Differing from the traditional wavelet neural network, a special type of discrete-time multiscale wavelet neural network (MWNN) using mesh grid is presented and investigated to solve the problem of identification of the autonomous nonlinear dynamical system. Inspired by the multiscale perception of biological neurons and the concept of continuous wavelet theory, multiscale and mesh grid proposed in this paper can be regarded as scale transformation and time translation in the mechanism of MWNN. For the convenience of digital processor realization, discrete-time expressions of weights updating and errors iteration are inferred by the Taylor expansion. In order to ensure the convergence of performance of this discrete-time model, the relation between the constant C in the equation of error iteration and sampling interval has been discovered by applying Z transform theory. The tracking error of autonomous nonlinear dynamical system will converge to the neighborhood of zero, which has been testified by discrete-time Lyapunov stability theory. For comparative purposes, discrete-time MWNN, Raised-Cosine Radial Basis Function Neural Network (RCRBFNN) and Gaussian Radial Basis Function Neural Network (GRBFNN) are used for solving the problem of autonomous nonlinear dynamical system identification. The Lorenz system and clinical electrocardiogram (ECG) dynamical system are applied to test the efficacy and superiority of the proposed discrete-time MWNN, in comparison with GRBFNN and RCRBFNN.

与传统的小波神经网络不同，提出并研究了一种特殊类型的离散时间多尺度小波神经网络(MWNN)，该网络使用网格网格来解决自主非线性动力系统的辨识问题。受生物神经元的多尺度感知和连续小波理论概念的启发，本文提出的多尺度和网格网格可以看作是MWNN机制中的尺度变换和时间平移。为方便数字处理器实现，通过泰勒展开式推导出权重更新和误差迭代的离散时间表达式。为了保证这个离散时间模型的性能收敛，常数C之间的关系应用Z变换理论发现了误差迭代和采样间隔的方程。离散时间李雅普诺夫稳定性理论证明了自主非线性动力系统的跟踪误差会收敛到零附近。为便于比较，离散时间 MWNN、升余弦径向基函数神经网络 (RCRBFNN) 和高斯径向基函数神经网络 (GRBFNN) 用于解决自主非线性动力系统识别问题。与 GRBFNN 和 RCRBFNN 相比，洛伦兹系统和临床心电图 (ECG) 动力系统用于测试所提出的离散时间 MWNN 的功效和优越性。