The existing solutions for nonconvex optimization problems show satisfactory performance in noise-free scenarios. However, they are prone to yield inaccurate results in the presence of noise in real-world problems, which may lead to failures in optimizing nonconvex problems. To this end, in this article, we propose a coevolutionary neural solution (CNS) by combining a simplified neurodynamics (SND) model with the particle swarm optimization (PSO) algorithm. Specifically, the proposed SND model does not leverage the time-derivative information, exhibiting greater stability compared to existing models. Furthermore, due to the noise tolerance capacity and rapid convergence property exhibited by the SND model, the CNS can rapidly achieve the optimal solution even in the presence of various perturbations. Theoretical analyses ensure that the proposed CNS is globally convergent with robustness and probability. In addition, the effectiveness of the CNS is compared with those of the existing solutions by a class of illustrative examples. We further apply the proposed solution to design a finite impulse response (FIR) filter and a pressure vessel to demonstrate its performance.

Due to the significant role of sea ice in the Arctic-related research, developing high-precision and robust Arctic sea ice extraction techniques for multi-source remote-sensing images encounters a great challenge. In the light of the constrained energy minimization scheme, this article provides a generalized complex-valued constrained energy minimization (GCVCEM) scheme for the Arctic sea ice extraction with strong robustness and accessible implementation. Given the fact that the image extraction process is easily disturbed by noise in real-life application scenarios, a modified Newton integration (MNI) neural algorithm with the noise-tolerance ability and high extraction accuracy is proposed to aid the GCVCEM scheme. Its key idea is to add an error integration feedback term on the basis of the Newton–Raphson iterative (NRI) algorithm to resist noise perturbation on the solution process of the GCVCEM scheme for high-precision and robust extraction of the Arctic sea ice. Besides, the corresponding convergence analyses and robustness proofs on the proposed MNI neural algorithm are furnished. To evaluate the extraction performance of the proposed MNI neural algorithm, multiple comparative experiments with different sea ice observation images and different noise workspaces are performed. Both the visualized and quantitative experimental results substantiate the superiorities of the proposed MNI neural algorithm aided the GCVCEM scheme for the Arctic sea ice extraction.

Currently, the Newton–Raphson iterative algorithm has been extensively employed in the fields of basic research and engineering. However, when noise components exist in a system, its performance is largely affected. To remedy shortcomings that the conventional computing methods have encountered in a noisy workspace, a novel modified Newton integration (MNI) algorithm is proposed in this article. In addition, the steady-state error of the proposed MNI algorithm is smaller than that of the Newton–Raphson algorithm under a noise-free or noisy workspace. To lay the foundations for the corresponding theoretical analyses, the proposed MNI algorithm is first converted into a homogeneous linear equation with a residual term. Then, the related theoretical analyses are carried out, which indicate that the MNI algorithm possesses noise-tolerance ability under various noisy environments. Finally, multiple computer simulations and physical experiments on robot control applications are performed to verify the feasibility and advantage of the proposed MNI algorithm.

In this article, the existing approaches, including numerical algorithms as well as neural networks to solve dynamic linear matrix equations, have been presented and reviewed. Specifically, the conventional gradient recurrent neural networks (CGRNNs) and the conventional zeroing neural networks (CZNNs) are successively provided to solve the dynamic problems and linear matrix equations, both of which manifest inherent limitations during the solving procedures. To remedy the drawbacks on convergence time, nonzero residual error, and large computational load of the traditional models, an adaptive gradient recurrent neural network (AGRNN) to solve dynamic linear matrix equations is proposed. This proposed inversion-free model possesses rapid convergence rate and accurate calculated solutions. Moreover, theoretical analyses guarantee the advantages of the AGRNN compared with the CGRNN and the CZNN to solve dynamic linear matrix equations. Finally, three numerical experiments, and applications to a PUMA 560 robot motion planning and a mobile subject localization based on angle-of-arrival technique are implemented to testify the advantages of the AGRNN.

A dynamic complex-valued matrix pseudoinversion (DCVMP) is encountered in some special environments, where the system parameters contain the dynamic, magnitude, and phase information. Currently, most of the existing models are employed to the DCVMP under a noise-free workspace. However, the noise perturbation is unavoidable in the practical application scenarios. Therefore, the motivation of this article is to design a computational model for the DCVMP with strong robustness and high-precision computing solutions. To this end, a modified Newton integration (MNI) neural algorithm is proposed for the DCVMP with noise-suppressing ability in this article. Besides, the corresponding convergence proofs on the MNI neural algorithm are provided. Furthermore, the numerical simulations and an application to the estimation of mobile object localization, are demonstrated to illustrate the superiority of the MNI neural algorithm.

Many methods are known to solve the problem of real-valued and static quadratic programming (QP) effectively. However, few of them are still useful to solve the time-varying QP problem in the complex domain. In this study, a nonconvex and bound constraint zeroing neural network (NCZNN) model is designed and theorized to solve the time-varying complex-valued QP with linear equation constraint. Besides, we construct several new types of nonconvex and bound constraint complex-valued activation functions by extending real-valued activation functions to the complex domain. Subsequently, corresponding simulation experiments are conducted, and the simulation results verify the effectiveness and robustness of the proposed NCZNN model. Moreover, the model proposed in this article is further applied to solve the issue of small target detection in remote sensing images, which is modeled to QP problem with linear equation constraint by a serial of conversions based on constrained energy minimization algorithm.

The issue of impulse noise detection and reduction is a critical problem for image processing application systems. In order to detect impulse noises in corrupted images, a statistic named local consensus index (LCI) is proposed for quantitatively evaluating how noise free a pixel is, and then an impulse noise detection scheme based on LCI is introduced. First, the similarity between arbitrary two pixels in an image is quantified based on both their geometric distance and intensity difference, and the LCI of arbitrary pixel is calculated by summing all the similarity values of pixels in its neighborhood. As a new statistic, the value of LCI indicates the local consensus of the concerned pixel regarding its neighbors and could also tell whether a pixel is noise free or impulsive. Therefore, LCI can be directly used as an efficient indicator of impulse noise. Furthermore, to improve the performance of impulse noise detection, different strategies are applied to the pixels at flat regions and the ones with complex textures, since distributions of LCI value within those regions are totally different. As for impulse noise filtering, a hybrid graph Laplacian regularization (HGLR) method is introduced to restore the intensities of those pixels degraded by impulse noise. We conduct extensive experiments to verify the effectiveness of our impulsive noise detection and reduction method, and the results show that the proposed method outperforms the state-of-the-art techniques in terms of impulse detection and noise removal.

A generalized Sylvester equation is a special formulation containing the Sylvester equation, the Lyapunov equation and the Stein equation, which is often encountered in various fields. However, the time-variant generalized Sylvester equation (TVGSE) is rarely investigated in the existing literature. In this article, we propose a noise-suppressing recurrent neural network (NSRNN) model activated by saturation-allowed functions to solve the TVGSE. For comparison, the existing zeroing neural network (ZNN) models and some improved ZNN models are introduced. Additionally, theoretical analysis on the convergence and robustness of the NSRNN model is given. Furthermore, computer simulations on illustrative examples and applications to robots and acoustic source localization are carried out. Validation results synthesized by the NSRNN model and other ZNN models are provided to illustrate the ability in solving the TVGSE and dealing with noises of the NSRNN model, and the inaction of other ZNN models to noises.

In this paper, in order to analyze the existing repetitive motion planning (RMP) schemes for kinematic control of redundant robot manipulators, a generalized RMP scheme, which systematizes the existing RMP schemes, is presented. Then, the corresponding dynamic neural networks are derived, which leverage the gradient descent method with the velocity compensation with the feasibility proven theoretically. Given that the position errors of the end-effector should be tiny enough in the applications of redundant robot manipulators when executing a given task, especially for a precision instrument, the performance analyses on the control schemes are urgently desirable. In this paper, the upper bound of the position error on the existing RMP schemes is deduced theoretically and verified by computer simulations, with the relationship between the position error and the manipulability derived. In addition, dynamic neural networks are constructed to solve the generalized RMP schemes, with the joint velocity limits in RMP schemes extended to the nonconvex constraint. Finally, computer simulations based on different redundant robot manipulators and comparisons based on different controllers are conducted to verify the feasibility of the generalized RMP scheme and the proposed dynamic neural networks.