Zero Dynamics Attacks Subject to Actuator Saturation: A Constrained Optimization Approach

Zero dynamics attacks (ZDAs) have received considerable attention in the control systems literature, as they can be disruptive while being almost virtually to detect from the measured output of the plant. However, as ZDAs require an unbounded input sequence, the effect of physical constraints on the actuators, in the form of saturation, must be taken into account. In this work, we show that conventional methods for constructing ZDAs, when subject to input saturation, can make these attacks no longer disruptive, stealthy, or both. While this might imply that some systems are safe from ZDAs, we introduced a new attack called a relaxed ZDA, which can be disruptive and practically stealthy even under input constraints. For the construction of relaxed ZDAs, we propose a method that involves solving an optimization problem offline. We demonstrate the versatility of the proposed method and show it succeeds where conventional ZDAs fall short by means of an illustrative example on a cyber-physical system (CPS).