Mean Square Consensus of Stochastic Multi-agent Systems with Delays via Intermittent Dynamic Event-triggered Control

This article systematically investigates the leaderless mean-square exponential consensus(MSEC) issue of stochastic multi-agent systems (MASs) on directed graphs through periodically intermittent event-triggered control mechanisms. Due to stochastic effects, the system state is hard to predict and dominate, and the system behavior would vary with every trial (i.e., sample path), even for the same initial condition. This gives rise to substantial challenges, especially in determining the execution/sampling times, which urges us to develop powerful and sophisticated methods for the analysis and design of stochastic event-triggered control. Therefore, periodically intermittent dynamic event-triggering mechanisms are proposed with enforcing a fixed positive lower bound for the inter-execution times to avoid Zeno behavior. For solving the challenge problem caused by intermittent control, the auxiliary system with a dynamic event triggering mechanism (DETM) is introduced. Based on the auxiliary system method, some sufficient conditions are presented to ensure the leaderless mean square consensus for MASs under the continue-time control protocol in the frame of the Lyapunov theorem and Halanay inequality. Finally, the applicability and effectiveness of the proposed design techniques are demonstrated by numerical examples.