Terminal Set-Based Cyberattack Detection in Model Predictive Control Systems with Zero False Alarms

Abstract

This work presents an attack detection scheme for systems regulated by model predictive control (MPC) that guarantees zero false alarms, focusing on a regulating MPC formulation with a quadratic stage cost and a quadratic terminal cost. We consider steady-state operation because many systems are operated over long periods near a desired operating 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 that 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 positive 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 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 accessed. 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.

Keywords: Model Predictive Control, Cyberattack Detection, False Alarms, Process Control Systems