Identification of autonomous nonlinear dynamical system based on discrete-time multiscale wavelet neural network

作者：Luo, Guo; Yang, Zhi^*; Zhang, Qizhi

来源：NEURAL COMPUTING & APPLICATIONS, 2021, 33(22): 15191-15203.

DOI：10.1007/s00521-021-06142-z

• Identification of autonomous nonlinear dynamical system
• Multiscale wavelet neural network (MWNN)
• Discrete-time
• Z transform
• Lyapunov stability

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.

• 单位
  中山大学