Terminal set-based cyberattack detection in model predictive control systems with zero false alarms

The increased reliance of industrial control systems on networked components has made them more vulnerable to cyberattacks, necessitating cyberattack detection schemes specifically designed for detecting cyberattacks affecting industrial control systems. This work presents a set-membership-based detection scheme for systems under model predictive control (MPC). Specifically, we consider steady-state operation because many systems operate over long periods near a desired steady state. Provided the disturbances and measurement noise acting on the system are sufficiently small, we show that the closed-loop system under MPC is equivalent to the closed-loop system under a linear quadratic regulator, formulated with the same stage cost and weighting matrices, in a region containing the desired operating point. This equivalence is leveraged to show that the minimum robust positively invariant (mRPI) sets under both controllers are equivalent, enabling the calculation of the mRPI set for the closed-loop system under MPC. Using the mRPI set of the attack-free system, we present an attack detection scheme for systems under MPC and derive conditions under which the attack detection scheme applied to the attack-free closed-loop system does not raise an alarm. The detection scheme is applied to a simplified (linear) building space-cooling system to demonstrate that it does not raise false alarms during attack-free operation and that it successfully detects attacks when the system is subjected to a multiplicative false-data injection attack altering the data communicated over the sensor-controller link. Furthermore, the detection scheme’s applicability to nonlinear systems is assessed. Specifically, the detection scheme is applied to a nonlinear chemical process to demonstrate that the detection scheme does not raise false alarms during attack-free operation and successfully detects an attack when the process is subjected to a false-data injection cyberattack.