Double integral-enhanced Zeroing neural network with linear noise rejection for time-varying matrix inverse

In engineering fields,time-varying matrix inversion(TVMI)issue is often encountered.Zeroing neural network(ZNN)has been extensively employed to resolve the TVMI problem.Nevertheless,the original ZNN(OZNN)and the integral-enhanced ZNN(IEZNN)usually fail to deal with the TVMI problem under unbounded noises,such as linear noises.Therefore,a neural network model that can handle the TVMI under linear noise interference is urgently needed.This paper develops a double integral-enhanced ZNN(DIEZNN)model based on a novel integral-type design formula with inherent linear-noise tolerance.Moreover,its convergence and robustness are verified by deriva-tion strictly.For comparison and verification,the OZNN and the IEZNN models are adopted to resolve the TVMI under multiple identical noise environments.The experi-ments proved that the DIEZNN model has excellent advantages in solving TVMI problems under linear noises.In general,the DIEZNN model is an innovative work and is proposed for the first time.Satisfyingly,the errors of DIEZNN are always less than 1�10−3 under linear noises,whereas the error norms of OZNN and IEZNN models are not convergent to zero.In addition,these models are applied to the control of the controllable permanent magnet synchronous motor chaotic system to indicate the superiority of the DIEZNN.

A Double-Weighted Deterministic Extreme Learning Machine Based on Sparse Denoising Autoencoder and Its Applications

Extreme learning machine (ELM) is a feedforward neural network-based machine learning method that has the benefits of short training times, strong generalization capabilities, and will not fall into local minima. However, due to the traditional ELM shallow architecture, it requires a large number of hidden nodes when dealing with high-dimensional data sets to ensure its classification performance. The other aspect, it is easy to degrade the classification performance in the face of noise interference from noisy data. To improve the above problem, this paper proposes a double pseudo-inverse extreme learning machine (DPELM) based on Sparse Denoising AutoEncoder (SDAE) namely, SDAE-DPELM. The algorithm can directly determine the input weight and output weight of the network by using the pseudo-inverse method. As a result, the algorithm only requires a few hidden layer nodes to produce superior classification results when classifying data. And its combination with SDAE can effectively improve the classification performance and noise resistance. Extensive numerical experiments show that the algorithm has high classification accuracy and good robustness when dealing with high-dimensional noisy data and high-dimensional noiseless data. Furthermore, applying such an algorithm to Miao character recognition substantiates its excellent performance, which further illustrates the practicability of the algorithm.