Local recurrent sigmoidal–wavelet neurons in feed-forward neural network for forecasting of dynamic systems: Theory

Externally Recurrent Neural Network based identification of dynamic systems using Lyapunov stability analysis

This paper proposes an Externally Recurrent Neural Network (ERNN) for approximating the unknown dynamics of complex nonlinear systems and time series prediction. The proposed model utilizes the present as well as delayed values of the system outputs as well as of the external input. The weight update equations are tested for their boundedness by applying the Lyapunov stability method. Further, the error convergence proof is also given. The proposed model is put to test by considering various nonlinear examples and its performance is also compared with other state of the art methods. The results obtained in the present study indicate that the method is efficient and has provided accurate results.

Temporally local recurrent radial basis function network for modeling and adaptive control of nonlinear systems

In this paper, a novel temporally local recurrent radial basis function network for modeling and adaptive control of nonlinear systems is proposed. The proposed structure consists of recurrent hidden neurons having weighted self-feedback loops and a weighted linear feed-through from the input layer directly to the output layer neuron(s). The dynamic back-propagation algorithm is developed and used for updating the parameters of the proposed structure. To improve the performance of learning algorithm, discrete Lyapunov stability method is used to develop an adaptive learning rate scheme. This scheme ensures the faster convergence of the parameters and maintains the stability of the system. A total of 5 complex nonlinear systems are used to test and compare the performance of the proposed network with other neural network structures. The disturbance rejection tests are also carried out to check whether the proposed scheme is able to handle the external disturbance/noise signals effects or not. The obtained results show the efficacy of the proposed method.

A wavelet neural control scheme for a quadrotor unmanned aerial vehicle

Wavelets are designed to have compact support in both time and frequency, giving them the ability to represent a signal in the two-dimensional time-frequency plane. The Gaussian, the Mexican hat and the Morlet wavelets are crude wavelets that can be used only in continuous decomposition. The Morlet wavelet is complex-valued and suitable for feature extraction using the continuous wavelet transform. Continuous wavelets are favoured when high temporal and spectral resolution is required at all scales. In this paper, considering the properties from the Morlet wavelet and based on the structure of a recurrent high-order neural network model, a novel wavelet neural network structure, here called a recurrent Morlet wavelet neural network, is proposed in order to achieve a better identification of the behaviour of dynamic systems. The effectiveness of our proposal is explored through the design of a decentralized neural backstepping control scheme for a quadrotor unmanned aerial vehicle. The performance of the overall neural identification and control scheme is verified via simulation and real-time results.This article is part of the theme issue 'Redundancy rules: the continuous wavelet transform comes of age'.