Department of Mathematics, Harbin Institute of Technology, Weihai, 264209, China.
Neural Netw. 2020 Dec;132:269-280. doi: 10.1016/j.neunet.2020.09.009. Epub 2020 Sep 15.
Mittag-Leffler stabilization is studied for fractional reaction-diffusion cellular neural networks (FRDCNNs) in this paper. Different from previous literature, the FRDCNNs in this paper are high-dimensional systems, and boundary control and observed-based boundary control are both used to make FRDCNNs achieve Mittag-Leffler stability. First, a state-dependent boundary controller is designed when system states are available. By employing the spatial integral functional method and some inequalities, a criterion ensuring Mittag-Leffler stability of FRDCNNs is presented. Then, when the information of system states is not fully accessible, an observer is presented to estimate the system states based on boundary output and an observer-based boundary controller is provided aiming to stabilize the considered FRDCNNs. Furthermore, a robust observer-based boundary controller is proposed to ensure the Mittag-Leffler stability for FRDCNNs with uncertainties. Examples are given to illustrate the effectiveness of obtained theoretical results.
本文研究了分数阶反应扩散细胞神经网络（FRDCNNs）的 Mittag-Leffler 稳定性。与以往的文献不同，本文中的 FRDCNNs 是高维系统，同时使用边界控制和基于观测器的边界控制使 FRDCNNs 达到 Mittag-Leffler 稳定性。首先，当系统状态可用时，设计了一个状态相关的边界控制器。通过使用空间积分泛函方法和一些不等式，给出了一个确保 FRDCNNs 的 Mittag-Leffler 稳定性的准则。然后，当系统状态的信息不完全可用时，提出了一个观测器来基于边界输出估计系统状态，并提供了一个基于观测器的边界控制器，以稳定所考虑的 FRDCNNs。此外，提出了一个鲁棒的基于观测器的边界控制器，以确保具有不确定性的 FRDCNNs 的 Mittag-Leffler 稳定性。给出了实例来说明所得到的理论结果的有效性。
