Resilient Tube-Based MPC for Cyber-Physical Systems with False Data Injection Attacks

In this paper, our focus is on a cyber-physical system that incorporates actuator input saturation and physical constraints on system states. Consequently, we face the challenge of dealing with both state and control input constraints while ensuring the resilience of signal channels against false data injection attacks. Model predictive control (MPC) is an optimal method of academic interest that offers unique advantages for addressing multi-constraint problems (MPCconstraints, 20XX). Furthermore, MPC can handle such problems while mitigating the impact of temporary system open-loop situations through its inherent rolling optimization characteristics. As a result, it is often employed in countering denial-of-service (DoS) and severe deception attacks (Sunqi_DoS, Franze_severe, 20XX).

However, traditional robust MPC schemes, including min-max MPC, exhibit undesirable performance when faced with cyber attacks (Sunqi_phd, 20XX). To overcome this limitation, the tube-based model predictive control algorithm utilizes the properties of disturbance invariant sets, ensuring that the disturbed system consistently follows the nominal system (Mayne2005, 20XX). While this algorithm performs well against bounded disturbances and amplitude-bounded false data injection attacks, it encounters challenges in scenarios with higher levels of attacks.

Some scholars have explored resilient approaches using control buffers to maintain stability during temporary system open-loop situations (Sunqi_DoS, 20XX). However, their assumptions are limited to a maximum duration of attack, without considering the probability model of attacks or designing the buffer length accordingly. Additionally, certain newly proposed resilient MPC algorithms may result in false triggering due to system uncertainty, resulting in wasted computing resources (Franze_severe, Eventtrigger, 20XX).

Therefore, in this study, we propose a resilient tube-based MPC scheme that addresses the identified problem. This scheme is based on recognizing the false data injection attack model and utilizing a control buffer with a calculated minimum length. The core idea is to handle uncertainty and low-level false data injection attacks using a robust invariant set while evading attacks that exceed a certain threshold by introducing a pre-designed period of system open-loop operation, all while ensuring stability.