$L_2$ Gain Secure Control of Cyber-Physical Systems Under Fast Time-Varying Cyber Attacks

Abstract

Cyber attacks may cause significant damage to cyber-physical systems (CPSs). Secure control is an effective measure to resist cyber attacks. While efforts have been made in developing secure control methods, the secure control problem for fast time-varying cyber attacks has not been well investigated. This paper presents a secure control strategy for mitigating fast time-varying actuator attacks in CPSs. For attacked CPSs, a nonlinear disturbance observer (NDO) is firstly constructed to estimate the lumped uncertainty. Then, to ensure the security of attacked CPSs, a <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$L_2$</tex-math></inline-formula> gain secure controller is designed to guarantee the stability of the CPSs. It is capable of handling not only constant and slow time-varying attacks but also fast time-varying cyber attacks to a certain extent. Compared with existing secure controllers, the secure controller designed in this paper withstands attacks with a wider range of frequencies, thus enhancing the resilience of the CPSs against unknown attacks. Simulations are conducted to verify the effectiveness of the proposed secure control strategy.