Secure Control for Cyber-Physical System under Stealthy Attacks using Lifted System Model

Stealthy attacks, which can evade detection, may lead to serious damage to cyber-physical systems. It is of vital importance to design controllers to defend stealthy attacks. Current works related to secure control only focus on single-rate systems. Whereas multi-rate systems exist widely in practical application, in this paper, the secure control problem for multi-rate cyber-physical systems under stealthy attacks is studied. The system is modeled by a lifted system model and an χ<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> anomaly detector is adopted to detect possible attacks. For the purpose of minimizing the influence of the attacks on system performance, a state feedback controller is devised, so that system state can always be kept within a safe region. Firstly, the relationship between controller parameter and system’s reachable set is given according to the range of detector residual and noise. Secondly, secure control parameters and corresponding invariant reachable set are solved by designing an invertible linear transformation and constructing a convex optimization problem. Finally, the validity of our control method is confirmed through a numerical simulation example.