider two classes of feedback controllers: a static output-feedback controller, and a dynamical gradient-flow controller that seeks to steer the output of the plant towards the solution of a convex optimization problem. In both cases, we analyze the stability properties of the closed-loop system under a class of switching attacks that persistently modify the control inputs generated by the controllers. Our stability analysis leverages the framework of hybrid dynamical systems, Lyapunov-based arguments for switching systems with unstable modes, and singular perturbation theory. Our results reveal that, under a suitable time-scale separation between plant and controllers, the stability of…
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Taxonomy
TopicsSmart Grid Security and Resilience
