A novel recurrent neural network and its finite-time solution to time-varying complex matrix inversion

Design and Analysis of Anti-Noise Parameter-Variable Zeroing Neural Network for Dynamic Complex Matrix Inversion and Manipulator Trajectory Tracking

Dynamic complex matrix inversion (DCMI) problems frequently arise in the territories of mathematics and engineering, and various recurrent neural network (RNN) models have been reported to effectively find the solutions of the DCMI problems. However, most of the reported works concentrated on solving DCMI problems in ideal no noise environment, and the inevitable noises in reality are not considered. To enhance the robustness of the existing models, an anti-noise parameter-variable zeroing neural network (ANPVZNN) is proposed by introducing a novel activation function (NAF). Both of mathematical analysis and numerical simulation results demonstrate that the proposed ANPVZNN model possesses fixed-time convergence and robustness for solving DCMI problems. Besides, a successful ANPVZNN-based manipulator trajectory tracking example further verifies its robustness and effectiveness in practical applications.

Marine Data Prediction: An Evaluation of Machine Learning, Deep Learning, and Statistical Predictive Models

Nowadays, ocean observation technology continues to progress, resulting in a huge increase in marine data volume and dimensionality. This volume of data provides a golden opportunity to train predictive models, as the more the data is, the better the predictive model is. Predicting marine data such as sea surface temperature (SST) and Significant Wave Height (SWH) is a vital task in a variety of disciplines, including marine activities, deep-sea, and marine biodiversity monitoring. The literature has efforts to forecast such marine data; these efforts can be classified into three classes: machine learning, deep learning, and statistical predictive models. To the best of the authors' knowledge, no study compared the performance of these three approaches on a real dataset. This paper focuses on the prediction of two critical marine features: the SST and SWH. In this work, we proposed implementing statistical, deep learning, and machine learning models for predicting the SST and SWH on a real dataset obtained from the Korea Hydrographic and Oceanographic Agency. Then, we proposed comparing these three predictive approaches on four different evaluation metrics. Experimental results have revealed that the deep learning model slightly outperformed the machine learning models for overall performance, and both of these approaches greatly outperformed the statistical predictive model.

Constrained Quaternion-Variable Convex Optimization: A Quaternion-Valued Recurrent Neural Network Approach

This paper proposes a quaternion-valued one-layer recurrent neural network approach to resolve constrained convex function optimization problems with quaternion variables. Leveraging the novel generalized Hamilton-real (GHR) calculus, the quaternion gradient-based optimization techniques are proposed to derive the optimization algorithms in the quaternion field directly rather than the methods of decomposing the optimization problems into the complex domain or the real domain. Via chain rules and Lyapunov theorem, the rigorous analysis shows that the deliberately designed quaternion-valued one-layer recurrent neural network stabilizes the system dynamics while the states reach the feasible region in finite time and converges to the optimal solution of the considered constrained convex optimization problems finally. Numerical simulations verify the theoretical results.

Computing Time-Varying Quadratic Optimization With Finite-Time Convergence and Noise Tolerance: A Unified Framework for Zeroing Neural Network

Zeroing neural network (ZNN), as a powerful calculating tool, is extensively applied in various computation and optimization fields. Convergence and noise-tolerance performance are always pursued and investigated in the ZNN field. Up to now, there are no unified ZNN models that simultaneously achieve the finite-time convergence and inherent noise tolerance for computing time-varying quadratic optimization problems, although this superior property is highly demanded in practical applications. In this paper, for computing time-varying quadratic optimization within finite-time convergence in the presence of various additive noises, a new framework for ZNN is designed to fill this gap in a unified manner. Specifically, different from the previous design formulas either possessing finite-time convergence or possessing noise-tolerance performance, a new design formula with finite-time convergence and noise tolerance is proposed in a unified framework (and thus called unified design formula). Then, on the basis of the unified design formula, a unified ZNN (UZNN) is, thus, proposed and investigated in the unified framework of ZNN for computing time-varying quadratic optimization problems in the presence of various additive noises. In addition, theoretical analyses of the unified design formula and the UZNN model are given to guarantee the finite-time convergence and inherent noise tolerance. Computer simulation results verify the superior property of the UZNN model for computing time-varying quadratic optimization problems, as compared with the previously proposed ZNN models.

A new noise-tolerant and predefined-time ZNN model for time-dependent matrix inversion

In this work, a new zeroing neural network (ZNN) using a versatile activation function (VAF) is presented and introduced for solving time-dependent matrix inversion. Unlike existing ZNN models, the proposed ZNN model not only converges to zero within a predefined finite time but also tolerates several noises in solving the time-dependent matrix inversion, and thus called new noise-tolerant ZNN (NNTZNN) model. In addition, the convergence and robustness of this model are mathematically analyzed in detail. Two comparative numerical simulations with different dimensions are used to test the efficiency and superiority of the NNTZNN model to the previous ZNN models using other activation functions. In addition, two practical application examples (i.e., a mobile manipulator and a real Kinova JACO² robot manipulator) are presented to validate the applicability and physical feasibility of the NNTZNN model in a noisy environment. Both simulative and experimental results demonstrate the effectiveness and tolerant-noise ability of the NNTZNN model.