A Complex Varying-Parameter Convergent-Differential Neural-Network for Solving Online Time-Varying Complex Sylvester Equation

Modified RNN for Solving Comprehensive Sylvester Equation With TDOA Application

The augmented Sylvester equation, as a comprehensive equation, is of great significance and its special cases (e.g., Lyapunov equation, Sylvester equation, Stein equation) are frequently encountered in various fields. It is worth pointing out that the current research on simultaneously eliminating the lagging error and handling noises in the nonstationary complex-valued field is rather rare. Therefore, this article focuses on solving a nonstationary complex-valued augmented Sylvester equation (NCASE) in real time and proposes two modified recurrent neural network (RNN) models. The first proposed modified RNN model possesses gradient search and velocity compensation, termed as RNN-GV model. The superiority of the proposed RNN-GV model to traditional algorithms including the complex-valued gradient-based RNN (GRNN) model lies in completely eliminating the lagging error when employed in the nonstationary problem. The second model named complex-valued integration enhanced RNN-GV with the nonlinear acceleration (IERNN-GVN) model is proposed to adapt to a noisy environment and accelerate the convergence process. Besides, the convergence and robustness of these two proposed models are proved via theoretical analysis. Simulative results on an illustrative example and an application to the moving source localization coincide with the theoretical analysis and illustrate the excellent performance of the proposed models.

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.

Zeroing Neural Network With Coefficient Functions and Adjustable Parameters for Solving Time-Variant Sylvester Equation

To solve the time-variant Sylvester equation, in 2013, Li et al. proposed the zeroing neural network with sign-bi-power function (ZNN-SBPF) model via constructing a nonlinear activation function. In this article, to further improve the convergence rate, the zeroing neural network with coefficient functions and adjustable parameters (ZNN-CFAP) model as a variation in zeroing neural network (ZNN) model is proposed. On the basis of the introduced coefficient functions, an appropriate ZNN-CFAP model can be chosen according to the error function. The high convergence rate of the ZNN-CFAP model can be achieved by choosing appropriate adjustable parameters. Moreover, the finite-time convergence property and convergence time upper bound of the ZNN-CFAP model are proved in theory. Computer simulations and numerical experiments are performed to illustrate the efficacy and validity of the ZNN-CFAP model in time-variant Sylvester equation solving. Comparative experiments among the ZNN-CFAP, ZNN-SBPF, and ZNN with linear function (ZNN-LF) models further substantiate the superiority of the ZNN-CFAP model in view of the convergence rate. Finally, the proposed ZNN-CFAP model is successfully applied to the tracking control of robot manipulator to verify its practicability.

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.

First/second-order predefined-time convergent ZNN models for time-varying quadratic programming and robotic manipulator application

Zeroing neural network (ZNN) model, an important class of recurrent neural network, has been widely applied in the field of computation and optimization. In this paper, two ZNN models with predefined-time convergence are proposed for the time-varying quadratic programming (TVQP) problem. First, in the framework of the traditional ZNN model, the first-order predefined-time convergent ZNN (FPTZNN) model is proposed in combination with a predefined-time controller. Compared with the existing ZNN models, the proposed ZNN model is error vector combined with sliding mode control technique. Then, the FPTZNN model is further extended and the second-order predefined-time convergent ZNN (SPTZNN) model is developed. Combined with the Lyapunov method and the concept of predefined-time stability, it is shown that the proposed FPTZNN and SPTZNN models have the properties of predefined-time convergence, and their convergence time can be flexibly adjusted by predefined-time control parameters. Finally, the proposed FPTZNN and SPTZNN models are compared with the existing ZNN models for the TVQP problem in simulation experiment, and the simulation experiment results verify the effectiveness and superior performance of the proposed FPTZNN and SPTZNN models. In addition, the proposed FPTZNN model for robot motion planning problem is applied and successfully implemented to verify the practicality of the model.

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.

Robust Finite-Time Zeroing Neural Networks With Fixed and Varying Parameters for Solving Dynamic Generalized Lyapunov Equation

For solving dynamic generalized Lyapunov equation, two robust finite-time zeroing neural network (RFTZNN) models with stationary and nonstationary parameters are generated through the usage of an improved sign-bi-power (SBP) activation function (AF). Taking differential errors and model implementation errors into account, two corresponding perturbed RFTZNN models are derived to facilitate the analyses of robustness on the two RFTZNN models. Theoretical analysis gives the quantitatively estimated upper bounds for the convergence time (UBs-CT) of the two derived models, implying a superiority of the convergence that varying parameter RFTZNN (VP-RFTZNN) possesses over the fixed parameter RFTZNN (FP-RFTZNN). When the coefficient matrices and perturbation matrices are uniformly bounded, residual error of FP-RFTZNN is bounded, whereas that of VP-RFTZNN monotonically decreases at a super-exponential rate after a finite time, and eventually converges to 0. When these matrices are bounded but not uniform, residual error of FP-RFTZNN is no longer bounded, but that of VP-RFTZNN still converges. These superiorities of VP-RFTZNN are illustrated by abundant comparative experiments, and its application value is further proved by an application to robot.

Performance Analysis and Applications of Finite-Time ZNN Models With Constant/Fuzzy Parameters for TVQPEI

Based on extensive applications of the time-variant quadratic programming with equality and inequality constraints (TVQPEI) problem and the effectiveness of the zeroing neural network (ZNN) to address time-variant problems, this article proposes a novel finite-time ZNN (FT-ZNN) model with a combined activation function, aimed at providing a superior efficient neurodynamic method to solve the TVQPEI problem. The remarkable properties of the FT-ZNN model are faster finite-time convergence and preferable robustness, which are analyzed in detail, where in the case of the robustness discussion, two kinds of noises (i.e., bounded constant noise and bounded time-variant noise) are taken into account. Moreover, the proposed several theorems all compute the convergent time of the nondisturbed FT-ZNN model and the disturbed FT-ZNN model approaching to the upper bound of residual error. Besides, to enhance the performance of the FT-ZNN model, a fuzzy finite-time ZNN (FFT-ZNN), which possesses a fuzzy parameter, is further presented for solving the TVQPEI problem. A simulative example about the FT-ZNN and FFT-ZNN models solving the TVQPEI problem is given, and the experimental results expectably conform to the theoretical analysis. In addition, the designed FT-ZNN model is effectually applied to the repetitive motion of the three-link redundant robot and image fusion to show its potential practical value.

7-Instant Discrete-Time Synthesis Model Solving Future Different-Level Linear Matrix System via Equivalency of Zeroing Neural Network

Differing from the common linear matrix equation, the future different-level linear matrix system is considered, which is much more interesting and challenging. Because of its complicated structure and future-computation characteristic, traditional methods for static and same-level systems may not be effective on this occasion. For solving this difficult future different-level linear matrix system, the continuous different-level linear matrix system is first considered. On the basis of the zeroing neural network (ZNN), the physical mathematical equivalency is thus proposed, which is called ZNN equivalency (ZE), and it is compared with the traditional concept of mathematical equivalence. Then, on the basis of ZE, the continuous-time synthesis (CTS) model is further developed. To satisfy the future-computation requirement of the future different-level linear matrix system, the 7-instant discrete-time synthesis (DTS) model is further attained by utilizing the high-precision 7-instant Zhang et al. discretization (ZeaD) formula. For a comparison, three different DTS models using three conventional ZeaD formulas are also presented. Meanwhile, the efficacy of the 7-instant DTS model is testified by the theoretical analyses. Finally, experimental results verify the brilliant performance of the 7-instant DTS model in solving the future different-level linear matrix system.

Recurrent Neural Dynamics Models for Perturbed Nonstationary Quadratic Programs: A Control-Theoretical Perspective

Recent decades have witnessed a trend that control-theoretical techniques are widely leveraged in various areas, e.g., design and analysis of computational models. Computational methods can be modeled as a controller and searching the equilibrium point of a dynamical system is identical to solving an algebraic equation. Thus, absorbing mature technologies in control theory and integrating it with neural dynamics models can lead to new achievements. This work makes progress along this direction by applying control-theoretical techniques to construct new recurrent neural dynamics for manipulating a perturbed nonstationary quadratic program (QP) with time-varying parameters considered. Specifically, to break the limitations of existing continuous-time models in handling nonstationary problems, a discrete recurrent neural dynamics model is proposed to robustly deal with noise. This work shows how iterative computational methods for solving nonstationary QP can be revisited, designed, and analyzed in a control framework. A modified Newton iteration model and an improved gradient-based neural dynamics are established by referring to the superior structural technology of the presented recurrent neural dynamics, where the chief breakthrough is their excellent convergence and robustness over the traditional models. Numerical experiments are conducted to show the eminence of the proposed models in solving perturbed nonstationary QP.

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.

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.

Design and Analysis of a Novel Integral Recurrent Neural Network for Solving Time-Varying Sylvester Equation

To solve a general time-varying Sylvester equation, a novel integral recurrent neural network (IRNN) is designed and analyzed. This kind of recurrent neural networks is based on an error-integral design equation and does not need training in advance. The IRNN can achieve global convergence performance and strong robustness if odd-monotonically increasing activation functions [i.e., the linear, bipolar-sigmoid, power, or sigmoid-power activation functions (SP-AFs)] are applied. Specifically, if linear or bipolar-sigmoid activation functions are applied, the IRNN possess exponential convergence performance. The IRNN has finite-time convergence property by using power activation function. To obtain faster convergence performance and finite-time convergence property, an SP-AF is designed. Furthermore, by using the discretization method, the discrete IRNN model and its convergence analysis are also presented. Practical application to robot manipulator and computer simulation results with using different activation functions and design parameters have verified the effectiveness, stability, and reliability of the proposed IRNN.

Convergence and Robustness Analysis of Novel Adaptive Multilayer Neural Dynamics-Based Controllers of Multirotor UAVs

Because of the simple structure and strong flexibility, multirotor unmanned aerial vehicles (UAVs) have attracted considerable attention among scientific researches and engineering fields during the past decades. In this paper, a novel adaptive multilayer neural dynamic (AMND)-based controllers design method is proposed for designing the attitude angle (the roll angle ϕ , the pitch angle θ , and the yaw angle ψ ), height ( z ), and position ( x and y ) controllers of a general multirotor UAV model. Global convergence and strong robustness of the proposed AMND-based method and controllers are analyzed and proved theoretically. By incorporating the adaptive control method into the general multilayer neural dynamic-based controllers design method, multirotor UAVs with unknown disturbances can complete time-varying trajectory tracking tasks. AMND-based controllers with the self-tuning rates can estimate the unknown disturbances and solve the model uncertainty problems. Both the theoretical theorems and simulation results illustrate that the proposed design method and its controllers with strong anti-interference property can achieve the time-varying trajectory tracking control stably, reliably, and effectively. Moreover, a practical experiment by using a mini multirotor UAV illustrates the practicability of the AMND-based method.

Model-free motion control of continuum robots based on a zeroing neurodynamic approach

As a result of inherent flexibility and structural compliance, continuum robots have great potential in practical applications and are attracting more and more attentions. However, these characteristics make it difficult to acquire the accurate kinematics of continuum robots due to uncertainties, deformation and external loads. This paper introduces a method based on a zeroing neurodynamic approach to solve the trajectory tracking problem of continuum robots. The proposed method can achieve the control of a bellows-driven continuum robot just relying on the actuator input and sensory output information, without knowing any information of the kinematic model. This approach reduces the computational load and can guarantee the real time control. The convergence, stability, and robustness of the proposed approach are proved by theoretical analyses. The effectiveness of the proposed method is verified by simulation studies including tracking performance, comparisons with other three methods, and robustness tests.