Time-varying linear equations (TVLEs) play a fundamental role in the engineering field and are of great practical value. Existing methods for the TVLE still have issues with long computation time and insufficient noise resistance. Zeroing neural network (ZNN) with parallel distribution and interference tolerance traits can mitigate these deficiencies and thus are good candidates for the TVLE. Therefore, a new predefined-time adaptive ZNN (PTAZNN) model is proposed for addressing the TVLE in this article. Unlike previous ZNN models with time-varying parameters, the PTAZNN model adopts a novel error-based adaptive parameter, which makes the convergence process more rapid and avoids unnecessary waste of computational resources caused by large parameters. Moreover, the stability, convergence, and robustness of the PTAZNN model are rigorously analyzed. Two numerical examples reflect that the PTAZNN model possesses shorter convergence time and better robustness compared with several variable-parameter ZNN models. In addition, the PTAZNN model is applied to solve the inverse kinematic solution of UR5 robot on the simulation platform CoppeliaSim, and the results further indicate the feasibility of this model intuitively.

Current variable-convergence-parameter zeroing neural networks (ZNNs), including the VCP-ZNN and the FCP-ZNN, are either inefficient or unintelligent. Although researchers have discussed the application of ZNN in chaos synchronization, these ZNN-based chaos synchronization controllers are rarely used in real-world applications. To the best of the authors’ knowledge, no researchers have applied the ZNN-based chaos synchronization controllers in secure voice communication. In this study, we established a novel chaos synchronization controller based on the proportional–integral-convergence-parameter ZNN (PICP-ZNN) model, which is both computationally efficient and intelligent. It was then used in secure voice communication. To demonstrate the superior features of the proposed PICP-ZNN model, we presented both theoretical analysis and numerical experiments to show its fixed-time convergence, robustness, and adaptiveness. In addition, a detailed comparison with other state-of-the-art variable-convergence-parameter ZNNs was presented to highlight our contribution further. The upper bound of the settling time is also estimated in both noisy and noise-free environments. Overall, this study offers a novel ZNN-based secure communication scheme. The PICP-ZNN models may serve as a novel source of inspiration for enhancing the variable-convergence-parameter ZNN even further.

The decline of point cloud registration efficiency caused by bad initial position and disordered registration direction has not been effectively solved. Herein, we propose a robust registration algorithm to tackle these drawbacks. First, a novel automatic point cloud alignment strategy considering the normal vector of feature points is demonstrated. This strategy ensures fast convergence in the case of bad initial position. Second, we introduce a cross iterative optimization strategy, which combines the alignment algorithm with an improved ICP (Point-Surface ICP) version based on surface constraints to complete faster and more orderly registration. In order to reduce the computational complexity, we present a linearization for the Point-Surface ICP based on Rodrigues rotation parameterization with the small incremental rotation assumption. In the elimination of outliers, we use the normal distribution of multiple errors to automatically select the threshold interval. Eventually, a large number of experiments are conducted on some public data-sets for performance evaluation of the as-proposed algorithm. Compared with other optimal methods, our method achieves a 17.1$\%$and 58.98$\%$increase in registration accuracy in Dragon dataset and Armadillo dataset, respectively, indicating the higher superiority of our algorithm.Note to Practitioners—This paper was motivated by solving the problem of registering two PCs. Most existing approaches generally can’t solve the decline of point cloud registration efficiency caused by bad initial position and disordered registration direction. In this paper, the position information and normal vector information of feature points are considered as the constraint conditions of pose alignment, and the improved ICP is used for further registration. In order to reduce the influence of outliers, an adaptive comprehensive elimination condition is proposed. We have demonstrated through extensive experiments that the proposed registration algorithm achieves improved accuracy, robustness to point clouds of different scales, and faster convergence speed.

Taking advantage of the burgeoning zeroing neural network (ZNN) and the widely used fuzzy logic system (FLS), a novel double integral noise-tolerant fuzzy ZNN (DINTFZNN) model for solving the time-varying Sylvester matrix equation (TVSME) is proposed in this article. The special feature of the DINTFZNN model lies in the adoption of a double integral design formula, which makes the DINTFZNN model has superb robustness, that is, it can effectively suppress not only linear noise but also quadratic noise. In addition, the DINTFZNN model utilizes a fuzzy parameter generated by FLS as the design parameter, which can adaptively adjust the convergence rate and enhance the robustness and adaptability of the DINTFZNN model. Theories have rigorously demonstrated the convergence and robustness of the DINTFZNN model. By the comparison experiments with the single integral noise-tolerant ZNN model, the superiority of the DINTFZNN model is further confirmed. In the end, the design method of the DINTFZNN model is applied to the synchronization of Chua's circuit chaotic systems, which epitomizes its excellent applicability.

A dynamic gain fixed-time (FXT) robust zeroing neural network (DFTRZNN) model is proposed to effectively solve time-variant equality constrained quaternion least squares problem (TV-EQLS). The proposed approach surmounts the shortcomings of conventional numerical algorithms which fail to address time-variant problems. The DFTRZNN model is constructed with a novel dynamic gain parameter and a novel activation function (NAF), which differs from previous zeroing neural network (ZNN) models. Moreover, the comprehensive theoretical derivation of the FXT stability and robustness of the DFTRZNN model is presented in detail. Simulation results further confirm the availability and superiority of the DFTRZNN model for solving TV-EQLS. Finally, the consensus protocols of multiagent systems are presented by utilizing the design scheme of the DFTRZNN model, which further demonstrates its practical application value.

Quadratic programming with equality constraint (QPEC) problems have extensive applicability in many industries as a versatile nonlinear programming modeling tool. However, noise interference is inevitable when solving QPEC problems in complex environments, so research on noise interference suppression or elimination methods is of great interest. This article proposes a modified noise-immune fuzzy neural network (MNIFNN) model and use it to solve QPEC problems. Compared with the traditional gradient recurrent neural network (TGRNN) and traditional zeroing recurrent neural network (TZRNN) models, the MNIFNN model has the advantage of inherent noise tolerance ability and stronger robustness, which is achieved by combining proportional, integral, and differential elements. Furthermore, the design parameters of the MNIFNN model adopt two disparate fuzzy parameters generated by two fuzzy logic systems (FLSs) related to the residual and residual integral term, which can improve the adaptability of the MNIFNN model. Numerical simulations demonstrate the effectiveness of the MNIFNN model in noise tolerance.

In this article, a novel distributed gradient neural network (DGNN) with predefined-time convergence (PTC) is proposed to solve consensus problems widely existing in multiagent systems (MASs). Compared with previous gradient neural networks (GNNs) for optimization and computation, the proposed DGNN model works in a nonfully connected way, in which each neuron only needs the information of neighbor neurons to converge to the equilibrium point. The convergence and asymptotic stability of the DGNN model are proved according to the Lyapunov theory. In addition, based on a relatively loose condition, three novel nonlinear activation functions are designed to speedup the DGNN model to PTC, which is proved by rigorous theory. Computer numerical results further verify the effectiveness, especially the PTC, of the proposed nonlinearly activated DGNN model to solve various consensus problems of MASs. Finally, a practical case of the directional consensus is presented to show the feasibility of the DGNN model and a corresponding connectivity-testing example is given to verify the influence on the convergence speed.

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.

This article aims to studying how to solve dynamic Sylvester quaternion matrix equation (DSQME) using the neural dynamic method. In order to solve the DSQME, the complex representation method is first adopted to derive the equivalent dynamic Sylvester complex matrix equation (DSCME) from the DSQME. It is proven that the solution to the DSCME is the same as that of the DSQME in essence. Then, a state-of-the-art neural dynamic method is presented to generate a general dynamic-varying parameter zeroing neural network (DVPZNN) model with its global stability being guaranteed by the Lyapunov theory. Specifically, when the linear activation function is utilized in the DVPZNN model, the corresponding model [termed linear DVPZNN (LDVPZNN)] achieves finite-time convergence, and a time range is theoretically calculated. When the nonlinear power-sigmoid activation function is utilized in the DVPZNN model, the corresponding model [termed power-sigmoid DVPZNN (PSDVPZNN)] achieves the better convergence compared with the LDVPZNN model, which is proven in detail. Finally, three examples are presented to compare the solution performance of different neural models for the DSQME and the equivalent DSCME, and the results verify the correctness of the theories and the superiority of the proposed two DVPZNN models.

Sylvester equation is often applied to various fields, such as mathematics and control systems due to its importance. Zeroing neural network (ZNN), as a systematic design method for time-variant problems, has been proved to be effective on solving Sylvester equation in the ideal conditions. In this paper, in order to realize the predefined-time convergence of the ZNN model and modify its robustness, two new noise-tolerant ZNNs (NNTZNNs) are established by devising two novelly constructed nonlinear activation functions (AFs) to find the accurate solution of the time-variant Sylvester equation in the presence of various noises. Unlike the original ZNN models activated by known AFs, the proposed two NNTZNN models are activated by two novel AFs, therefore, possessing the excellent predefined-time convergence and strong robustness even in the presence of various noises. Besides, the detailed theoretical analyses of the predefined-time convergence and robustness ability for the NNTZNN models are given by considering different kinds of noises. Simulation comparative results further verify the excellent performance of the proposed NNTZNN models, when applied to online solution of the time-variant Sylvester equation.

This article aims to design an intelligent mobile charging control mechanism for electric vehicles (EVs), by promoting charging reservations (including service start time, expected charging time, and charging location). EV mobile charging could be implemented as an alternative recharging solution, wherein charge replenishment is provided by economically mobile plug-in chargers, capable of providing on-site charging services. With intelligent charging management, readily available mobile chargers are predictable and could be efficiently scheduled toward EVs with charging demand, based on updated context collected from across the charging network. The context can include critical information relating to charging sessions and charging demand. Furthermore, with reservations introduced, accurate estimations on charging demand for a future moment are achievable, and correspondingly, optimal mobile chargers selection can be obtained. Therefore, charging demands across the network can be efficiently and effectively satisfied, with the support of intelligent system-level decisions. In order to evaluate critical performance attributes, we further carry out extensive simulation experiments with practical concerns to verify our insights observed from the theoretical analysis. Results show great performance gains by promoting the reservation-based mobile charger selection, especially for mobile chargers equipped with suffice power capacity. Note to Practitioners-The convenience of charging service is one major concern for EVs, especially when an urgent charging is required while none charging points are reachable. Recently, a Chinese EV company (NIO, Inc., Shanghai, China) is promoting its mobile charger (ES8 model) to Tesla. Driven by such market trend, this article proposes an efficient approach toward intelligent scheduling of mobile chargers toward parked EVs. Different from fixed charging stations focusing on the problem of long waiting times, the proposed solution is applicable to charging-on-demand with precharging appointment at mobile chargers. Preliminary experiments show great charging efficiency achieved by concerning the issue of where to reserve, i.e., the consideration of optimal selection on mobile chargers. Such mobile charging services can coexist with the governmental or pilots' initiated charging station deployment. However, future research will need to evaluate the holistic service platform.

Complex-valued time-dependent matrix inversion (TDMI) is extensively exploited in practical industrial and engineering fields. Many current neural models are presented to find the inverse of a matrix in an ideal noise-free environment. However, the outer interferences are normally believed to be ubiquitous and avoidable in practice. If these neural models are applied to complex-valued TDMI in a noise environment, they need to take a lot of precious time to deal with outer noise disturbances in advance. Thus, a noise-suppression model is urgent to be proposed to address this problem. In this article, a complex-valued noise-tolerant zeroing neural network (CVNTZNN) on the basis of an integral-type design formula is established and investigated for finding complex-valued TDMI under a wide variety of noises. Furthermore, both convergence and robustness of the CVNTZNN model are carefully analyzed and rigorously proved. For comparison and verification purposes, the existing zeroing neural network (ZNN) and gradient neural network (GNN) have been presented to address the same problem under the same conditions. Numerical simulation consequences demonstrate the effectiveness and excellence of the proposed CVNTZNN model for complex-valued TDMI under various kinds of noises, by comparing the existing ZNN and GNN models.

Zeroing neural network (ZNN) is a powerful tool to address the mathematical and optimization problems broadly arisen in the science and engineering areas. The convergence and robustness are always co-pursued in ZNN. However, there exists no related work on the ZNN for time-dependent nonlinear minimization that achieves simultaneously limited-time convergence and inherently noise suppression. In this article, for the purpose of satisfying such two requirements, a limited-time robust neural network (LTRNN) is devised and presented to solve time-dependent nonlinear minimization under various external disturbances. Different from the previous ZNN model for this problem either with limited-time convergence or with noise suppression, the proposed LTRNN model simultaneously possesses such two characteristics. Besides, rigorous theoretical analyses are given to prove the superior performance of the LTRNN model when adopted to solve time-dependent nonlinear minimization under external disturbances. Comparative results also substantiate the effectiveness and advantages of LTRNN via solving a time-dependent nonlinear minimization problem.

Further accelerated by the Internet of Things (IoT) concept, various devices are being continuously introduced into diverse application scenarios. To achieve unattended updates of IoT smart object(s), there remains a challenging problem concerning how to efficiently deliver messages to specific groups of target nodes, especially considering node mobility. In this paper, the relay selection problem is investigated on the basis of directional movement with randomness (e.g., typically associated with the searching or migrating behavior of animals). Unlike numerous works tackling one-to-one communication, we focus on efficient group delivery (one-to-many). A two-level delay budget model is considered to reflect the flexibility of delay tolerance, which brings potential efficiency gains for group delivery compared with using a single budget boundary. Following the description of the system model, a combinatorial bi-objective optimization problem is formulated and solutions are proposed. Simulation results show that the greedy algorithm can achieve comparable performance to an evolutionary algorithm when the delivery satisfaction outweighs efficiency. Furthermore, we show that our proposed greedy scheme can outperform the state-of-the-art when the delivery efficiency becomes increasingly important.

This paper introduces a new and low-cost tissue stiffness simulation technique for surgical training and robot-assisted minimally invasive surgery (RMIS) with pseudo-haptic feedback based on tissue stiffness maps provided by rolling mechanical imaging. Superficial palpation and deep palpation pseudo-haptic simulation methods are presented. Although without expensive haptic interfaces users receive only visual feedback (pseudo-haptics) when maneuvering a cursor over the surface of a virtual soft-tissue organ by means of an input device such as a mouse, a joystick, or a touch-sensitive tablet, the alterations to the cursor behavior induced by the method creates the experience of actual interaction with a tumor in the users' minds. The proposed methods are experimentally evaluated for tissue abnormality identification. It is shown that users can recognize tumors with these two methods and the rate of correctly recognized tumors in deep palpation pseudo-haptic simulation is higher than superficial palpation simulation.

This paper presents a novel optical fiber-based rolling indentation probe designed to measure the stiffness distribution of a soft tissue while rolling over the tissue surface during minimally invasive surgery. By fusing the measurements along rolling paths, the probe can generalize a mechanical image to visualize the stiffness distribution within the internal tissue structure. Since tissue abnormalities are often firmer than the surrounding organ or parenchyma, a surgeon then can localize abnormalities by analyzing the image. The performance of the developed probe was validated using simulated soft tissues. Results show that the probe can measure both force and indentation depth accurately with different orientations when the probe approached and rolled on the tissue surface. In addition, experiments for tumor, identification through rolling indentation were conducted. The size and embedded depth of the tumor, as well as the stiffness ratio between the tumor and tissue, were varied during tests. Results demonstrate that the probe can effectively and accurately identify the embedded tumors.

This paper presents a novel miniaturized force-indentation depth (FID) sensor designed to conduct indentation on soft tissue during minimally invasive surgery. It can intra-operatively aid the surgeon to rapidly identify the tissue abnormalities within the tissue. The FID sensor can measure the indentation depth of a semi-spherical indenter and the tissue reaction force simultaneously. It make use of with fiber optical fiber sensing method measure indentation depth and force and is small enough to fit through a standard trocar port with a diameter of 11 mm. The created FID sensor was calibrated and tested on silicone block simulating soft tissue. The results show that the sensor can measure the indentation depth accurately and also the orientation of the sensor with respect to the tissue surface whilst performing indentation.