Observer-Based Control for the Two-Time-Scale Cyber-Physical Systems: The Dual-Scale DoS Attacks Case

Abstract

This paper concerns the observer-based control problem for a class of two-time-scale cyber-physical systems (TTSCPSs) under dual-scale denial-of-service (DoS) attacks. A TTSCPSs model is first proposed with slow and fast transmission channels, because that slow and fast dynamics are operating and communicating with slow and fast sampling rates, respectively. Due to the time scale difference between slow and fast transmission channels, the model of dual-scale DoS attacks is constructed by characterizing the attack frequency and duration on different time scales. A novel <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\varepsilon$</tex-math></inline-formula> -dependent switched observer is formulated, and corresponding security controller is designed to stabilize the TTSCPSs under dual-scale DoS attacks. By constructing an <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\varepsilon$</tex-math></inline-formula> -dependent Lyapunov function, sufficient conditions for the desired observer-based controller are derived such that the closed-loop TTSCPSs can be input-to-state stable. Moreover, ill-conditioned numerical issue caused by the two-time-scale feature can be avoided in the proposed design methods. Finally, examples are given to verify the effectiveness of the proposed algorithm.