Integration enhanced and noise tolerant ZNN for computing various expressions involving outer inverses

A Survey on Biomimetic and Intelligent Algorithms with Applications

The question "How does it work" has motivated many scientists. Through the study of natural phenomena and behaviors, many intelligence algorithms have been proposed to solve various optimization problems. This paper aims to offer an informative guide for researchers who are interested in tackling optimization problems with intelligence algorithms. First, a special neural network was comprehensively discussed, and it was called a zeroing neural network (ZNN). It is especially intended for solving time-varying optimization problems, including origin, basic principles, operation mechanism, model variants, and applications. This paper presents a new classification method based on the performance index of ZNNs. Then, two classic bio-inspired algorithms, a genetic algorithm and a particle swarm algorithm, are outlined as representatives, including their origin, design process, basic principles, and applications. Finally, to emphasize the applicability of intelligence algorithms, three practical domains are introduced, including gene feature extraction, intelligence communication, and the image process.

Spacecraft Attitude Measurement and Control Using VSMSCSG and Fractional-Order Zeroing Neural Network Adaptive Steering Law

In order to improve the accuracy and convergence speed of the steering law under the conditions of high dynamics, high bandwidth, and a small deflection angle, and in an effort to improve attitude measurement and control accuracy of the spacecraft, a spacecraft attitude measurement and control method based on variable speed magnetically suspended control sensitive gyroscopes (VSMSCSGs) and the fractional-order zeroing neural network (FO-ZNN) steering law is proposed. First, a VSMSCSG configuration is designed to realize attitude measurement and control integration in which the VSMSCSGs are employed as both actuators and attitude-rate sensors. Second, a novel adaptive steering law using FO-ZNN is designed. The matrix pseudoinverses are replaced by FO-ZNN outputs, which solves the problem of accuracy degradation in the traditional pseudoinverse steering laws due to the complexity of matrix pseudoinverse operations under high dynamics conditions. In addition, the convergence and robustness of the FO-ZNN are proven. The results show that the proposed FO-ZNN converges faster than the traditional zeroing neural network under external disturbances. Finally, a new weighting function containing rotor deflection angles is added to the steering law to ensure that the saturation of the rotor deflection angles can be avoided. Semi-physical simulation results demonstrate the correctness and superiority of the proposed method.

Novel adaptive zeroing neural dynamics schemes for temporally-varying linear equation handling applied to arm path following and target motion positioning

While the handling for temporally-varying linear equation (TVLE) has received extensive attention, most methods focused on trading off the conflict between computational precision and convergence rate. Different from previous studies, this paper proposes two complete adaptive zeroing neural dynamics (ZND) schemes, including a novel adaptive continuous ZND (ACZND) model, two general variable time discretization techniques, and two resultant adaptive discrete ZND (ADZND) algorithms, to essentially eliminate the conflict. Specifically, an error-related varying-parameter ACZND model with global and exponential convergence is first designed and proposed. To further adapt to the digital hardware, two novel variable time discretization techniques are proposed to discretize the ACZND model into two ADZND algorithms. The convergence properties with respect to the convergence rate and precision of ADZND algorithms are proved via rigorous mathematical analyses. By comparing with the traditional discrete ZND (TDZND) algorithms, the superiority of ADZND algorithms in convergence rate and computational precision is shown theoretically and experimentally. Finally, simulative experiments, including numerical experiments on a specific TVLE solving as well as four application experiments on arm path following and target motion positioning are successfully conducted to substantiate the efficacy, superiority, and practicability of ADZND algorithms.

Explicit Linear Left-and-Right 5-Step Formulas With Zeroing Neural Network for Time-Varying Applications

In this article, being different from conventional time-discretization (simply called discretization) formulas, explicit linear left-and-right 5-step (ELLR5S) formulas with sixth-order precision are proposed. The general sixth-order ELLR5S formula with four variable parameters is developed first, and constraints of these four parameters are displayed to guarantee the zero stability, consistence, and convergence of the formula. Then, by choosing specific parameter values within constraints, eight specific sixth-order ELLR5S formulas are developed. The general sixth-order ELLR5S formula is further utilized to generate discrete zeroing neural network (DZNN) models for solving time-varying linear and nonlinear systems. For comparison, three conventional discretization formulas are also utilized. Theoretical analyses are presented to show the performance of ELLR5S formulas and DZNN models. Furthermore, abundant experiments, including three practical applications, that is, angle-of-arrival (AoA) localization and two redundant manipulators (PUMA560 manipulator and Kinova manipulator) control, are conducted. The synthesized results substantiate the efficacy and superiority of sixth-order ELLR5S formulas as well as the corresponding DZNN models.

Bio-Inspired Machine Learning for Distributed Confidential Multi-Portfolio Selection Problem

The recently emerging multi-portfolio selection problem lacks a proper framework to ensure that client privacy and database secrecy remain intact. Since privacy is of major concern these days, in this paper, we propose a variant of Beetle Antennae Search (BAS) known as Distributed Beetle Antennae Search (DBAS) to optimize multi-portfolio selection problems without violating the privacy of individual portfolios. DBAS is a swarm-based optimization algorithm that solely shares the gradients of portfolios among the swarm without sharing private data or portfolio stock information. DBAS is a hybrid framework, and it inherits the swarm-like nature of the Particle Swarm Optimization (PSO) algorithm with the BAS updating criteria. It ensures a robust and fast optimization of the multi-portfolio selection problem whilst keeping the privacy and secrecy of each portfolio intact. Since multi-portfolio selection problems are a recent direction for the field, no work has been done concerning the privacy of the database nor the privacy of stock information of individual portfolios. To test the robustness of DBAS, simulations were conducted consisting of four categories of multi-portfolio problems, where in each category, three portfolios were selected. To achieve this, 200 days worth of real-world stock data were utilized from 25 NASDAQ stock companies. The simulation results prove that DBAS not only ensures portfolio privacy but is also efficient and robust in selecting optimal portfolios.

Solving Complex-Valued Time-Varying Linear Matrix Equations via QR Decomposition With Applications to Robotic Motion Tracking and on Angle-of-Arrival Localization

The problem of solving linear equations is considered as one of the fundamental problems commonly encountered in science and engineering. In this article, the complex-valued time-varying linear matrix equation (CVTV-LME) problem is investigated. Then, by employing a complex-valued, time-varying QR (CVTVQR) decomposition, the zeroing neural network (ZNN) method, equivalent transformations, Kronecker product, and vectorization techniques, we propose and study a CVTVQR decomposition-based linear matrix equation (CVTVQR-LME) model. In addition to the usage of the QR decomposition, the further advantage of the CVTVQR-LME model is reflected in the fact that it can handle a linear system with square or rectangular coefficient matrix in both the matrix and vector cases. Its efficacy in solving the CVTV-LME problems have been tested in a variety of numerical simulations as well as in two applications, one in robotic motion tracking and the other in angle-of-arrival localization.

Zeroing Neural Network Approaches Based on Direct and Indirect Methods for Solving the Yang–Baxter-like Matrix Equation

This research introduces three novel zeroing neural network (ZNN) models for addressing the time-varying Yang–Baxter-like matrix equation (TV-YBLME) with arbitrary (regular or singular) real time-varying (TV) input matrices in continuous time. One ZNN dynamic utilizes error matrices directly arising from the equation involved in the TV-YBLME. Moreover, two ZNN models are proposed using basic properties of the YBLME, such as the splitting of the YBLME and sufficient conditions for a matrix to solve the YBLME. The Tikhonov regularization principle enables addressing the TV-YBLME with an arbitrary input real TV matrix. Numerical experiments, including nonsingular and singular TV input matrices, show that the suggested models deal effectively with the TV-YBLME.

Discrete-Time Advanced Zeroing Neurodynamic Algorithm Applied to Future Equality-Constrained Nonlinear Optimization With Various Noises

This research first proposes the general expression of Zhang et al. discretization (ZeaD) formulas to provide an effective general framework for finding various ZeaD formulas by the idea of high-order derivative simultaneous elimination. Then, to solve the problem of future equality-constrained nonlinear optimization (ECNO) with various noises, a specific ZeaD formula originating from the general ZeaD formula is further studied for the discretization of a noise-perturbed continuous-time advanced zeroing neurodynamic model. Subsequently, the resulting noise-perturbed discrete-time advanced zeroing neurodynamic (NP-DTAZN) algorithm is proposed for the real-time solution to the future ECNO problem with various noises suppressed simultaneously. Moreover, theoretical and numerical results are presented to show the convergence and precision of the proposed NP-DTAZN algorithm in the perturbation of various noises. Finally, comparative numerical and physical experiments based on a Kinova JACO² robot manipulator are conducted to further substantiate the efficacy, superiority, and practicability of the proposed NP-DTAZN algorithm for solving the future ECNO problem with various noises.

Zeroing Neural Network for Pseudoinversion of an Arbitrary Time-Varying Matrix Based on Singular Value Decomposition

Many researchers have investigated the time-varying (TV) matrix pseudoinverse problem in recent years, for its importance in addressing TV problems in science and engineering. In this paper, the problem of calculating the inverse or pseudoinverse of an arbitrary TV real matrix is considered and addressed using the singular value decomposition (SVD) and the zeroing neural network (ZNN) approaches. Since SVD is frequently used to compute the inverse or pseudoinverse of a matrix, this research proposes a new ZNN model based on the SVD method as well as the technique of Tikhonov regularization, for solving the problem in continuous time. Numerical experiments, involving the pseudoinversion of square, rectangular, singular, and nonsingular input matrices, indicate that the proposed models are effective for solving the problem of the inversion or pseudoinversion of time varying matrices.

Novel Discrete-Time Recurrent Neural Networks Handling Discrete-Form Time-Variant Multi-Augmented Sylvester Matrix Problems and Manipulator Application

In this article, the discrete-form time-variant multi-augmented Sylvester matrix problems, including discrete-form time-variant multi-augmented Sylvester matrix equation (MASME) and discrete-form time-variant multi-augmented Sylvester matrix inequality (MASMI), are formulated first. In order to solve the above-mentioned problems, in continuous time-variant environment, aided with the Kronecker product and vectorization techniques, the multi-augmented Sylvester matrix problems are transformed into simple linear matrix problems, which can be solved by using the proposed discrete-time recurrent neural network (RNN) models. Second, the theoretical analyses and comparisons on the computational performance of the recently developed discretization formulas are presented. Based on these theoretical results, a five-instant discretization formula with superior property is leveraged to establish the corresponding discrete-time RNN (DTRNN) models for solving the discrete-form time-variant MASME and discrete-form time-variant MASMI, respectively. Note that these DTRNN models are zero stable, consistent, and convergent with satisfied precision. Furthermore, illustrative numerical experiments are given to substantiate the excellent performance of the proposed DTRNN models for solving discrete-form time-variant multi-augmented Sylvester matrix problems. In addition, an application of robot manipulator further extends the theoretical research and physical realizability of RNN methods.

Double Accelerated Convergence ZNN with Noise-Suppression for Handling Dynamic Matrix Inversion

Matrix inversion is commonly encountered in the field of mathematics. Therefore, many methods, including zeroing neural network (ZNN), are proposed to solve matrix inversion. Despite conventional fixed-parameter ZNN (FPZNN), which can successfully address the matrix inversion problem, it may focus on either convergence speed or robustness. So, to surmount this problem, a double accelerated convergence ZNN (DAZNN) with noise-suppression and arbitrary time convergence is proposed to settle the dynamic matrix inversion problem (DMIP). The double accelerated convergence of the DAZNN model is accomplished by specially designing exponential decay variable parameters and an exponential-type sign-bi-power activation function (AF). Additionally, two theory analyses verify the DAZNN model’s arbitrary time convergence and its robustness against additive bounded noise. A matrix inversion example is utilized to illustrate that the DAZNN model has better properties when it is devoted to handling DMIP, relative to conventional FPZNNs employing other six AFs. Lastly, a dynamic positioning example that employs the evolution formula of DAZNN model verifies its availability.