Synchronization for stochastic coupled networks with Lévy noise via event-triggered control

• Published in: Neural networks Vol. 141; pp. 40 - 51
• Main Authors: Dong, Hailing, Luo, Ming, Xiao, Mingqing
• Format: Journal Article
• Language: English
• Published: United States Elsevier Ltd 01.09.2021
• Subjects: Almost sure synchronization; Event-triggered control; Lévy noise; Markovian switching; Lévy noise; Almost sure synchronization; Event-triggered control; Markovian switching
• ISSN: 0893-6080; 1879-2782
• DOI: 10.1016/j.neunet.2021.03.028

This paper addresses the realization of almost sure synchronization problem for a new array of stochastic networks associated with delay and Lévy noise via event-triggered control. The coupling structure of the network is governed by a continuous-time homogeneous Markov chain. The nodes in the networks communicate with each other and update their information only at discrete-time instants so that the network workload can be minimized. Under the framework of stochastic process including Markov chain and Lévy process, and the convergence theorem of non-negative semi-martingales, we show that the Markovian coupled networks can achieve the almost sure synchronization by event-triggered control methodology. The results are further extended to the directed topology, where the coupling structure can be asymmetric. Furthermore, we also proved that the Zeno behavior can be excluded under our proposed approach, indicating that our framework is practically feasible. Numerical simulations are provided to demonstrate the effectiveness of the obtained theoretical results. •Almost sure synchronization for stochastic network is achieved.•The developed event-triggered sampling control has the adaptive capacity.•Both direct and undirect topology structures with Lévy noise are investigated.•Our approach can reduce the network workload and eliminate the Zeno behavior.