School of Mathematics and Statistics, Shenzhen University, Shenzhen 518060, China.
Department of Mathematics, Southern Illinois University, Carbondale, Illinois 62901, USA.
Neural Netw. 2021 Sep;141:40-51. doi: 10.1016/j.neunet.2021.03.028. Epub 2021 Mar 24.
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.
本文通过事件触发控制研究了与延迟和 Lévy 噪声相关的新型随机网络阵列的几乎必然同步问题。网络的耦合结构由连续时间齐次马尔可夫链控制。网络中的节点仅在离散时间点相互通信并更新信息，从而最小化网络工作量。在包含马尔可夫链和 Lévy 过程的随机过程框架内，并应用非负半鞅的收敛定理，我们表明通过事件触发控制方法可以实现马尔可夫耦合网络的几乎必然同步。研究结果进一步扩展到有向拓扑，其中耦合结构可以是不对称的。此外，我们还证明了在我们提出的方法下可以排除零和行为，表明我们的框架在实际中是可行的。数值仿真结果验证了所得到的理论结果的有效性。
