Security Control for Multi-Time-Scale CPSs Under DoS Attacks: An Improved Dynamic Event-Triggered Mechanism

Abstract

This article is concerned with the event-based security control problem for a class of multi-time-scale cyber physical systems (MTSCPSs) subject to DoS attacks. To tackle the difficulties caused by DoS attacks and the multi-time-scale feature (MTSF), a security control framework is developed to co-design the switched controller and event-triggered mechanism (ETM). An improved dynamic ETM is proposed, with which the closed-loop system can achieve a better control performance than traditional dynamic ETMs in the transient process. 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">$\epsilon$</tex-math></inline-formula> -dependent Lyapunov-Krasovskii functional is also established, via which sufficient conditions are derived to ensure the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$H_{\infty }$</tex-math></inline-formula> performance index of the closed-loop system and further cope with the ill-conditioned numerical issues generated by the MTSF. Finally, a simulation on a mini mining-tram drive control system is presented to demonstrate the correctness and merits of the proposed algorithm.