IEEE Trans Cybern. 2014 Mar;44(3):329-41. doi: 10.1109/TCYB.2013.2254113. Epub 2013 Apr 16.
This paper aims to propose a more efficient control algorithm for chaos time-series prediction and synchronization. A novel type-2 fuzzy cerebellar model articulation controller (T2FCMAC) is proposed. In some special cases, this T2FCMAC can be reduced to an interval type-2 fuzzy neural network, a fuzzy neural network, and a fuzzy cerebellar model articulation controller (CMAC). So, this T2FCMAC is a more generalized network with better learning ability, thus, it is used for the chaos time-series prediction and synchronization. Moreover, this T2FCMAC realizes the un-normalized interval type-2 fuzzy logic system based on the structure of the CMAC. It can provide better capabilities for handling uncertainty and more design degree of freedom than traditional type-1 fuzzy CMAC. Unlike most of the interval type-2 fuzzy system, the type-reduction of T2FCMAC is bypassed due to the property of un-normalized interval type-2 fuzzy logic system. This causes T2FCMAC to have lower computational complexity and is more practical. For chaos time-series prediction and synchronization applications, the training architectures with corresponding convergence analyses and optimal learning rates based on Lyapunov stability approach are introduced. Finally, two illustrated examples are presented to demonstrate the performance of the proposed T2FCMAC.
本文旨在提出一种更有效的混沌时间序列预测和同步控制算法。提出了一种新型的 2 型模糊小脑模型关节控制器（T2FCMAC）。在某些特殊情况下，这种 T2FCMAC 可以简化为区间 2 型模糊神经网络、模糊神经网络和模糊小脑模型关节控制器（CMAC）。因此，这种 T2FCMAC 是一种具有更好学习能力的更通用的网络，因此，它被用于混沌时间序列预测和同步。此外，这种 T2FCMAC 基于 CMAC 的结构实现了非归一化的 2 型模糊逻辑系统。与传统的 1 型模糊 CMAC 相比，它可以提供更好的处理不确定性的能力和更多的设计自由度。与大多数区间 2 型模糊系统不同，由于非归一化区间 2 型模糊逻辑系统的特性，T2FCMAC 的类型简化被绕过。这使得 T2FCMAC 的计算复杂度更低，更实用。对于混沌时间序列预测和同步应用，引入了基于李雅普诺夫稳定性方法的相应收敛分析和最优学习率的训练架构。最后，给出了两个实例来说明所提出的 T2FCMAC 的性能。
