An Intermittent Volatile Event-Triggered Synchronization Approach for Multi-Layer Networks with Noise Coupling under an Almost Sure Framework

In this paper, the almost sure synchronization of stochastic multi-layer networks with noise coupling is studied by means of pinning intermittent volatile event-triggered control. During the control interval, the determination of control updates follows an event-triggered mechanism with waiting time, which avoids continuous monitoring and also eliminates Zeno behavior. In contrast to the existing literature that focuses on moment synchronization, we study almost sure synchronization on stochastic multi-layer networks, where noise coupling with time-varying and nonlinear features plays an active role. In addition, the control gain displays sign-indefinite characteristics that follow some volatility patterns, including synchronizing control and desynchronizing inputs. A concept of average volatile control gain is presented to quantify the control gain. To cope with the challenges posed by volatile gain and intermittent control input, a generalization of Halanay-type inequality is proposed, its coefficients are time-varying and piecewise continuous, which shows that the results have a wider range of applications. Based on the stochastic analysis technique, graph theory, and Lyapunov method, the synchronization criteria are established. Finally, the feasibility is illustrated by simulation examples. Note to Practitioners - This paper was motivated by existing results on pinning intermittent control and event-triggered control about almost sure synchronization. The existing results mainly require that the control signals were updated in a consecutive manner during control activation intervals, which may hardly be implemented on digital computers. This paper designs a novel hybrid control method named pinning intermittent volatile event-triggered control, and therefore, the proposed approach is more friendly for control engineers. In addition, the volatile control gain is considered. The results obtained are applied to a spring-mass-damper system, demonstrating their effectiveness and it is expected that the proposed approach can be extended to more practical physical engineering systems.