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首页> 外文期刊>Applied Soft Computing >Type-2 fuzzy wavelet networks (T2FWN) for system identification using fuzzy differential and Lyapunov stability algorithm
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Type-2 fuzzy wavelet networks (T2FWN) for system identification using fuzzy differential and Lyapunov stability algorithm

机译：使用模糊微分和Lyapunov稳定性算法进行系统识别的2型模糊小波网络（T2FWN）

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摘要

We propose a novel method for the identification of non-linear system by utilizing some of the important properties of wavelets like denoising, compression, multiresolution along with the concepts of fuzzy logic. Two new type-2 fuzzy wavelet networks (T2FWNs) are proposed here. These T2FWNs can handle rule uncertainties in a better way because of using the type-2 fuzzy sets in modeling and fuzzy differential (FD) and Lyapunov stability during learning. Lot of work has been done in the identification of non-linear system by using the models based on type-1 fuzzy logic system (FLS). But in practice they are unable to handle uncertainties in the rules. The robustness of the system is assured by Lyapunov stability (LS). Also we have explored the properties of wavelets and FLS to handle the uncertainties efficiently. As the stability of the model is highly dependent on the learning of the system we use Lyapunov stability in combination with fuzzy differential. FD gives the range of variation of parameters having lower and upper bound in which the system is stable. The performance of T2FWN is compared with type-1 FLS, FWN [D.W.C. Ho, P.-A. Zhang, J. Xu, Fuzzy wavelet networks for function learning, IEEE Trans. Fuzzy Syst. 9 (February (1)) 2000] and FWNN [S. Srivastava, M. Singh, M. Hanmandlu, A.N. Jha, New fuzzy wavelet neural networks for system identification and control, Intl. J. Appl. Soft Comput. 6 (November (I)) 2005, 1-17]. It is shown that noise and disturbance in the reference signal are reduced with wavelets. A comparison of three learning algorithms: (i) gradient descent (GD) (ii) a combination of Lyapunov stability and fuzzy differential (LSFD) and, (iii) a combination of (i) and (ii) is done.
机译：我们利用小波的一些重要特性，如去噪，压缩，多分辨率以及模糊逻辑的概念，提出了一种识别非线性系统的新方法。这里提出了两个新的类型2模糊小波网络（T2FWNs）。这些T2FWN可以更好地处理规则不确定性，因为在建模过程中使用了2型模糊集，并且在学习过程中使用了模糊微分（FD）和Lyapunov稳定性。通过使用基于类型1模糊逻辑系统（FLS）的模型，在识别非线性系统方面已经进行了大量工作。但是实际上，他们无法处理规则中的不确定性。 Lyapunov稳定性（LS）确保了系统的鲁棒性。我们还探索了小波和FLS的特性，以有效地处理不确定性。由于模型的稳定性高度依赖于系统的学习，因此我们将Lyapunov稳定性与模糊微分结合使用。 FD给出了系统在其中具有上下限的参数变化范围。将T2FWN的性能与1型FLS，FWN [D.W.C.何，P.-A. Zhang，J。Xu，《函数学习的模糊小波网络》，IEEE Trans。模糊系统2000年2月9日（1月9日）和FWNN [S. Srivastava，M.Singh，M.Hanmandlu，A.N。 Jha，用于系统识别和控制的新型模糊小波神经网络，国际。 J.应用软计算。参见，J.Med.Chem.Sci.6（11（I）），1-17]。结果表明，利用小波可以减小参考信号中的噪声和干扰。三种学习算法的比较：（i）梯度下降（GD）（ii）Lyapunov稳定性和模糊微分（LSFD）的组合，以及（iii）（i）和（ii）的组合。

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