Constraining Attacker Capabilities Through Actuator Saturation
For control system designers, this offers a method to guarantee safety against attacks by leveraging physical actuator limits without requiring attack detection, though it is incremental as it extends existing reachability analysis to constrained actuators.
The paper provides LMI-based tools to compute outer ellipsoidal bounds on reachable sets under actuator saturation and to design artificial actuator limits that prevent dangerous states while maximizing the retained reachable set volume, demonstrated on a vehicle platoon simulation.
For LTI control systems, we provide mathematical tools - in terms of Linear Matrix Inequalities - for computing outer ellipsoidal bounds on the reachable sets that attacks can induce in the system when they are subject to the physical limits of the actuators. Next, for a given set of dangerous states, states that (if reached) compromise the integrity or safe operation of the system, we provide tools for designing new artificial limits on the actuators (smaller than their physical bounds) such that the new ellipsoidal bounds (and thus the new reachable sets) are as large as possible (in terms of volume) while guaranteeing that the dangerous states are not reachable. This guarantees that the new bounds cut as little as possible from the original reachable set to minimize the loss of system performance. Computer simulations using a platoon of vehicles are presented to illustrate the performance of our tools.