Dong Hailing, Zhou Jiamu, Wang Bingchang, Xiao Mingqing
IEEE Trans Neural Netw Learn Syst. 2018 Nov;29(11):5691-5700. doi: 10.1109/TNNLS.2018.2812102. Epub 2018 Mar 26.
This paper studies the exponential synchronization problem for a new array of nonlinearly and stochastically coupled networks via events-triggered sampling (ETS) by self-adaptive learning. The networks include the following features: 1) a Bernoulli stochastic variable is introduced to describe the random structural coupling; 2) a stochastic variable with positive mean is used to model the coupling strength; and 3) a continuous time homogeneous Markov chain is employed to characterize the dynamical switching of the coupling structure and pinned node sets. The proposed network model is capable to capture various stochastic effect of an external environment during the network operations. In order to reduce networks' workload, different ETS strategies for network self-adaptive learning are proposed under continuous and discrete monitoring, respectively. Based on these ETS approaches, several sufficient conditions for synchronization are derived by employing stochastic Lyapunov-Krasovskii functions, the properties of stochastic processes, and some linear matrix inequalities. Numerical simulations are provided to demonstrate the effectiveness of the theoretical results and the superiority of the proposed ETS approach.
本文通过自适应学习的事件触发采样（ETS）研究了一类新的非线性随机耦合网络阵列的指数同步问题。这些网络具有以下特点：1）引入伯努利随机变量来描述随机结构耦合；2）使用均值为正的随机变量对耦合强度进行建模；3）采用连续时间齐次马尔可夫链来刻画耦合结构和固定节点集的动态切换。所提出的网络模型能够捕捉网络运行过程中外部环境的各种随机效应。为了减轻网络的工作量，分别在连续监测和离散监测下提出了用于网络自适应学习的不同ETS策略。基于这些ETS方法，利用随机Lyapunov-Krasovskii函数、随机过程的性质以及一些线性矩阵不等式，推导了几个同步的充分条件。通过数值模拟验证了理论结果的有效性以及所提出的ETS方法的优越性。
