In this paper, a novel fuzzy neural network structure for uncertain nonlinear systems is proposed. This network is called wavelet Takagi–Sugeno–Kang (TSK) fuzzy cerebellar model neural network, which includes the framework of a cerebellar model neural network (CMNN) and the wavelet-function-based TSK fuzzy inference model. In order to effectively solve the uncertainty problem of nonlinear systems, a new structure is proposed where the wavelet function is used in the consequent parts of TSK-type fuzzy CMNN instead of the linear combination of the input variables in the traditional TSK fuzzy systems. This structure combines the advantages of the wavelet function, the CMNN and the TSK fuzzy inference system; thus, it is a more effective model for the uncertain nonlinear systems. In order to provide fast training, parameter update laws of the proposed model are derived based on the gradient descent method in which the learning-rates are online adapted. Furthermore the Lyapunov function is used to analyze the convergence of the considered systems. Finally, four different types of applications are applied to demonstrate the effectiveness of the proposed model. The simulation comparisons with other neural network models have verified the effectiveness of the new model.

中文翻译：

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不确定非线性系统的小波-TSK型模糊小脑模型神经网络

本文提出了一种用于不确定非线性系统的新型模糊神经网络结构。该网络称为小波Takagi-Sugeno-Kang（TSK）模糊小脑模型神经网络，它包括小脑模型神经网络（CMNN）的框架和基于小波函数的TSK模糊推理模型。为有效解决非线性系统的不确定性问题，提出了一种新的结构，在TSK型模糊CMNN的后续部分使用小波函数代替传统TSK模糊系统中输入变量的线性组合。这种结构结合了小波函数、CMNN和TSK模糊推理系统的优点；因此，对于不确定的非线性系统，它是一种更有效的模型。为了提供快速的培训，所提出模型的参数更新规律是基于梯度下降法推导出来的，其中学习率是在线适应的。此外，Lyapunov 函数用于分析所考虑系统的收敛性。最后，应用四种不同类型的应用程序来证明所提出模型的有效性。与其他神经网络模型的仿真对比验证了新模型的有效性。