Fixed-Time Discontinuous Control for Cluster Secure Synchronization of Interlayer Switching Networks Under Attacks

This paper mainly concentrates on the issue of fixed-time cluster secure synchronization upon interlayer switching networks with DoS attacks, in which the DoS attacks may cause random damage to the nodes/edges in networks and then generate impulsive disturbances. To resist the attacks, one robust fixed-time discontinuous control strategy is proposed, such that all the nodes in interlayer switching networks can achieve the cluster secure synchronization even when the communication topology are disconnected or changed over time after being influenced by attacks. By using the Lyapunov method, several effective conditions for fixed-time cluster secure synchronization and the maximum convergence time near to the actual value are obtained. In view of the comparison principle, a suitable estimation method upon stability time for the switching networks is established, and the stability time is computable and controllable. Moreover, the correlation among attack intensity, connectivity network, impulsive interval, impulsive disturbance intensity and synchronization time is revealed. Simulation case is finally supplied to manifest the availability of the obtained outcomes. Note to Practitioners—This work aims at devising an efficient discontinuous control strategy within fixed-time for interlayer switching networks under attacks, such as power networks, industrial networks, and etc. In practical applications, the state of attacked nodes may transform unexpectedly and the nodes as well as their links may not operate under certain circumstances, while the classical time-controllable methods usually overlook these practical constraints. Consequently, by applying a discontinuous control with fixed-time strategy, not only the transmission efficiency is improved but also the control cost against attacks is reduced. Additionally, the fixed-time approach is designed such that the destructiveness of attacks and synchronized time are all predictable and controllable, even if the communication topology may be disconnected and changed over time after being affected by attacks, the given scheme is more effective for realistic requirements.