Adaptive event-triggered impulsive control for stochastic complex networks with delays under deception attacks

This paper investigates the exponential synchronization of time-delayed stochastic complex networks under deception attacks. Unlike traditional methods that rely on fixed or preset impulsive sequences, a state-dependent dynamic event-triggered impulsive control strategy is proposed, integrating the advantages of both event-triggered mechanisms and impulsive control. This strategy dynamically adjusts the impulsive moments by monitoring the system’s dynamic state. Adaptive parameters are incorporated into the event-triggered conditions, resulting in a Lyapunov-based adaptive event-triggered mechanism driven by subsystem state information. This mechanism allows each subsystem to independently determine its trigger moments using only its state information, rather than the whole system information. Additionally, stochastic variables following the Bernoulli distribution are introduced to model deception attacks, making the control strategy more applicable to real-world scenarios. Based on the Lyapunov functions of subsystems and graph theory, sufficient conditions for ensuring exponential synchronization are provided, excluding Zeno behavior. Finally, numerical simulations confirm the effectiveness and practicality of the theoretical results.