Fuzzy neural networks, with suitable learning strategy, have been demonstrated as an effective tool for online data modeling. However, it is a challenging task to construct a model to ensure its quality and stability for non-stationary dynamic systems with some uncertainties. To solve this problem, this paper presents a novel identification model based on recurrent interval type-2 fuzzy wavelet neural network (RIT2FWNN) with new learning algorithm. The model benefits from both advantages of recurrent and wavelet neural networks such as use of temporal data and fast convergence properties. The proposed antecedent and consequent parameters update rules are derived using sliding-mode-control-theory. To evaluate the proposed fuzzy model, it is utilized to design a nonlinear model-based predictive controller and is applied for the synchronization of fractional-order time-delay chaotic systems. Using Lyapunov stability analysis, it is shown that all update rules of the parameters are uniformly ultimately bounded. The adaptation laws obtained in this method are very simple and have closed forms. Some stability conditions are derived to prove learning dynamics and asymptotic stability of the network by using an appropriate Lyapunov function. The efficacy and performance of the proposed method is verified by simulation examples.

中文翻译：

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具有稳定学习算法的递归区间2型模糊小波神经网络：在基于模型的预测控制中的应用

具有适当学习策略的模糊神经网络已被证明是在线数据建模的有效工具。然而，构建模型以确保具有不确定性的非平稳动态系统的质量和稳定性是一项艰巨的任务。为了解决这个问题，本文提出了一种基于递归区间2型模糊小波神经网络（RIT2FWNN）的新型学习模型。该模型受益于递归和小波神经网络的优点，例如使用时间数据和快速收敛性。利用滑模控制理论推导了提出的先验参数及其后续参数更新规则。为了评估提出的模糊模型，它被用来设计基于非线性模型的预测控制器，并被用于分数阶时滞混沌系统的同步。使用李雅普诺夫稳定性分析，表明所有参数更新规则最终都统一有界。用这种方法获得的适应定律非常简单并且具有封闭形式。通过使用适当的Lyapunov函数，推导了一些稳定性条件，以证明网络的学习动力学和渐近稳定性。仿真实例验证了该方法的有效性和有效性。通过使用适当的Lyapunov函数，推导了一些稳定性条件，以证明网络的学习动力学和渐近稳定性。仿真实例验证了该方法的有效性和有效性。通过使用适当的Lyapunov函数，推导了一些稳定性条件，以证明网络的学习动力学和渐近稳定性。仿真实例验证了该方法的有效性和有效性。