IEEE Trans Neural Netw Learn Syst. 2017 Dec;28(12):2885-2898. doi: 10.1109/TNNLS.2016.2609439. Epub 2016 Sep 27.
This paper discusses the problem of adaptive exponential synchronization in mean square for a new neural network model with the following features: 1) the noise is characterized by the Lévy process and the parameters of the model change in line with the Markovian process; 2) the master system is also disturbed by the same Lévy noise; and 3) there are multiple slave systems, and the state matrix of each slave system is an affine function of the state matrices of all slave systems. Based on the Lyapunov functional theory, the generalized Itô's formula, -matrix method, and the adaptive control technique, some criteria are established to ensure the adaptive exponential synchronization in the mean square of the master system and each slave system. Moreover, the update law of the control gain and the dynamic variation of the parameters of the slave systems are provided. Finally, the effectiveness of the synchronization criteria proposed in this paper is verified by a practical example.
1）噪声由 Lévy 过程表征，模型参数随马尔可夫过程变化；2）主系统也受到相同 Lévy 噪声的干扰；3）存在多个从系统，每个从系统的状态矩阵是所有从系统的状态矩阵的仿射函数。基于 Lyapunov 泛函理论、广义 Itô 公式、-矩阵方法和自适应控制技术，建立了一些准则来保证主系统和每个从系统的均方自适应指数同步。此外，还给出了控制增益的更新律和从系统参数的动态变化。最后，通过一个实际例子验证了本文提出的同步判据的有效性。
