Online Optimization of LTI Systems Under Persistent Attacks: Stability, Tracking, and Robustness

Abstract

We study the stability properties of the interconnection of an LTI dynamical plant and a controller that generates control signals that are maliciously compromised by an attacker. We consider two classes of 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. We analyze the stability of the system under a class of switching attacks that persistently modify the control inputs generated by the controllers. The stability analysis leverages the framework of Hybrid Dynamical Systems, Lyapunov-based arguments for switching systems with unstable modes, and singular perturbation theory. Our results show that the stability of the interconnected system can be preserved when an attack defense mechanism can mitigate "sufficiently often" the activation time of the attack action in any bounded time interval. We present simulation results that corroborate the technical findings.