Stochastic Tube-based Model Predictive Control for Cyber-Physical Systems under False Data Injection Attacks with Bounded Probability

Abstract

This paper addresses the challenge of amplitude-unbounded false data injection (FDI) attacks targeting the sensor-to-controller (S-C) channel in cyber-physical systems (CPSs). We introduce a resilient tube-based model predictive control (MPC) scheme. This scheme incorporates a threshold-based attack detector and a control sequence buffer to enhance system security. We mathematically model the common FDI attacks and derive the maximum duration of such attacks based on the hypothesis testing principle. Following this, the minimum feasible sequence length of the control sequence buffer is obtained. The system is proven to remain input-to-state stable (ISS) under bounded external disturbances and amplitude-unbounded FDI attacks. Moreover, the feasible region under this scenario is provided in this paper. Finally, the proposed algorithm is validated by numerical simulations and shows superior control performance compared to the existing methods.