Optimal actuator and sensor attack strategies against controllability and observability

This paper investigates the problem of designing optimal actuator and sensor attack strategies from the attacker's perspective. The first objective is to compromise system controllability and observability with minimal cost by attacking the smallest number of actuators and sensors. However, since certain actuators or sensors may be inherently difficult or costly to compromise, we further investigate the scenario in which the attacker aims to determine the minimum cardinality such that attacking any set of components of this size inevitably renders the system uncontrollable or unobservable. This essentially corresponds to disrupting the controllability and observability resilience of the system. If the system matrix A has no repeated eigenvalues, both problems can be solved in polynomial time. When the system matrix A has repeated eigenvalues, two algorithms, called the forward and reverse greedy algorithms, are proposed to address the fragility and resilience problems. Compared with the existing greedy algorithms, the proposed forward and reverse greedy algorithms initiate attacks from the empty set and the full set of actuators and sensors, thereby further reducing the computational complexity. We evaluate the proposed methods on a cruise-mode aircraft control system and identify minimum-size actuator and sensor attack sets. By attacking these selected actuators and sensors, the system becomes uncontrollable and unobservable, thus validating the effectiveness of the algorithms.