Power-Type Varying-Parameter RNN for Solving TVQP Problems: Design, Analysis, and Applications

A Dynamic-Varying Parameter Enhanced ZNN Model for Solving Time-Varying Complex-Valued Tensor Inversion With Its Application to Image Encryption

Time-varying complex-valued tensor inverse (TVCTI) is a public problem worthy of being studied, while numerical solutions for the TVCTI are not effective enough. This work aims to find the accurate solution to the TVCTI using zeroing neural network (ZNN), which is an effective tool in terms of solving time-varying problems and is improved in this article to solve the TVCTI problem for the first time. Based on the design idea of ZNN, an error-adaptive dynamic parameter and a new enhanced segmented signum exponential activation function (ESS-EAF) are first designed and applied to the ZNN. Then a dynamic-varying parameter-enhanced ZNN (DVPEZNN) model is proposed to solve the TVCTI problem. The convergence and robustness of the DVPEZNN model are theoretically analyzed and discussed. In order to highlight better convergence and robustness of the DVPEZNN model, it is compared with four varying-parameter ZNN models in the illustrative example. The results show that the DVPEZNN model has better convergence and robustness than the other four ZNN models in different situations. In addition, the state solution sequence generated by the DVPEZNN model in the process of solving the TVCTI cooperates with the chaotic system and deoxyribonucleic acid (DNA) coding rules to obtain the chaotic-ZNN-DNA (CZD) image encryption algorithm, which can encrypt and decrypt images with good performance.

DCDLN: A densely connected convolutional dynamic learning network for malaria disease diagnosis

Malaria is a significant health concern worldwide, particularly in Africa where its prevalence is still alarmingly high. Using artificial intelligence algorithms to diagnose cells with malaria provides great convenience for clinicians. In this paper, a densely connected convolutional dynamic learning network (DCDLN) is proposed for the diagnosis of malaria disease. Specifically, after data processing and partitioning of the dataset, the densely connected block is trained as a feature extractor. To classify the features extracted by the feature extractor, a classifier based on a dynamic learning network is proposed in this paper. Based on experimental results, the proposed DCDLN method demonstrates a diagnostic accuracy rate of 97.23%, surpassing the diagnostic performance than existing advanced methods on an open malaria cell dataset. This accurate diagnostic effect provides convincing evidence for clinicians to make a correct diagnosis. In addition, to validate the superiority and generalization capability of the DCDLN algorithm, we also applied the algorithm to the skin cancer and garbage classification datasets. DCDLN achieved good results on these datasets as well, demonstrating that the DCDLN algorithm possesses superiority and strong generalization performance.

A Deep Ensemble Dynamic Learning Network for Corona Virus Disease 2019 Diagnosis

Corona virus disease 2019 is an extremely fatal pandemic around the world. Intelligently recognizing X-ray chest radiography images for automatically identifying corona virus disease 2019 from other types of pneumonia and normal cases provides clinicians with tremendous conveniences in diagnosis process. In this article, a deep ensemble dynamic learning network is proposed. After a chain of image preprocessing steps and the division of image dataset, convolution blocks and the final average pooling layer are pretrained as a feature extractor. For classifying the extracted feature samples, two-stage bagging dynamic learning network is trained based on neural dynamic learning and bagging algorithms, which diagnoses the presence and types of pneumonia successively. Experimental results manifest that using the proposed deep ensemble dynamic learning network obtains 98.7179% diagnosis accuracy, which indicates more excellent diagnosis effect than existing state-of-the-art models on the open image dataset. Such accurate diagnosis effects provide convincing evidences for further detections and treatments.

A collective neurodynamic penalty approach to nonconvex distributed constrained optimization

A nonconvex distributed optimization problem involving nonconvex objective functions and inequality constraints within an undirected multi-agent network is considered. Each agent communicates with its neighbors while only obtaining its individual local information (i.e. its constraint and objective function information). To overcome the challenge caused by the nonconvexity of the objective function, a collective neurodynamic penalty approach in the framework of particle swarm optimization is proposed. The state solution convergence of every neurodynamic penalty approach is directed towards the critical point ensemble of the nonconvex distributed optimization problem. Furthermore, employing their individual neurodynamic models, each neural network conducts accurate local searches within constraints. Through the utilization of both locally best-known solution information and globally best-known solution information, along with the incremental enhancement of solution quality through iterations, the globally optimal solution for a nonconvex distributed optimization problem can be found. Simulations and an application are presented to demonstrate the effectiveness and feasibility.

A varying-parameter fixed-time gradient-based dynamic network for convex optimization

We focus on the fixed-time convergence and robustness of gradient-based dynamic networks for solving convex optimization. Most of the existing gradient-based dynamic networks with fixed-time convergence have limited ability to resist interferences of noises. To improve the convergence of the gradient-based dynamic networks, we design a new activation function and propose a gradient-based dynamic network with fixed-time convergence. The proposed dynamic network has a smaller upper bound of the convergence time than the existing dynamic networks with fixed-time convergence. A time-varying scaling parameter is employed to speed up the convergence. Our gradient-based dynamic network is proved to be robust against bounded noises and is able to resist the interference of unbounded noises. The numerical tests illustrate the effectiveness and superiority of the proposed network.

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.

A Punishment Mechanism-Combined Recurrent Neural Network to Solve Motion-Planning Problem of Redundant Robot Manipulators

In order to make redundant robot manipulators (RRMs) track the complex time-varying trajectory, the motion-planning problem of RRMs can be converted into a constrained time-varying quadratic programming (TVQP) problem. By using a new punishment mechanism-combined recurrent neural network (PMRNN) proposed in this article with reference to the varying-gain neural-dynamic design (VG-NDD) formula, the TVQP problem-based motion-planning scheme can be solved and the optimal angles and velocities of joints of RRMs can also be obtained in the working space. Then, the convergence performance of the PMRNN model in solving the TVQP problem is analyzed theoretically in detail. This novel method has been substantiated to have a faster calculation speed and better accuracy than the traditional method. In addition, the PMRNN model has also been successfully applied to an actual RRM to complete an end-effector trajectory tracking task.

A Novel Neural Approach to Infinity-Norm Joint-Velocity Minimization of Kinematically Redundant Robots Under Joint Limits

Generally, the infinity-norm joint-velocity minimization (INVM) of physically constrained kinematically redundant robots can be formulated as time-variant linear programming (TVLP) with equality and inequality constraints. Zeroing neural network (ZNN) is an effective neural method for solving equality-constrained TVLP. For inequality-constrained TVLP, however, existing ZNNs become incompetent due to the lack of relevant derivative information and the inability to handle inequality constraints. Currently, there is no capable ZNN in the literature that has achieved the INVM of redundant robots under joint limits. To fill this gap, a classical INVM scheme is first introduced in this article. Then, a new joint-limit handling technique is proposed and employed to convert the INVM scheme into a unified TVLP with full derivative information. By using a perturbed Fisher-Burmeister function, the TVLP is further converted into a nonlinear equation. These conversion techniques lay a foundation for the success of designing a capable ZNN. To solve the nonlinear equation and the TVLP, a novel continuous-time ZNN (CTZNN) is designed and its corresponding discrete-time ZNN (DTZNN) is established using an extrapolated backward differentiation formula. Theoretical analysis is rigorously conducted to prove the convergence of the neural approach. Numerical studies are performed by comparing the DTZNN solver and the state-of-the-art (SOTA) linear programming (LP) solvers. Comparative results show that the DTZNN consumes the least computing time and can be a powerful alternative to the SOTA solvers. The DTZNN and the INVM scheme are finally applied to control two kinematically redundant robots. Both simulative and experimental results show that the robots successfully accomplish user-specified path-tracking tasks, verifying the effectiveness and practicability of the proposed neural approach and the INVM scheme equipped with the new joint-limit handling technique.

On a Finitely Activated Terminal RNN Approach to Time-Variant Problem Solving

This article concerns with terminal recurrent neural network (RNN) models for time-variant computing, featuring finite-valued activation functions (AFs), and finite-time convergence of error variables. Terminal RNNs stand for specific models that admit terminal attractors, and the dynamics of each neuron retains finite-time convergence. The might-existing imperfection in solving time-variant problems, through theoretically examining the asymptotically convergent RNNs, is pointed out for which the finite-time-convergent models are most desirable. The existing AFs are summarized, and it is found that there is a lack of the AFs that take only finite values. A finitely valued terminal RNN, among others, is taken into account, which involves only basic algebraic operations and taking roots. The proposed terminal RNN model is used to solve the time-variant problems undertaken, including the time-variant quadratic programming and motion planning of redundant manipulators. The numerical results are presented to demonstrate effectiveness of the proposed neural network, by which the convergence rate is comparable with that of the existing power-rate RNN.

Simultaneous Obstacle Avoidance and Target Tracking of Multiple Wheeled Mobile Robots With Certified Safety

Collision avoidance plays a major part in the control of the wheeled mobile robot (WMR). Most existing collision-avoidance methods mainly focus on a single WMR and environmental obstacles. There are few products that cast light on the collision-avoidance between multiple WMRs (MWMRs). In this article, the problem of simultaneous collision-avoidance and target tracking is investigated for MWMRs working in the shared environment from the perspective of optimization. The collision-avoidance strategy is formulated as an inequality constraint, which has proven to be collision free between the MWMRs. The designed MWMRs control scheme integrates path following, collision-avoidance, and WMR velocity compliance, in which the path following task is chosen as the secondary task, and collision-avoidance is the primary task so that safety can be guaranteed in advance. A Lagrangian-based dynamic controller is constructed for the dominating behavior of the MWMRs. Combining theoretical analyses and experiments, the feasibility of the designed control scheme for the MWMRs is substantiated. Experimental results show that if obstacles do not threaten the safety of the WMR, the top priority in the control task is the target track task. All robots move along the desired trajectory. Once the collision criterion is satisfied, the collision-avoidance mechanism is activated and prominent in the controller. Under the proposed scheme, all robots achieve the target tracking on the premise of being collision free.

Ensemble Support Vector Recurrent Neural Network for Brain Signal Detection

The brain-computer interface (BCI) P300 speller analyzes the P300 signals from the brain to achieve direct communication between humans and machines, which can assist patients with severe disabilities to control external machines or robots to complete expected tasks. Therefore, the classification method of P300 signals plays an important role in the development of BCI systems and technologies. In this article, a novel ensemble support vector recurrent neural network (E-SVRNN) framework is proposed and developed to acquire more accurate and efficient electroencephalogram (EEG) signal classification results. First, we construct a support vector machine (SVM) to formulate EEG signals recognizing model. Second, the SVM formulation is transformed into a standard convex quadratic programming (QP) problem. Third, the convex QP problem is solved by combining a varying parameter recurrent neural network (VPRNN) with a penalty function. Experimental results on BCI competition II and BCI competition III datasets demonstrate that the proposed E-SVRNN framework can achieve accuracy rates as high as 100% and 99%, respectively. In addition, the results of comparison experiments verify that the proposed E-SVRNN possesses the best recognition accuracy and information transfer rate (ITR) compared with most of the state-of-the-art algorithms.

A Barrier Varying-Parameter Dynamic Learning Network for Solving Time-Varying Quadratic Programming Problems With Multiple Constraints

Many scientific research and engineering problems can be converted to time-varying quadratic programming (TVQP) problems with constraints. Thus, TVQP problem solving plays an important role in practical applications. Many existing neural networks, such as the gradient neural network (GNN) or zeroing neural network (ZNN), were designed to solve TVQP problems, but the convergent rate is limited. The recent varying-parameter convergent-differential neural network (VP-CDNN) can accelerate the convergent rate, but it can only solve the equality-constrained problem. To remedy this deficiency, a novel barrier varying-parameter dynamic learning network (BVDLN) is proposed and designed, which can solve the equality-, inequality-, and bound-constrained problem. Specifically, the constrained TVQP problem is first converted into a matrix equation. Second, based on the modified Karush-Kuhn-Tucker (KKT) conditions and varying-parameter neural dynamic design method, the BVDLN model is conducted. The superiorities of the proposed BVDLN model can solve multiple-constrained TVQP problems, and the convergent rate can achieve superexponentially convergence. Comparative simulative experiments verify that the proposed BVDLN is more effective and more accurate. Finally, the proposed BVDLN is applied to solve a robot motion planning problems, which verifies the applicability of the proposed model.

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.

RNN for Repetitive Motion Generation of Redundant Robot Manipulators: An Orthogonal Projection-Based Scheme

For the existing repetitive motion generation (RMG) schemes for kinematic control of redundant manipulators, the position error always exists and fluctuates. This article gives an answer to this phenomenon and presents the theoretical analyses to reveal that the existing RMG schemes exist a theoretical position error related to the joint angle error. To remedy this weakness of existing solutions, an orthogonal projection RMG (OPRMG) scheme is proposed in this article by introducing an orthogonal projection method with the position error eliminated theoretically, which decouples the joint space error and Cartesian space error with joint constraints considered. The corresponding new recurrent neural networks (NRNNs) are structured by exploiting the gradient descent method with the assistance of velocity compensation with theoretical analyses provided to embody the stability and feasibility. In addition, simulation results on a fixed-based redundant manipulator, a mobile manipulator, and a multirobot system synthesized by the existing RMG schemes and the proposed one are presented to verify the superiority and precise performance of the OPRMG scheme for kinematic control of redundant manipulators. Moreover, via adjusting the coefficient, simulations on the position error and joint drift of the redundant manipulator are conducted for comparison to prove the high performance of the OPRMG scheme. To bring out the crucial point, different controllers for the redundancy resolution of redundant manipulators are compared to highlight the superiority and advantage of the proposed NRNN. This work greatly improves the existing RMG solutions in theoretically eliminating the position error and joint drift, which is of significant contributions to increasing the accuracy and efficiency of high-precision instruments in manufacturing production.

A bagging dynamic deep learning network for diagnosing COVID-19

COVID-19 is a serious ongoing worldwide pandemic. Using X-ray chest radiography images for automatically diagnosing COVID-19 is an effective and convenient means of providing diagnostic assistance to clinicians in practice. This paper proposes a bagging dynamic deep learning network (B-DDLN) for diagnosing COVID-19 by intelligently recognizing its symptoms in X-ray chest radiography images. After a series of preprocessing steps for images, we pre-train convolution blocks as a feature extractor. For the extracted features, a bagging dynamic learning network classifier is trained based on neural dynamic learning algorithm and bagging algorithm. B-DDLN connects the feature extractor and bagging classifier in series. Experimental results verify that the proposed B-DDLN achieves 98.8889% testing accuracy, which shows the best diagnosis performance among the existing state-of-the-art methods on the open image set. It also provides evidence for further detection and treatment.

A Penalty Strategy Combined Varying-Parameter Recurrent Neural Network for Solving Time-Varying Multi-Type Constrained Quadratic Programming Problems

To obtain the optimal solution to the time-varying quadratic programming (TVQP) problem with equality and multitype inequality constraints, a penalty strategy combined varying-parameter recurrent neural network (PS-VP-RNN) for solving TVQP problems is proposed and analyzed. By using a novel penalty function designed in this article, the inequality constraint of the TVQP can be transformed into a penalty term that is added into the objective function of TVQP problems. Then, based on the design method of VP-RNN, a PS-VP-RNN is designed and analyzed for solving the TVQP with penalty term. One of the greatest advantages of PS-VP-RNN is that it cannot only solve the TVQP with equality constraints but can also solve the TVQP with inequality and bounded constraints. The global convergence theorem of PS-VP-RNN is presented and proved. Finally, three numerical simulation experiments with different forms of inequality and bounded constraints verify the effectiveness and accuracy of PS-VP-RNN in solving the TVQP problems.

A Novel Supertwisting Zeroing Neural Network With Application to Mobile Robot Manipulators

Various zeroing neural network (ZNN) models have been investigated to address the tracking control of robot manipulators for the capacity of parallel processing and nonlinearity handling. However, two limitations occur in the existing ZNN models. The first one is the convergence time that tends to be infinitely large. The second one is the research of robustness that remains in the analyses of stability and asymptotic convergence. To simultaneously enhance the convergence performance and robustness, this article proposes a new ZNN model by using a supertwisting (ST) algorithm, termed STZNN model, for the tracking control of mobile robot manipulators. The proposed STZNN model inherently possesses the advantages of finite-time convergence and robustness making the control process fast and robust. The bridge from the sliding mode control to the ZNN is built, and the essential connection between the ST algorithm and ZNN is explored by constructing a unified design process. Theorems and proofs about global stability, finite-time convergence, and robustness are provided. Finally, path-tracking applications, comparisons, and tests substantiate the effectiveness and superiority of the STZNN model for the tracking control handling of mobile robot manipulators.

An Accelerated Finite-Time Convergent Neural Network for Visual Servoing of a Flexible Surgical Endoscope With Physical and RCM Constraints

This article designs and analyzes a recurrent neural network (RNN) for the visual servoing of a flexible surgical endoscope. The flexible surgical endoscope is based on a commercially available UR5 robot with a flexible endoscope attached as an end-effector. Most of the existing visual servo control frameworks of the robotic endoscopes or robot arms have not considered either the physical limits of the robot or the remote center of motion (RCM) constraints (i.e., the fulcrum effect). To tackle this issue, this article first conducts the kinematic modeling of the flexible robotic endoscope to achieve automation by visual servo control. The kinematic modeling results in a quadratic programming (QP) framework with physical limits and RCM constraints involved, making the UR5 robot applicable to surgical field. To solve the QP problem and accomplish the visual task, an RNN activated by a sign-bi-power activation function (AF) is proposed. The motivation of using the sign-bi-power AF is to enable the RNN to exhibit an accelerated finite-time convergence, which is more preferred in time-critical applications. Theoretically, the finite-time convergence of the RNN is rigorously proved using the Lyapunov theory. Compared with the previous AFs applied to the RNN, theoretical analysis shows that the RNN activated by the sign-bi-power AF delivers an accelerated convergence speed. Comparative validations are performed, showing that the proposed finite-time convergent neural network is effective to achieve visual servoing of the flexible endoscope with physical limits and RCM constraints handled simultaneously.

Complex-Valued Discrete-Time Neural Dynamics for Perturbed Time-Dependent Complex Quadratic Programming With Applications

It has been reported that some specially designed recurrent neural networks and their related neural dynamics are efficient for solving quadratic programming (QP) problems in the real domain. A complex-valued QP problem is generated if its variable vector is composed of the magnitude and phase information, which is often depicted in a time-dependent form. Given the important role that complex-valued problems play in cybernetics and engineering, computational models with high accuracy and strong robustness are urgently needed, especially for time-dependent problems. However, the research on the online solution of time-dependent complex-valued problems has been much less investigated compared to time-dependent real-valued problems. In this article, to solve the online time-dependent complex-valued QP problems subject to linear constraints, two new discrete-time neural dynamics models, which can achieve global convergence performance in the presence of perturbations with the provided theoretical analyses, are proposed and investigated. In addition, the second proposed model is developed to eliminate the operation of explicit matrix inversion by introducing the quasi-Newton Broyden-Fletcher-Goldfarb-Shanno (BFGS) method. Moreover, computer simulation results and applications in robotics and filters are provided to illustrate the feasibility and superiority of the proposed models in comparison with the existing solutions.

General 7-Instant DCZNN Model Solving Future Different-Level System of Nonlinear Inequality and Linear Equation

In this article, a novel and challenging problem called future different-level system of nonlinear inequality and linear equation (FDLSNILE) is proposed and investigated. To solve FDLSNILE, the corresponding continuous different-level system of nonlinear inequality and linear equation (CDLSNILE) is first analyzed, and then, a continuous combined zeroing neural network (CCZNN) model for solving CDLSNILE is proposed. To obtain a discrete combined zeroing neural network (DCZNN) model for solving FDLSNILE, a high-precision general 7-instant Zhang et al. discretization (ZeaD) formula for the first-order time derivative approximation is proposed. Furthermore, by applying the general 7-instant ZeaD formula to discretize the CCZNN model, a general 7-instant DCZNN (7IDCZNN) model is thus proposed for solving FDLSNILE. For comparison, by using three conventional ZeaD formulas, three conventional DCZNN models are also developed. Meanwhile, theoretical analyses and results guarantee the efficacy and superiority of the general 7IDCZNN model compared with the other three conventional DCZNN models for solving FDLSNILE. Finally, several comparative numerical experiments, including the motion control of a 5-link redundant manipulator, are provided to substantiate the efficacy and superiority of the general 7-instant ZeaD formula and the corresponding 7IDCZNN model.