IEEE Trans Cybern. 2013 Apr;43(2):648-59. doi: 10.1109/TSMCB.2012.2214209. Epub 2013 Mar 7.
In this paper, the robust synchronization problem of fuzzy complex dynamical networks is investigated. A fuzzy complex dynamical network is an extension to an uncertain complex dynamical network in which all sources of parametric uncertainties are modeled with fuzzy numbers, i.e., all nodes' dynamics are described by fuzzy differential equations (FDEs) that permit a better description of a real process occurring in the presence of inaccuracy. To resolve the synchronization problem, this paper introduces new adaptive and impulsive controllers in which globally exponential synchronization of fuzzy dynamical networks under easily verified conditions is guaranteed. Moreover, we propose an efficient method that helps to find certain suitable nodes to be impulsively controlled via pinning, noting that these nodes, in general, vary at distinct impulsive time instants. Therefore, by using adaptive controllers and applying impulsive controllers to only a small portion of nodes, the whole network will completely be synchronized to a certain objective state. Finally, two numerical examples are given to illustrate the effectiveness of the proposed controllers.
本文研究了模糊复动力网络的鲁棒同步问题。模糊复动力网络是不确定复动力网络的一种扩展，其中所有参数不确定性的来源都用模糊数来建模，即所有节点的动态都用模糊微分方程（FDE）来描述，这使得在存在不准确性的情况下，可以更好地描述实际发生的过程。为了解决同步问题，本文引入了新的自适应和脉冲控制器，在易于验证的条件下保证了模糊动力网络的全局指数同步。此外，我们提出了一种有效的方法，通过钉扎帮助找到某些合适的节点进行脉冲控制，注意到这些节点通常在不同的脉冲时间点变化。因此，通过使用自适应控制器并仅将脉冲控制器应用于一小部分节点，整个网络将完全同步到某个目标状态。最后，给出了两个数值例子来说明所提出控制器的有效性。
