The powerful generalization of Vision-Language-Action (VLA) models is bottlenecked by their heavy reliance on massive, redundant, and unevenly valued datasets, hindering their widespread application. Existing model-centric optimization paths, such as model compression (which often leads to performance degradation) or policy distillation (whose products are model-dependent and lack generality), fail to fundamentally address this data-level challenge. To this end, this paper introduces FT-NCFM, a fundamentally different, data-centric generative data distillation framework. Our framework employs a self-contained Fact-Tracing (FT) engine that combines causal attribution with programmatic contrastive verification to assess the intrinsic value of samples. Guided by these assessments, an adversarial NCFM process synthesizes a model-agnostic, information-dense, and reusable data asset. Experimental results on several mainstream VLA benchmarks show that models trained on just 5\% of our distilled coreset achieve a success rate of 85-90\% compared with training on the full dataset, while reducing training time by over 80\%. Our work demonstrates that intelligent data distillation is a highly promising new path for building efficient, high-performance VLA models.

Natural language programming of robotic systems presents significant challenges in bridging high-level intent with low-level motion planning, particularly for redundant manipulators in artistic or spatially constrained tasks. We present \textbf{BeetleBrush}, a novel LLM-powered robotic drawing framework that combines large-scale language understanding with bio-inspired optimization for trajectory execution. Natural language prompts are processed using Google Gemini 2.5 Flash within a Retrieval-Augmented Generation (RAG) system enhanced by a curated database of over 200 drawing examples. The resulting stroke sequences are translated into target end-effector trajectories, which are executed using a 7-DOF KUKA manipulator through an enhanced Beetle Antennae Search (BAS) algorithm operating in forward kinematics space-circumventing the need for analytical inverse kinematics. Our system achieves accurate, safe, and expressive robot drawings with real-time performance and high workspace compliance. Across 12 representative prompts of varying complexity, BeetleBrush achieved mean end-effector errors of 0.0048–0.0051 meters and RMSE values below 0.0051 meters in most cases, with maximum errors under 0.0173 meters. The system also exhibited stable convergence behavior and successfully executed 94.4\% of strokes across tasks, including geometrically constrained figures like cubes, cones, and composite scenes. BeetleBrush demonstrates how LLM-guided generation and bio-inspired control can be effectively integrated for robust, intuitive, and geometry-aware robot programming.

The trajectory planning problem is a key aspect of underwater robot operations. Most existing studies focus on a single underwater robot and environmental obstacles, with limited research on collision avoidance planning among multiple underwater robots. This paper addresses these issues for multiple underwater robots by performing the simultaneous target tracking (STT) from an optimization perspective. On the basis of the neurodynamic design method, the path tracking, collision avoidance, and communication maintenance are formulated as a series of inequality and equality constraints. By incorporating these constraints, the STT scheme, which is depicted as a unified quadratic program (QP) framework, is thus established for multiple underwater robots with certified safety. Such a QP-type STT scheme is then solved by using the Lagrangian-based recurrent neural network. Computer simulations are performed to further verify the effectiveness and feasibility of the proposed QP-type STT scheme. These results indicate that the multiple underwater robots via the proposed STT scheme can accomplish the assigned target-tracking tasks while maintaining the safe distance to avoid collision and staying within communication range throughout the tracking mission.

Sensor-related disturbances and measurement uncertainties often degrade the performance of dynamic neural network methods in solving time-varying problems, especially the time-varying generalized matrix inversion (TVGMI) problem, which serves as the computational foundation for real-time control and signal reconstruction tasks. Traditional zeroing neural network (ZNN) models for handling TVGMI problems usually require matrix inversion or vectorization operations, leading to high computational complexity and poor robustness under sensor disturbance or time-varying perturbations. To overcome these challenges, this paper proposes a novel low-complexity zeroing neural network (LCZNN) model that achieves efficient and unified computation of time-varying matrix inversion and pseudoinverse without involving inverse matrix computation. To further enhance robustness, the LCZNN model is extended to handle multilayered sensor-related disturbances, giving rise to three variants: the state-disturbed LCZNN (SDLCZNN), the velocity-disturbed LCZNN (VDLCZNN), and the hybrid-disturbed LCZNN (HDLCZNN) models. Each variant introduces structured compensation dynamics that enable accurate convergence under different disturbance scenarios. Rigorous theoretical analyses establish their convergence and stability properties. Comprehensive numerical experiments on representative TVGMI problems validate the low computational burden, fast convergence, and superior multilayered disturbance tolerance of the proposed LCZNN framework. Moreover, discrete algorithms derived via Euler discretization are applied to the real-time path-tracking inverse-kinematics control of robotic manipulators. Simulation and physical experimental results confirm that the proposed LCZNN-based algorithms achieve high tracking precision, strong robustness, and computational efficiency, making them well suited for real-time robotic and control applications.

Motion planning (MP) is one of fundamental issues in robot manipulators. Various MP schemes at joint velocity and acceleration levels are reported, but the noise impact is usually neglected. This paper presents an enhanced version of the acceleration-level MP (ALMP) method, incorporating additive noise considerations, specifically designed for robotic manipulators. Then, such an improved method, which is based on the pseudoinverse of robots’ Jacobian matrix, is theoretically proven to be robust against different types of noise. As case studies of the improved method, the noise-tolerance repetitive motion planning (NT-RMP) and the noise-tolerance minimum acceleration norm (NT-MAN) scheme are established for robot manipulators. Simulation and experiment results under the UR5 and Panda robot manipulators corrupted by different noises further validate the effectiveness and practicality of such two schemes and the improved ALMP method.

This study addresses the problem of stock investment strategy, aiming to select the optimal k (k < n) stocks from a set of n stocks within a distributed topology to maximize investment returns. To this end, we propose a dynamic and adaptive neural network model based on the distributed k-winner-take-all (k-WTA) protocol. Firstly, we reformulate the k-WTA problem as a constrained quadratic programming problem and utilize the Sigmoid activation function to relax equality and inequality constraints. Secondly, by combining the simplified constraints with the graph-based topology of stock interactions, we construct a Lagrangian function and develop a time-evolving dynamic neural network whose neuron states update continuously until convergence, reflecting temporal adaptability and convergence dynamics. Unlike traditional centralized methods, the proposed network allows each stock node to communicate only with its connected neighbors, ensuring decentralized computation and scalability. We further present the hardware implementation and theoretically prove the model's stability and convergence under connected graph topologies. Experiments include six static-input tests (different stock counts, parameters, and Gaussian noise) and dynamic validation using real-world stock data from 30 assets over 50 trading days. All seven experimental results confirm the feasibility, effectiveness, and robustness of the proposed model. Comparative analysis with existing WTA models also demonstrates superior adaptability and convergence performance.

In this paper, an adaptive force-motion control framework with orientation compliance is present for redundant manipulators in physical interaction with unknown surfaces. The proposed framework includes control task space definition and double-closed-loop control based on external force loop approach. Firstly, a specification matrix is designed merely through force feedback to ensure the control task space defined in orthogonal spaces. Then, an orientation compliance controller and a force-motion close-loop controller are constructed in the outer-loop control of external force feedback loop approach. Secondly, the output of outer-loop control task, along with boundary constraints and optimization indexes is formulated as a nolinear dynamic programming problem. Next a finite-time convergence neural network based inner-loop controller is proposed for this category of dynamic programming problem and its stability and convergence analysis are given. Simulations verify the convergence and effectiveness of the proposed framework. The real-world experiments show that the Mean Integral of the Absolute Error of the proposed control framework is reduced by 77.26% compared with constant impedance control.

Structural characteristics play a pivotal role in the cooperative control of multirobot systems. Although the gravity vector can often be obtained through precalibration, accurately determining the Jacobian, mass, and Coriolis matrices remains challenging because of structural variations and parameter uncertainties, which complicates precise control. This challenge can be reconceptualized as a game of incomplete information, in which each robot, acting as a player, operates with limited knowledge of its structural characteristics. To address this informational deficit, a kinematics- and dynamics-based scheme is proposed to efficiently estimate the Jacobian, mass, and Coriolis matrices of multirobot systems with partially unknown structural characteristics (MRSPUSC) using data-driven techniques. With these key structural matrices continuously estimated, a discrete-time neural dynamics model is then developed to search for the optimal strategy corresponding to the Nash equilibrium of the game. The resulting integrated scheme enables the effective control of MRSPUSC and demonstrates the capability of the proposed approach to overcome challenges arising from partially unknown structural characteristics

Physical layer secret key generation has emerged as a promising approach for secret key establishment in wireless networks. Unlike traditional quantization-based methods, recent studies have explored matching the patterns of segmented channel samples of equal length for key agreement. However, equal-length segmentation either suffers from inconsistencies between users for short segments or a reduced key generation rate for long ones. To address these issues, we propose a Variable-length Segment Matching-based Secret Key Generation method, VSM-SKG, which adaptively partitions channel samples into variable-length segments to enhance overall matching accuracy, key generation rate, and encryption strength. Specifically, we introduce a dissimilarity-enhanced segmentation and calibration strategy that partitions channel samples into variable-length segments to enlarge segment-wise dissimilarity. To achieve consistent key recovery between users, we develop a dynamic path-aware key generation method that identifies potential segmentation patterns and generates agreed-upon secret keys using a recursive approach combined with a fast retrieval mechanism. Theoretical analyses and real-world experiments validate the attributes of VSM-SKG in terms of accuracy, efficiency, and security in key generation.

In this research, an orthogonal projected gradient differential neural solution (OPGDNS) is introduced, specifically tailored for addressing linear and quadratic constrained optimization (LQCO) problems. The orthogonal projection theorem and gradient information are strategically leveraged, enabling the proposed solution to exhibit superior efficacy over existing methods, particularly those derived from a differential neural solution (DNS) standpoint, in handling linear and quadratic constraints. Theorems and proofs concerning the stability and convergence of the proposed OPGDNS model for LQCO problems are established. Finally, a numerical example is given, and experiments on the robust adaptive beamforming and the redundant robot are implemented, substantiating the applicability and advantage of the proposed OPGDNS model.

It is very challenging to precisely control a redundant manipulator with an unknown model during the end-effector tracking task. Adata-driven approach offers a promising solution for manipulator control under such conditions. In this article, two data-driven discrete neurodynamics (DDDN) schemes are proposed for redundant manipulator tracking control. First, utilizing discrete neurodynamics (DN) principles, the DDDN-1 scheme with an adaptive Jacobian matrix is developed. Subsequently, the DDDN-2 scheme is further presented, which eliminates the need for the Jacobian matrix inversion operation. Detailed theoretical analyses verify the effectiveness of DDDN-1 and DDDN-2 schemes. Additionally, detailed comparisons with existing schemes have been provided. Finally, simulative and physical experiments conducted using the UR5 manipulator validate the theoretical analyses, demonstrating the effectiveness and superiority of DDDN-1 and DDDN-2 schemes.

Metaheuristic algorithms solve optimization problems mostly by imitating behaviors observed in nature. Over time, these algorithms have proven to be very effective in solving complex optimization problems. Due to the rising complexity and scale of practical engineering problems, numerous metaheuristic algorithms have been developed recently and applied in various fields. In response to this need, researchers continue to explore novel approaches inspired by natural and social phenomena. Inspired by the competition among ancient tribes and their cooperative behavior, this paper proposes a meta-heuristic called the Competition of Tribes and Cooperation of Members Algorithm (CTCM). Experiments are conducted on 23 benchmark test functions and comprehensively compared with other state-of-the-art algorithms, including particle swarm optimization (PSO), grey wolf optimizer (GWO), sparrow search algorithm (SSA), egret swarm optimization (ESOA), beetle antennae search (BAS) and whale optimization (WOA). The standard deviation and average, as well as statistical tests are utilized to compare the performance of each algorithm, which demonstrates that CTCM is superior in the majority of problems. In addition, the results of Wilcoxon and Friedman rank tests show that the CTCM achieves the first place in all categories of problems. The results indicate that CTCM possesses strong global optimization search capability and stability, and has faster convergence speed. The paper also considers solving practical engineering optimization problems as proof-of-concept case studies , in which CTCM achieves all the optimal solutions for each engineering problem.

In recent years, multi-sensor fusion has gained significant attention from researchers and is used extensively in simultaneous localization and mapping (SLAM) applications, such as visual-inertial odometry (VIO). This technology primarily utilizes visual and odometry measurements for unmanned aerial vehicles (UAVs) to estimate their position, orientation, and environment. However, in most previous works, the input error data of sensors in the system were considered independent. To improve system precision and fully utilize sensor data, a new method called Multi-State Constraint Kalman Filter with NearSAC (MSCKF-NearSAC), based on the MSCKF, is proposed. This method eliminates outliers by limiting the range of selected points, which significantly improves the success rate of feature point matching in the front-end. Furthermore, the MSCKF-ZNN method is proposed for the back-end, and combines zeroing neural network (ZNN) (originated from the Hopfield-type neural network) and error state, resulting in an exponentially converging output trajectory error, thus improving the trajectory precision of the SLAM system. The proposed algorithms, MSCKF-NearSAC and MSCKF-ZNN, are used in the excellent work of the stereo multi-state constraint Kalman filter system (S-MSCKF). A plethora of comparison experiments, utilizing precise measurement and calibration techniques, are conducted on open-source datasets and real-world environments. Experimental results demonstrate that the introduced approach exhibits higher stability in contrast to other algorithms.

Driven by escalating demands for precision and speed in modern industrial applications, residual vibrations in flexible structures and underactuated systems have emerged as a critical technical challenge, particularly during high-speed emergency braking scenarios. Input shaping has proven to be an effective technique for vibration control. However, existing input shapers commonly encounter challenges with time delay and inaccurate parameters, leading to suboptimal control performance. To address these critical issues, this paper proposes an Unscented Kalman filter-based Residual negative equal-magnitude Shaping (URS) model with two-fold ideas: a) reducing the time delay and compensating the modeling error via the consideration of negative and residual impulse vector; and b) identifying system parameters using a data-driven unscented Kalman filter to enhance control effectiveness. To validate its performance, four experimental datasets from laboratory systems have been established and publicly released. Empirical studies demonstrate that the proposed URS model has achieved a significant vibration suppression effect over several state-of-the-art methods.

Real-time online optimisation plays a crucial role in high-frequency trading (HFT) strategies. The Markowitz model, as a Nobel Prize-winning framework, is widely used for portfolio management optimisation by framing the problem as a constrained quadratic programming task. While conventional analytical methods are typically effective for solving quadratic programming problems with linear constraints, the introduction of both linear equality and inequality constraints in the Markowitz model necessitates the use of numerical methods. The complexity of these numerical solutions presents technical challenges for real-time online optimisation, especially in HFT environments where computational speed and efficiency are critical. To address this challenge, we propose a simplified model that decomposes the problem into analytically solvable and unsolvable components, alongside an innovative dynamic neural network designed to quickly solve the unsolvable components. Overall, this method helps reduce computational load and is well-suited for real-time online computations in HFT settings. Furthermore, we conducted a theoretical analysis and proof of the optimality and global convergence of the solutions obtained using this method. Finally, based on a large set of real stock data, we performed three numerical experiments to validate its effectiveness. Notably, in an experiment using Dow Jones Industrial Average (DJIA) stock data, our approach reduced total costs by 5.54% compared to the commonly used MATLAB quadprog() solver, demonstrating the potential of this method as an efficient tool for portfolio management in HFT scenarios.

The existence of inner uncertainty and external perturbation usually becomes a hindrance for the effective time-variant control of robot manipulators. Both the robustness and convergence property are regarded as two significant issues to be addressed for preferred solutions to robot manipulators. To handle the time-variant motion control of robot manipulators in the presence of both uncertainty and perturbation, a robust recurrent neural network (RRNN) model with definable convergence time (DCT) property is proposed in this paper. Theoretical analysis based on Lyapunov theory rigorously proves that the proposed RRNN model inherently possesses the global stability, robustness and time efficiency. The solution synthesized via the proposed model with uncertainty and perturbation shows desirable time-variant control performance, i.e., faster convergence and higher accurate. In addition, detailed path-tracking examples, performance comparisons, visual-assisted depth maintenance tracking control demonstrations, and extensive tests by applying both PUMA 560 and INNFOS are presented to validate the effectiveness and superiority of the proposed RRNN model for time-variant control of robot manipulators. Note to Practitioners—This article addresses the issue of uncertainty in robot information, a common occurrence in real-time robot learning and control. This paper presents a precise, efficient, and stable solution that leverages real-time feedback information to resolve real-time control problems for robotic manipulators at the velocity level. Additionally, the paper provides a comprehensive overview of the algorithmic steps and theoretical foundations of the RRNN model to facilitate understanding. To validate the effectiveness and superiority of the proposed approach, the study conducts computer simulations and comparisons using actual parameters and models. Finally, an application to the depth maintenance trecking control of robot mainpulators provides an applicative demo of the porposed neural dynamics for practitioners.

With the rapid development of the multi-robot systems, formation control has become a fundamental challenge. Traditional approaches focus mainly on the design of control algorithms to realize specific formation patterns, while neglecting how to determine the desired formation. In this paper, the optimal formation problem based on shape theory is reformulated as a convex optimization problem. A predetermined time convergent zeroing neural dynamics (PDTZND) approach, derived from zeroing neural networks (ZNN), is proposed to efficiently solve this problem. The PDTZND approach ensures that the system error converges in a strict and predetermined time, which provides an efficient, accurate solution for optimal formation. In addition, the convergence of the proposed approach is rigorously analyzed by means of Lyapunov theory, and its validity and superiority are verified by numerical simulations and physical experiments.

The quadratic program (QP) with equality constraint is widely involved in science and engineering fields. Numerous solutions to the equality-constrained QP (ECQP) have been reported, particularly the zeroing neural network (ZNN) for the time-dependent ECQP. However, such solutions can be severely affected by the harmonic noise and may lose their efficacy. This study aims to address the above limitation by proposing the new ZNN model against harmonic noise with the only known frequency. Such a model, called the harmonic noise rejection ZNN (HNR-ZNN) model, is established by incorporating the dynamics of the harmonic signal (from which the unknown information for the signal's amplitude and phase can be eliminated). Theoretical analysis indicates that the proposed HNR-ZNN model effectively determines the optimal solution of time-dependent ECQP under harmonic noise interference. Comparative computer simulations and real-world robot applications further indicate the validity, excellence, and practicality of the presented HNR-ZNN model.

The parameter and model uncertainties are inevitable in modern industrial systems. To address this problem, a digital-twin-based model-free approximated optimal trajectory tracking control strategy is proposed in this article for the photoelectric tracking system (PTS). With the online operational data, the digital replica of the physical PTS is dynamically established based on the designed parameter learning law to estimate the model parameters iteratively for the subsequent control optimization. To prevent the direct solving of Hamilton–Jacobian–Bellman differential equation, the performance index in this article is estimated by employing the Taylor series expansion, and a computationally efficient control law with exponential convergence is explicitly derived based on the projection neural controller for model-free approximated optimal control of PTS. Additionally, comprehensive numerical simulation and experiments on a laboratory prototype of PTS verify the excellent performance and practical feasibility of the proposed method even in scenarios of serious perturbations.

UAV swarms have attracted much attention due to their high potential to execute complex missions more robustly and effectively. Essential technologies for swarms are the family of algorithms that allow the individual agents to undertake tasks intelligently, localize their relative positions, perceive surroundings, and plan and track collision-free and low-cost trajectories cooperatively so that the swarm’s overall objectives are efficiently achieved. There is still a lack of corresponding surveys that provide a systematic summary covering the control layer to task allocation and guide application-driven researchers in leveraging these capabilities for diverse UAV swarm applications. This survey debates the essential technologies of UAV swarms, including swarm trajectory planning, task assignment, control approaches, localization, perception, and communications. State-of-the-art algorithms and recent technical advancements have been investigated to expose the potential for developing highly autonomous and intelligent swarm systems. It further explores the use cases of UAV swarms in civil applications and critically analyzes existing technologies. The paper concludes by emphasizing the challenges for autonomous and intelligent UAV swarms and outlining potential future research directions. Overall, this paper provides a contemporary and comprehensive review of UAV swarm technologies and investigates their potential to transform civil application fields and support future technology advancement.

It is noteworthy that the Sylvester equation plays a pivotal role in the field of industrial intelligence control. To meet the demands of real-time applications, temporal-dependent Sylvester equations (TDSEs) are employed to formulate motion planning problems for robot manipulators. Traditionally, the classical Zhang neurodynamics (ZN) method is utilized to address the TDSE problems, which encounters challenges associated with temporal-dependent inverse matrix computations. In this article, we introduce an inverse-free approach based on energy zeroing, termed the reciprocal-kind ZN (RKZN) model, specifically designed to tackle the TDSE problem. Additionally, we propose a discrete RKZN (DRKZN) algorithm to address future Sylvester equation (FSE) problems and the motion planning challenges of robot manipulators. Furthermore, we conduct a thorough analysis of the convergence property and robustness of the RKZN method for addressing the TDSE problem. This analysis is grounded in the Lyapunov stability theory of nonlinear systems and a comparative method for nonlinear systems with temporal-dependent error-feedback-related uncertainty disturbances. Numerical experiments, simulations, and physical experiments substantiate the effectiveness and superiority of the developed RKZN method in addressing both the TDSE problem and the motion planning challenges of robot manipulators.

Redundant manipulators have been widely used in various industries whose applications not only improve production efficiency and reduce manual labor but also promote innovation in robotics and artificial intelligence. Kinematic control plays a fundamental and crucial role in robot control. Over the past few decades, numerous motion control schemes have been proposed and applied to trajectory tracking tasks. However, most of these schemes do not consider the introduction of sparsity into the motion control of redundant manipulators, resulting in excessive joint movements, which not only consume extra energy but also increase the risk of unexpected collisions in complex environments. To solve this problem, we transform the issue of increasing the sparsity into a nonconvex optimization problem. Furthermore, a collective neural dynamics for sparse motion planning (CNDSMP) scheme for motion planning of redundant manipulators is proposed. By incorporating sparsity into the control scheme, the excessive joint movements are minimized, leading to improved efficiency and reduced collision risks. Through simulations, comparisons, and physical experiments, the effectiveness and superiority of the proposed scheme are demonstrated.

This article first proposes an adaptive noise-learning differential neural solution (ANLDNS) model, which is able to simultaneously solve the time-dependent equality-constrained quadratic optimization (TD-ECQO) problem and effectively cope with noise disturbances during the solving process. The incorporated noise learning mechanism is designed to enhance the robustness of the ANLDNS model, which is achieved by learning the variation tendency of the involved noise disturbances. Furthermore, the convergence performance and noise-learning capacity of the ANLDNS model are substantiated with theoretical proofs. Finally, the time-dependent numerical examples and an application to the control of a redundant robot are provided to demonstrate the preeminent performance and practicability of the proposed model compared with existing state-of-the-art methods.

The absolute positioning accuracy of an industrial robot arm is vital for advancing manufacturing-related applications like automatic assembly, which can be improved via the data-driven approaches to robot arm calibration. Existing data-driven calibrators have illustrated their efficiency in addressing the issue of robot arm calibration. However, they mostly are single learning models that can be easily affected by the insufficient representation of the solution space, therefore, suffering from the calibration accuracy loss. To address this issue, this study proposes a calibrator fuzzy ensemble (CFE) with twofold ideas: 1) implementing eight data-driven calibrators relying on different sophisticated machine learning algorithms for an industrial robot arm, which guarantees the accuracy of individual base models and 2) innovatively developing a fuzzy ensemble of the obtained eight diversified calibrators to obtain impressively high calibration accuracy for an industrial robot arm. Extensive experiments on an ABB IRB120 industrial robot implemented with MATLAB demonstrate that compared with state-of-the-art calibrators, CFE decreases the maximum error at 8.59%. Hence, it has great potential for real applications.

A series of discrete time-variant matrix inequalities is generally regarded as one of the challenging problems in science and engineering fields. As a discrete time-variant problem, the existing solving schemes generally need the theoretical support under the continuous-time framework, and there is no independent solving scheme under the discrete-time framework. The theoretical deficiency of solving scheme greatly limits the theoretical research and practical application of discrete time-variant matrix inequalities. In this article, new discrete-time recurrent neural network (RNN) algorithms are proposed, analyzed, and investigated for solving different time-variant matrix inequalities under the discrete-time framework, including discrete time-variant matrix vector inequality (discrete time-variant MVI), discrete time-variant generalized matrix inequality (discrete time-variant GMI), discrete time-variant generalized-Sylvester matrix inequality (discrete time-variant GSMI), and discrete time-variant complicated-Sylvester matrix inequality (discrete time-variant CSMI), and all solving processes are based on the direct discretization thought. Specifically, first of all, four discrete time-variant matrix inequalities are presented as the target problems of these researches. Second, for solving such problems, we propose corresponding discrete-time recurrent neural network (RNN) (DT-RNN) algorithms (termed DT-RNN-MVI algorithm, DT-RNN-GMI algorithm, DT-RNN-GSMI algorithm, and DT-RNN-CSMI algorithm), which are different from the traditional DT-RNN design thought because second-order Taylor expansion is applied to derive the DT-RNN algorithms. This creative process avoids the intervention of continuous-time framework. Then, theoretical analyses are presented, which show the convergence and precision of the DT-RNN algorithms. Abundant numerical experiments are further carried out, which further confirm the excellent properties of the DT-RNN algorithms.

Calculation of the time-varying (TV) matrix generalized inverse has grown into an essential tool in many fields, such as computer science, physics, engineering, and mathematics, in order to tackle TV challenges. This work investigates the challenge of finding a TV extension of a subclass of inner inverses on real matrices, known as generalized-outer (G-outer) inverses. More precisely, our goal is to construct TV G-outer inverses (TV-GOIs) by utilizing the zeroing neural network (ZNN) process, which is presently thought to be a state-of-the-art solution to tackling TV matrix challenges. Using known advantages of ZNN dynamic systems, a novel ZNN model, called ZNNGOI, is presented in the literature for the first time in order to compute TV-GOIs. The ZNNGOI performs excellently in performed numerical simulations and an application on addressing localization problems. In terms of solving linear TV matrix equations, its performance is comparable to that of the standard ZNN model for computing the pseudoinverse.

The image-based visual servoing (IBVS) of manipulators is important for intelligent manipulation using visual feedbacks. While the traditional IBVS methods for manipulators require the knowledge of the depth information in the interaction matrix, in this article, we propose a novel IBVS method for manipulators without depth estimation by leveraging the property of the associated image Jacobian. Because of a novel transformation, the IBVS problem is converted into a convex optimization problem subject to the kinematic constraint, joint constraints, and other constraints that are not explicitly related to the depth information. The problem is then solved by developing a recurrent neural network of global asymptotic convergence, and a dynamic neural control law without depth estimation emerges for the IBVS of manipulators. The theoretical guarantee and simulation results are provided to show the efficacy of the proposed method.

Thek-winner-takes-all (k-WTA) problem involves selecting the topkagents with the highest inputs from a set ofncandidates. This problem plays a fundamental role in modeling competitive behaviors in social systems and economic environments. In this article, we propose a structurally simplified dynamic neural network to solve thek-WTA problem efficiently. The originalk-WTA task is first reformulated as a constrained quadratic programming (QP) problem. A smooth sigmoid function is then introduced to encode inequality constraints implicitly, simplifying the representation. Based on this formulation, we develop a continuous-time neural dynamic model capable of solving the problem in real time. The proposed model is theoretically proven to achieve global convergence and optimality with respect to thek-WTA solution. Extensive numerical experiments, including tests on real-world data, validate the effectiveness of the proposed approach, demonstrating fast convergence, robustness, and practical applicability.

Real-time high-frequency trading poses a significant challenge to the classical portfolio allocation problem, demanding rapid computational efficiency for constructing Markowitz model-based portfolios. Building on the principles of arbitrage pricing theory (APT), this study introduces a dynamic neural network model aimed at minimizing investment risk, optimizing portfolio allocation within predefined constraints, and maximizing returns. First, a convex optimization objective function incorporating risk constraints is formulated based on APT principles. This is followed by the introduction of a novel dynamic neural network model designed to solve the convex optimization problem, accompanied by comprehensive theoretical analysis and rigorous proofs. The study uses two distinct datasets sourced from Yahoo Finance, consisting of 30 selected stocks, covering a span of 250 valid trading days to validate the proposed methodology. The results of 30 different stock market scenario experiments indicate that, when the upper limit for investment risk is set at$3.285 \times 10^{-4}$, the expected maximum investment return exceeds the Dow Jones Industrial Average (DJIA) index by 16.2816%. These empirical findings highlight the viability, stability, and efficacy of the proposed approach and framework, demonstrating its potential applicability for real-time, high-frequency trading scenarios. Furthermore, the outcomes suggest policy implications for risk management and portfolio optimization in dynamic financial environments.

Industrial robots inevitably incur kinematic errors in the advanced manufacturing and assembly processes, resulting in the severe reduction of the absolute positioning accuracy (APA). Kinematic calibration (KC) is well-known as a vital technique in APA-promoting tasks. However, existing KC models generally adopt a single distance-oriented Loss, e.g., an$L_{2}$norm-oriented one that neglects the featured$L_{p}$norms. In response to this critical issue, this study presents an Adaptive p-norms-oriented Kinematic Calibration (ApKC) model on the basis of threefold ideas: 1) studying the effects of diversified$L_{p}$norms on the industrial robot calibration performance; 2) combining multiple$L_{p}$norms to obtain the aggregated loss with the hybrid effects by different norms; and 3) implementing the weight adaptation on the norm components of the aggregated loss, and rigorously prove its ensemble capability benefiting the calibration performance. Afterwards, a novel Newton interpolated Adaptive Differential Evolution (NADE) algorithm is further proposed to optimize the ApKC model. Empirical studies on an HRS JR680 industrial robot demonstrate that the achieved ApKC-NADE calibrator can significantly reduce the robot’s maximum positioning error from 4.610 to 0.856 mm. It can vigorously support the high-accuracy application of industrial robots.

Temporal-variant linear equations (TVLEs) are widely acknowledged for their pivotal role in various engineering fields, offering a potent means to model dynamic processes and evolving relationships over time. A conventional approach involves leveraging the zeroing neural network (ZNN) model for tackling TVLE problems. In response to challenges associated with inverse matrix computations and infinite-time convergence constraints, we introduce an innovative single inverse-free finite-time reciprocal ZNN (FRZNN) model constructed to effectively address TVLE problems without using the activation functions. The convergence property and robustness of the FRZNN model are thoroughly examined adopting Lyapunov stability method of the nonlinear system and a comparative approach for nonlinear perturbed systems. Through two numerical experiments and an Angle-of-Arrival (AOA) simulation, the performance of the FRZNN model is thoroughly evaluated, revealing its validity and superior effectiveness when compared to state-of-the-art approaches. In detail, the performance improvement ratio (PIR) of the FRZNN model in addressing the AOA problem is 60.52%, and under a noise environment, the PIR of the FRZNN model is 99.99%.

Time-dependent Lyapunov matrix equation (TDLME) plays a central role in the control of linear and nonlinear systems. Existing models, including the classical zeroing neural dynamics (ZNDs) model and its variants, have been used to address the TDLME problem. However, those models require time-dependent matrix inversion, which is computationally demanding, and they primarily focus on measurement-related noise, overlooking other sources of system uncertainty. To overcome these challenges, we propose an inverse-free reciprocal-type ZND (RTZND) model. This model integrates an energy-based error function with the ZND framework, eliminating the need for matrix inversion and incorporating error-feedback-related noise through its closed-loop control structure. We establish the convergence and robustness of the RTZND model using Lyapunov stability theory and assess its performance under external disturbances. Numerical simulations confirm its effectiveness and improved computational efficiency in solving the TDLME problem. We further confirm its applicability through two case studies, a time-dependent linear system and a nonlinear system modeled by the single machine infinite bus (SMIB) system, highlighting the RTZND model’s practical value in addressing TDLME problems.

Optical image stabilization (OIS), powered by a special micro-electromechanical structure in the camera lenses to compensate for the optical distortion caused by camera shakes, has become an indispensable feature in many smartphones. However, we discover that this seemingly benign component can be exploited to eavesdrop on nearby audio signals, posing a significant threat to people's privacy during conversations or phone calls. Specifically, the OIS component can be influenced by external acoustic stimuli leading to slight vibrations, and at the same time, the coil and magnetized components inside the OIS induce electromagnetic leakage as they vibrate, according to Faraday's Law of Electromagnetic Induction. This electro-magnetic leakage contains voice information that can be used to recover the audio signals if intercepted by individuals with malicious intent. Inspired by the above discovery, we propose OISMic, a new acoustic eavesdropping attack that takes advantage of sound-induced OIS vibrations on smartphones. Unlike other existing acoustic eavesdropping attacks, eavesdropping exploiting OIS vibrations not only overcomes the constraints imposed by system permissions for many sensor-based approaches but is also immune to ultrasonic jammer that hinders the methods relying on microwave or light reflections to sense sound-induced vibrations. To execute this non-trivial attack in practical scenarios, we developed a prototype circuit that has a compact design capable of capturing the electromagnetic leakage caused by OIS vibrations. After converting the collected leaked electromagnetic signals into audio signals, a software-based phase-locked loop (PLL) method is developed to enhance the representation of voice components. Meanwhile, to reconstruct the weak audio signals, we also designed a diffusion-based neural network to learn the distribution of electromagnetic noise within the audio spectrum. Extensive experiments indicate that OISMic can accurately reconstruct voice under various scenarios, achieving an average word correct rate of 90.57 % across different devices.

Within the context of intelligent manufacturing, industrial robots have a pivotal function. Nonetheless, extended operational periods cause a decline in their absolute positioning accuracy, preventing them from meeting high precision. To address this issue, this paper presents a novel robot algorithm that combines an adaptive and momental bound algorithm with decoupled weight decay (AdaModW), which has three-fold ideas: a) adopting an adaptive moment estimation (Adam) algorithm to achieve a high convergence rate, b) introducing a hyperparameter into the Adam algorithm to define the length of memory, effectively addressing the issue of the abnormal learning rate, and c) interpolating a weight decay coefficient to improve its generalization. Numerous experiments on an HRS-JR680 industrial robot show that the presented algorithm significantly outperforms state-of-the-art algorithms in robot calibration performance. Thus, in light of its reliability, this algorithm provides an efficient way to address robot calibration concerns.

With the rapid development of industry, there is a growing concern over the vibration control challenges associated with flexible structures and underactuated systems. Input shaping technology enables stable performance for high-speed motion in industrial motion systems. However, existing input shapers commonly suffer from the ineffective control performance caused by the ignorance of observation error errors. To address this critical issue, this paper proposes an Extended Kalman Filter-incorporated Residual Neural Network-based input Shaping (ERS) model for vibration control. Its main ideas are two-fold: a) adopting an extended Kalman filter to address a vertical flexible beam's model errors; and b) adopting a residual neural network to cascade with the extended Kalman filter for eliminating the remaining observation errors. Detailed experiments on a real dataset collected from a vertical flexible beam demonstrate that the proposed ERS model has achieved significant vibration control performance over several state-of-the-art models.

The immediate feedback tracking control system design of heterogeneous robots with uncertainty is considered to be a significant issue in robotic research. Note that when the robot information is uncertain, the scale of computation would become increasingly large and the accuracy of tracking control would become exceptionally low. The realization of the immediate feedback control system of heterogeneous robots with uncertainty remains to be a challenging problem. Many conventional zeroing neural network (CZNN) models have been developed accordingly. However, most of them are supported by the hypothesis that the robot parameters are complete and accurate, and the associated models possess the exponential convergence property. To handle the robot uncertainty as well as to improve the convergence performance, a new zeroing neural network (ZNN) with super-exponential convergence (SEC) rate is put forward in this paper termed SEC-ZNN, to resolve the robust control issue of uncertain heterogeneous robots. The proposed SEC-ZNN takes full advantage of effector real-time information, with robust controlling and super-exponential convergence performance so far as to the robot information is uncertain. Theoretically, the super-exponential convergence properties including lower error bound and faster convergence rate are rigorously proved. Moreover, circular path-tracking example, comparisons and tests via MATLAB, Coppeliasim and experiment via robot INNFOS substantiate the efficaciousness and preponderance of the SEC-ZNN for the immediate feedback control system for heterogeneous robots with uncertainty.Note to Practitioners—This paper is motivated by the problem that most robots which need real-time tracking control in real applications come with uncertainty. It is important to note that traditional robot tracking control algorithms mostly require complete robot information or assume information complete, which does not correspond to the actual situation of robot control. Moreover, for practical applications in robotics, the real-time tracking control problem is very attractive. Therefore, an accurate, efficient and stable solution is of great significance to practitioners in this area. In this paper, the SEC-ZNN algorithm is proposed to solve the problem of real-time control of heterogeneous robots with uncertainty in real applications for practitioners. The proposed methos makes full use of the real-time feedback infromation to solve the real-time tracking control problem of heterogeneous robots with uncertainty at the velocity level. The algorithmic steps and principle explanation of the SEC-ZNN scheme are also presented for better understanding. Simulation studies and comparisons are performed on a Stewart robot to confirm the effectiveness and superiority of the proposed scheme. Furthermore, the simulation experiment in Coppeliasim platform is performed to confirm the possibility of portability of the SEC-ZNN to real robot operations. Finally, applications on a real-world robot INNFOS verify the physical relizability of the proposed SEC-ZNN for the engineering practice via heterogeneous robots.

Estimates of agents in a distributed consensus control are aligned with a particular value through interacting on communication graphs, which are of particular interest for researchers in the field of multi-agent coordination. Following this pattern, a discrete-time constrained consensus issue with generalized time delays is first established in this article, which is manipulated into an optimization problem via a quadratic performance index introduced as a global objective function. Then, a novel consensus scheme is investigated and proposed for handling this problem, enabling the consensus to approach the desired state globally and rapidly with optimal system property ensured. Besides, to advance the convergence speed and stability in resisting constant bias or oscillation, an adjustment control method is explored to construct a modified consensus scheme; further, to enhance the scene adaptability, fix topologies are extended to switching ones, and the latter is involved to develop another scheme on this basis. Moreover, the convergence and robustness of these three proposed consensus schemes are substantiated by theoretical analysis and numerical simulations. To highlight the practical implementations, the proposed consensus schemes are incorporated with a winner-take-all operation to accomplish multi-agent competitive coordination in a distributed way, and the results embody their effectiveness and superior consensus control ability, along with strong plasticity.Note to Practitioners—This paper is dedicated to investigating and optimizing distributed consensus schemes with time delays and output saturation with application to the competitive coordination of multi-agent systems. On the one hand, the consensus problem with output saturation receives limited attention, and few consensus algorithms consider both saturation limitation and channel gain. On the other hand, most existing studies on consensus with saturation consider simply the dynamic behaviour of agents without employing optimization, thus limiting further improvement of system performance. In this paper, a consensus algorithm is built from an optimization perspective that guarantees the state consensus of a multi-agent system with output constraints and generalized time delays. In addition, a consensus scheme is designed in a discrete-time framework and further modified and perfected along with the idea of considering time delays and expanding diverse topologies. Finally, experiments are conducted by applying the consensus scheme to a winner-take-all operation, with contributions of this paper verified.

Latent factor analysis (LFA) is efficient in knowledge discovery from a high-dimensional and incomplete (HDI) matrix frequently encountered in industrial big data-related applications. A stochastic gradient descent (SGD) algorithm is commonly adopted as a learning algorithm for LFA owing to its high efficiency. However, its sequential nature makes it less scalable when processing large-scale data. Although alternating SGD decouples an LFA process to achieve parallelization, its performance relies on its hyper-parameters that are highly expensive to tune. To address this issue, this paper presents three extended alternating SGD algorithms whose hyper-parameters are made adaptive through particle swarm optimization. Correspondingly, three Parallel Adaptive LFA (PAL) models are proposed and achieve highly efficient latent factor acquisition from an HDI matrix. Experiments have been conducted on four HDI matrices collected from industrial applications, and the benchmark models are LFA models based on state-of-the-art parallel SGD algorithms including the alternative SGD, Hogwild!, distributed gradient descent, and sparse matrix factorization parallelization. The results demonstrate that compared with the benchmarks, with 32 threads, the proposed PAL models achieve much speedup gain. They achieve the highest prediction accuracy for missing data on most cases.Note to Practitioners—HDI data are commonly encountered in many industrial big data-related applications, where rich knowledge and patterns can be extracted efficiently. An SGD based-LFA model is popular in addressing HDI data due to its efficiency. Yet when dealing with large-scale HDI data, its serial nature greatly reduces its scalability. Although alternating SGD can decouple an LFA process to implement parallelization, its performance depends on its hyper-parameter whose tuning is tedious. To address this vital issue, this study proposes three extended alternating SGD algorithms whose hyper-parameters are made via through a particle swarm optimizer. Based on them, three models are realized, which are able to efficiently obtain latent factors from HDI matrices. Compared with the existing and state-of-the-art models, they enjoy their hyper-parameter-adaptive learning process, as well as highly competitive computational efficiency and representation learning ability. Hence, they provide practitioners with more scalable solutions when addressing large HDI data from industrial applications.

Different from conventional motion/force control strategies based on robotic dynamics, this paper presents a kinematic perspective to convert the motion/force control problem into a bi-criteria optimization problem. Specifically, the motion and force errors are formulated as an equality constraint at the kinematics level. Through a weight coefficient, the minimum infinite norm of joint velocity and the alternative kinematic index are integrated as a bi-criteria objective function. On this basis, a bi-criteria hybrid motion/force control (BHMFC) strategy is proposed with kinematic analyses on robotic manipulators. This bi-criteria kinematic strategy fulfills the potentials of robotic manipulators involving the functions of hybrid index optimization, hybrid control of motion and force, end-effector posture maintaining, and physical constraints. Furthermore, the related dynamic neural network (DNN) with theoretical analyses is presented to explore the optimal solution to the BHMFC strategy. Finally, computer simulations, physical experiments, and strategy comparisons are conducted to demonstrate the feasibility, efficiency, and superiority of the proposed BHMFC strategy. This work presents an efficient kinematic approach to address robot motion/force control problems with promising research prospects.Note to Practitioners—This paper is motivated by potential improvements of motion/force hybrid control schemes of robotic manipulators in a kinematic manner. Existing motion/force control methods typically rely on robot dynamics, which are difficult to satisfy kinematic task requirements, such as physical constraints and task optimizations. To this end, a bi-criteria hybrid motion/force control (BHMFC) strategy is proposed to achieve kinematic performance improvements in a quadratic program framework. Specifically, the designed constraints exploit the functions of hybrid control of motion and force, physical constraints, and end-effector posture maintaining. Besides, the kinematic optimization and joint velocity reduction are implemented by a bi-criteria objective function. Besides, we propose a dynamic neural network (DNN) based on Karush-Kuhn-Tucker conditions to solve the BHMFC strategy and theoretically analyze its global convergence ability and convergence rate. Simulative and experimental results show that the proposed method outperforms the traditional pseudoinverse method in terms of accurate position/force control performance and end-effector posture maintenance. In addition, computational analysis of control signals and comparisons with existing technologies highlight the feasibility and superiority of the proposed method.

Time-variant problems are widespread in science and engineering, and discrete-time recurrent neurodynamics (DTRN) method has been proved to be an effective way to deal with a variety of discrete time-variant problems. However, this DTRN method is usually based on the study of continuous time-variant problems and lacks a direct study of discrete time-variant problems. To solve the abovementioned problem, based on a pioneering direct discretization technique, we study and develop a new DTRN method to solve equality-constrained discrete time-variant nonlinear optimization (EC-DTVNO) problem. Specifically, first, to solve the EC-DTVNO problem, the recent method widely used by researchers is Lagrange multiplier method. By introducing Lagrange multiplier to construct Lagrange function, the objective function and equality constraint are integrated into a discrete time-variant nonlinear system. Then, the corresponding error function is defined, and the corresponding DTRN method for solving the EC-DTVNO problem can be obtained by direct discretization technique. Thereafter, this DTRN method is analyzed theoretically and its convergence is proved. In addition, numerical experiments and application experiments further confirm the effectiveness and superiority of DTRN method.

This paper proposes the distance- and velocity-based simultaneous obstacle avoidance and target tracking (DV-SOATT) method for the trajectory tracking problem of multiple wheeled mobile robots (MWMRs) operating in a shared workspace based on the relative positions and velocities of the wheeled mobile robots (WMRs) and their encountered obstacles. Compared to the previous arts considered only their relative positions, the DV-SOATT method that adds an auxiliary velocity vector lessens needless activation of the collision avoidance maneuvers, where the DV-SOATT introduces radial bounds for forecasting a collision. We provide two decision criteria for the addition of the auxiliary velocity term and compare the DV-SOATT method with the original method proposed by Li et al. (2021). The problem of the WMRs pause from the path conflict is addressed. Bound constraints on MWMRs’ velocities are considered to restrict the movement speed of the robot so as to ensure smoothness. The control law is built on Lagrange multipliers on basis of constructing a quadratic programming problem. Slack variables are discarded. Bound constraints on optimization variables are included in the piecewise-linear projection function. The stability of the control law, together with the efficiency of the DV-SOATT method, is discussed based on the Lyapunov function. The efficiency is tested on multiple omnidirectional Mecanum-wheeled mobile robots and validated through physical experiments and simulation.

Physical-layer key generation has emerged as a promising avenue for establishing secret keys using reciprocal channel measurements between wireless devices. However, channel reciprocity may suffer degradation from ambient noise and cause mismatched secret bits, while existing methods mitigating this issue may yet face limitations in key efficiency. The root cause behind such limitations is the heavy reliance on channel measurements, which can be naturally susceptible to channel non-reciprocity attributed to environmental factors. Instead of direct key extraction from channel measurements, we seek to share a pre-defined key and utilize channel measurements as a bearer to facilitate key transmission. We propose an accurate and efficient key generation method (KeyCome) to ensure secure key sharing by encapsulating it with channel state information (CSI) obfuscation matrices through circulant convolution. To this end, we develop a reliable key derivation through a quadratic programming method with matrix equilibration, ensuring stable and rapid solutions. Notably, the transmitter can control the key beforehand for enhanced communication efficiency and combine it with an error correction mechanism for accurate key derivation. Furthermore, a lightweight reconciliation scheme is designed to minimize mismatched bits caused by occasional non-reciprocity. Comprehensive experiments demonstrate KeyCome's high accuracy and efficiency in key generation.

Portfolio analysis is a crucial subject within modern finance. However, the classical Markowitz model, which was awarded the Nobel Prize in Economics in 1991, faces new challenges in contemporary financial environments. Specifically, it fails to consider transaction costs and cardinality constraints, which have become increasingly critical factors, particularly in the era of high-frequency trading. To address these limitations, this research is motivated by the successful application of machine learning tools in various engineering disciplines. In this work, three novel dynamic neural networks are proposed to tackle nonconvex portfolio optimization under the presence of transaction costs and cardinality constraints. The neural dynamics are intentionally designed to exploit the structural characteristics of the problem, and the proposed models are rigorously proven to achieve global convergence. To validate their effectiveness, experimental analysis is conducted using real stock market data of companies listed in the Dow Jones Index (DJI), covering the period from November 8, 2021 to November 8, 2022, encompassing an entire year. The results demonstrate the efficacy of the proposed methods. Notably, the proposed model achieves a substantial reduction in costs (which combines investment risk and reward) by as much as 56.71% compared with portfolios that are averagely selected.

High-frequency trading proposes new challenges to classical portfolio selection problems. Especially, the timely and accurate solution of portfolios is highly demanded in financial market nowadays. This article makes progress along this direction by proposing novel neural networks with softmax equalization to address the problem. To the best of our knowledge, this is the first time that softmax technique is used to deal with equation constraints in portfolio selections. Theoretical analysis shows that the proposed method is globally convergent to the optimum of the optimization formulation of portfolio selection. Experiments based on real stock data verify the effectiveness of the proposed solution. It is worth mentioning that the two proposed models achieve 5.50% and 5.47% less cost, respectively, than the solution obtained by using MATLAB dedicated solvers, which demonstrates the superiority of the proposed strategies.

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.

As a type of recurrent neural networks (RNNs) modeled as dynamic systems, the gradient neural network (GNN) is recognized as an effective method for static matrix inversion with exponential convergence. However, when it comes to time-varying matrix inversion, most of the traditional GNNs can only track the corresponding time-varying solution with a residual error, and the performance becomes worse when there are noises. Currently, zeroing neural networks (ZNNs) take a dominant role in time-varying matrix inversion, but ZNN models are more complex than GNN models, require knowing the explicit formula of the time-derivative of the matrix, and intrinsically cannot avoid the inversion operation in its realization in digital computers. In this article, we propose a unified GNN model for handling both static matrix inversion and time-varying matrix inversion with finite-time convergence and a simpler structure. Our theoretical analysis shows that, under mild conditions, the proposed model bears finite-time convergence for time-varying matrix inversion, regardless of the existence of bounded noises. Simulation comparisons with existing GNN models and ZNN models dedicated to time-varying matrix inversion demonstrate the advantages of the proposed GNN model in terms of convergence speed and robustness to noises.

As an effective alternative to recurrent neural networks, the echo state network (ESN) has achieved great success. However, the commonly-used batch learning-based algorithms prevent the ESN from being able to learn and train online. In this article, inspired by the Woodbury matrix identity, an online learning ESN named Woodbury online learning ESN (WOLESN) is proposed, which allows new data to arrive in a one-by-one or block-by-block manner. Experiments on the benchmark datasets of time series prediction and comparison models verify the effectiveness and superiority of the WOLESN. In addition, observing the relationship between the time series prediction and robot control, experiments on the redundant manipulator are designed with the aid of the proposed WOLESN, of which results indicate that the WOLESN does an excellent job of predicting the trajectory of the robot with tiny errors. The code of WOLESN is publicly available athttps://github.com/LongJin-lab/the-supplementary-file-for-WOLESN.

Recently, recurrent neural networks have been extensively utilized to address a time-dependent system of linear equations (TDSLEs) with inequality systems. Nevertheless, these existing studies only limit the variable without considering constraints on its derivatives, which may be challenging to accomplish a given task in practical applications when additional constraints are introduced. Beyond that, the matrix pseudoinverse is performed, and non-negative slack variables are introduced in the solution process, which increases the model’s complexity and leads to a high computational burden. To remedy these deficiencies, this article makes improvements via proposing a novel recurrent neural dynamics (RND) model for solving the TDSLEs with constraints on the variable and its derivatives. Specifically, such a model neither needs to compute the pseudoinverse of a matrix nor to introduce non-negative slack variables, thereby enhancing its computational efficiency and accuracy. Corresponding theoretical analysis is provided to ensure its convergence performance. Finally, numerical results, comparisons with other models, and applications to single and multiple robots are provided, which substantiates the availability and meliority of the pseudoinverse-free RND model for disposing of the TDSLEs with constraints on the variable and its derivatives.

The user authentication has drawn increasingly attention as the smart speaker becomes more prevalent. For example, smart speakers that can verify who is sending voice commands can mitigate various types of attacks such as replay attack or impersonation attack. Existing user authentication solutions either cannot be applicable to smart speakers directly or require certain additional user-device interaction or pre-installed infrastructure, which may severely affect the user experience and create extra burdens to users. In this work, we propose a user authentication system EchoImage utilizing acoustic images, which are derived from the smart speaker by emitting beep signals and sensing echoes from the user's body with its microphone array, as the proof for user authentication. Given the acoustic samplings of the reflected beep signal, our system designs a distance estimation component by applying a correlation based technique on the beamformed signal to estimate the distance between the user and microphone array. Our image construction component then constructs a virtual imaging plane using the estimated distance and steers the array towards each grid of the plane to generate an acoustic image of the user. Moreover, we propose a transfer learning-based method to derive efficient features from the constructed images, and employ SVM classifiers for accurate user authentication. Our extensive experiments demonstrate that our system is robust and accurate across various scenarios.

Personal Identification Number (PIN), as one of the primary means of protecting digital properties and privacy on mobile devices, has been suffering from shoulder surfing attacks and weak password guessing for the long term. Recent years witness the growing interest in two-factor authentication that takes advantage of two different ways for mutual verification, thereby strengthening user authentication's accuracy and reliability. Especially with the popularity of smartwatches, more physiological signals are readily available to facilitate two-factor authentication. This paper presents a lightweight and unobtrusive two-factor authentication scheme, P2Auth, integrating the PIN and unique keystroke-related Photoplethysmography (PPG) measurement on wearables. Specifically, we propose the transformation of the multivariate PPG signal induced by the keystrokes to extract reliable biometric features. We develop short-time energy-based methods to identify the input cases, thus enabling support the authentication for both one-handed and two-handed input cases. Furthermore, we also consider the situation where there is no fixed PIN and design a new enhanced privacy scheme by combining the PPG measurements of different keystrokes to improve authentication security. The experiments involving 15 volunteers demonstrate that our prototype system can achieve an average authentication accuracy of over 95% for one-handed cases and over 90% for two-handed cases.

Simultaneous Localization and Mapping (SLAM) has developed as a fundamental method for intelligent robot perception over the past decades. Most of the existing feature-based SLAM systems relied on traditional hand-crafted visual features and a strong static world assumption, which makes these systems vulnerable in complex dynamic environments. In this paper, we propose a robust monocular SLAM system by combining geometry-based methods with two convolutional neural networks. Specifically, a lightweight deep local feature detection network is proposed as the system front-end, which can efficiently generate keypoints and binary descriptors robust against variations in illumination and viewpoint. Besides, we propose a motion segmentation and depth estimation network for simultaneously predicting pixel-wise motion object segmentation and depth map, so that our system can easily discard dynamic features and reconstruct 3D maps without dynamic objects. The comparison against state-of-the-art methods on publicly available datasets shows the effectiveness of our system in highly dynamic environments.

Calibration technology is an essential technique to boost the absolute positioning accuracy of robots. However, an industrial robot's working space is mostly restricted in real working environments, making the collected samples fail in covering the actual working space to result in the overall migration data. To address this vital issue, this work proposes a novel industrial robot calibrator that integrates a measurement configurations selection (MCS) method and an alternation-direction-method-of-multipliers with multiple planes constraints (AMPC) algorithm into its working process, whose ideas are three-fold: a) selecting a group of optimal measurement configurations based on the observability index to suppress the measurement noises, b) developing an AMPC algorithm that evidently enhances the calibration accuracy and suppresses the long-tail convergence, c) proposing an industrial robot calibration algorithm that incorporates MCS and AMPC to optimize an industrial robot's kinematic parameters efficiently. For validating its performance, a public-available dataset (HRS-P) is established on an HRS-JR680 industrial robot. Extensive experimental results demonstrate that the proposed calibrator outperforms several state-of-the-art models in calibration accuracy.

The Markowitz model, a Nobel Prize winning model for portfolio analysis, paves the theoretical foundation in finance for modern investment. However, it remains a challenging problem in the high frequency trading (HFT) era to find a more time efficient solution for portfolio analysis, especially when considering circumstances with the dynamic fluctuation of stock prices and the desire to pursue contradictory objectives for less risk but more return. In this paper, we establish a recurrent neural network model to address this challenging problem in runtime. Rigorous theoretical analysis on the convergence and the optimality of portfolio optimization are presented. Numerical experiments are conducted based on real data from Dow Jones Industrial Average (DJIA) components and the results reveal that the proposed solution is superior to DJIA index in terms of higher investment returns and lower risks.

Distributed k-winners-takes-all (k-WTA) neural network (k-WTANN) models have better scalability than centralized ones. In this work, a distributed k-WTANN model with a simple structure is designed for the efficient selection of k winners among a group of more than k agents via competition based on their inputs. Unlike an existing distributed k-WTANN model, the proposed model does not rely on consensus filters, and only has one state variable. We prove that under mild conditions, the proposed distributed k-WTANN model has global asymptotic convergence. The theoretical conclusions are validated via numerical examples, which also show that our model is of better convergence speed than the existing distributed k-WTANN model.

A new competition model is developed in this article, which aims to describe the competitive behavior in social systems. Taking social networks as an example, the constructed model describes the development speed of each opinion, its attractiveness to people, and the influence of the social environment on its development. The final result is that a certain number of opinions win the competition and are implemented. Specifically, we define various components of social networks as some parameters, and use changes in parameters to describe the dynamic changes of opinions. Furthermore, this article proves the stability and convergence of the constructed competition model in theory. A series of simulation experiments are conducted to simulate competitive activities in real life, and application scenarios suitable for the model are provided in this work.

An echo state network (ESN) draws widespread attention and is applied in many scenarios. As the most typical approach for solving the ESN, the matrix inverse operation of high computational complexity is involved. However, in the modern big data era, addressing the heavy computational burden problem is necessary. In order to reduce the computational load, an inverse-free ESN (IFESN) is proposed for the first time in this article. Besides, an incremental IFESN is constructed to attain the network topology with theoretical proof on the training error's monotone decline property. Simulations and experiments are conducted on several numerical and real-world time-series benchmarks, and corresponding results indicate that the proposed model is superior to some existing models and possesses excellent practical application potential. The source code is publicly available at https://github.com/LongJin-lab/the-supplementary-file-for-CYB-E-2021-04-0944.

In this article, we proposed an equivalent formulation of the k-winners-take-all (k-WTA) problem as a constrained optimization problem by including the Laplacian matrix of the undirected connected communication graph to adapt to the distributed computing scenario, where an additional auxiliary variable is introduced. To solve the optimization problem in a distributed fashion, we design projection neural networks by using the convex optimization theory, leading to the emergence of a distributed k-WTA network. Our theoretical analysis shows that the proposed distributed k-WTA network has a globally asymptotically stable equilibrium that is identical to the optimal solution to the optimization problem, that is, the correct k-WTA solution. The effectiveness and advantages, including the extendability to constrained k-WTA problems, of the proposed k-WTA network are demonstrated via simulations.

To solve nonlinear optimization problems under multiple set constraints, a modified gradient projection neural network (MGPNN) is proposed and investigated. Different from existing approaches specialized for linear constrained optimizations, such as the gradient-based recurrent neural network or dynamic-parameter zeroing neural network, the MGPNN is intrinsically designed from the perspective of the multiple set constrained optimization (MSCO), which is a more generalized form for the linear constrained optimization. The MGPNN is able to efficiently and conveniently provide a feasible solution to the MSCO problem. Ultimately, compared with existing solution methods, numerical simulations and applications to the control of an underactuated portal crane system are provided for verifications of the robust stability and preponderance of the proposed MGPNN model.

In recent years, the cable-driven planar robot has made fruitful achievements in many fields, but the related researches are scarce yet in the industrial engineering field. In this article, as a powerful tool for solving discrete time-varying problems, the discrete-time recurrent neural network (DTRNN) is extended to drive the cable-driven planar robot for discrete real-time tracking control, which is derived by a new immediate discretization method, and thus, is termed as ID-DTRNN model. Specifically, first, we present the physical structure and mathematical model of the cable-driven planar robot. Then, the new ID-DTRNN model is proposed and applied for driving such cable-driven planar robot, which bases on the a different way of construction of the traditional DTRNN model. Through numerical experiments, the feasibility, validity, and physical reliability of the ID-DTRNN model for discrete real-time tracking control of the cable-driven planar robot are fully verified. In addition, in the real world, physical experiments of the cable-driven planar robot are presented, which successfully promote the development of physical application of the ID-DTRNN model, and fill the gap of such model in the industrial engineering field.

With the rapid development and wide applications of industrial manipulators, a vital concern rises regarding a manipulator's absolute positioning accuracy. The manipulator calibration models have proven to be highly efficient in improving the absolute positioning accuracy of an industrial manipulator. However, existing calibration models commonly suffer from the low calibration accuracy caused by the ignorance of nongeometric errors. To address this critical issue, this article proposes anextended Kalman filter-incorporatedResidual Neural Network-basedCalibration (ERC) model for kinematic calibration. Its main ideas are two-fold: 1) adopting anextended Kalman filter (EKF) to address a manipulator's geometric errors; and 2) adopting aresidual neural network to cascade with theEKFfor eliminating the remaining nongeometric errors. Detailed experiments on three real datasets collected from industrial manipulators demonstrate that the proposed ERC model has achieved significant calibration accuracy gain over several state-of-the-art models.

Convolutional neural networks (CNNs) are widely used in the field of medical imaging diagnosis but have the disadvantages of slow training speed and low diagnostic accuracy due to the initialization of parameters before training. In this article, a CNN optimization method based on the beetle antennae search (BAS) optimization algorithm is proposed. The method optimizes the initial parameters of the CNN through the BAS optimization algorithm. Based on this optimization approach, a novel CNN model with a pretrained BAS optimization algorithm was developed and applied to the analysis and diagnosis of medical imaging data for intracranial hemorrhage. Experimental results on 330 test images show that the proposed method has a better diagnostic performance than the traditional CNN. The proposed method achieves a diagnostic accuracy of 93.9394% and 100% recall, and the diagnosis of 66 human head computerized tomography image data only takes 0.1596 s. Moreover, the proposed method has more advantages than the three other optimization algorithms.

Recently, neural network model-based control has received wide interests in kinematics control of manipulators. To enhance learning ability of neural network models, the autoencoder method is used as a powerful tool to achieve deep learning and has gained success in recent years. However, the performance of existing autoencoder approaches for manipulator control may be still largely dependent on the quality of data, and for extreme cases with noisy data it may even fail. How to incorporate the model knowledge into the autoencoder controller design with an aim to increase the robustness and reliability remains a challenging problem. In this work, a sparse autoencoder controller for kinematic control of manipulators with weights obtained directly from the robot model rather than training data is proposed for the first time. By encoding and decoding the control target though a new dynamic recurrent neural network architecture, the control input can be solved through a new sparse optimization formulation. In this work, input saturation, which holds for almost all practical systems but usually is ignored for analysis simplicity, is also considered in the controller construction. Theoretical analysis and extensive simulations demonstrate that the proposed sparse autoencoder controller with input saturation can make the end-effector of the manipulator system track the desired path efficiently. Further performance comparison and evaluation against the additive noise and parameter uncertainty substantiate robustness of the proposed sparse autoencoder manipulator controller.

Recently, robot arms have become an irreplaceable production tool, which play an important role in the industrial production. It is necessary to ensure the absolute positioning accuracy of the robot to realize automatic production. Due to the influence of machining tolerance, assembly tolerance, the robot positioning accuracy is poor. Therefore, in order to enable the precise operation of the robot, it is necessary to calibrate the robotic kinematic parameters. The least square method and Levenberg-Marquardt (LM) algorithm are commonly used to identify the positioning error of robot. However, it generally has the overfitting caused by improper regularization schemes. To solve this problem, this article discusses six regularization schemes based on its error models, i.e.,$L_{1}$,$L_{2}$, dropout, elastic, log, and swish. Moreover, this article proposes a scheme with six regularization to obtain a reliable ensemble, which can effectively avoid overfitting. The positioning accuracy of the robot is improved significantly after calibration by enough experiments, which verifies the feasibility of the proposed method.

Controlling and processing of time-variant problem is universal in the fields of engineering and science, and the discrete-time recurrent neural network (RNN) model has been proven as an effective method for handling a variety of discrete time-variant problems. However, such model usually originates from the discretization research of continuous time-variant problem, and there is little research on the direct discretization method. To address the aforementioned problem, this article introduces a novel discrete-time RNN model for solving the discrete time-variant problem in a pioneering manner. Specifically, a discrete time-variant nonlinear system, which originates from the mathematical modeling of serial robot manipulator, is presented as a target problem. For solving the problem, first, the technique of second-order Taylor expansion is used to deal with the discrete time-variant nonlinear system, and the novel discrete-time RNN model is proposed subsequently. Second, the theoretical analyses are investigated and developed, which shows the convergence and precision of the proposed discrete-time RNN model. Furthermore, three distinct numerical experiments verify the excellent performance of the proposed discrete-time RNN model. In addition, a robot manipulator example further verifies the effectiveness and practicability of the proposed novel discrete-time RNN model.

The k -winners-take-all ( k -WTA) problem refers to the selection of k winners with the first k largest inputs over a group of n neurons, where each neuron has an input. In existing k -WTA neural network models, the positive integer k is explicitly given in the corresponding mathematical models. In this article, we consider another case where the number k in the k -WTA problem is implicitly specified by the initial states of the neurons. Based on the constraint conversion for a classical optimization problem formulation of the k -WTA, via modifying the traditional gradient descent, we propose an initialization-based k -WTA neural network model with only n neurons for n -dimensional inputs, and the dynamics of the neural network model is described by parameterized gradient descent. Theoretical results show that the state vector of the proposed k -WTA neural network model globally asymptotically converges to the theoretical k -WTA solution under mild conditions. Simulative examples demonstrate the effectiveness of the proposed model and indicate that its convergence can be accelerated by readily setting two design parameters.

The Markowitz model, a portfolio analysis model that won the Nobel Prize, lays the theoretical groundwork for modern finance. The transaction cost and the cardinality restriction, which were not covered in Markowitz model, are becoming increasingly important with the advent of high-frequency trading era. However, it remains a challenging problem to consider those constraints due to the nonconvex nature of the problem. A novel dynamic neural network, inspired by its successes in machine learning, is developed to tackle this difficult issue. Theoretical analysis is provided for the convergence of the designed neural network. Experimental results using real stock market data confirm the effectiveness of the proposed model. With the proposed model, the cost function characterizing the overall risks, and rewards is reduced by 123.6% from$-4.549\times 10^{-5}$to$-1.0173\times 10^{-4}$. This indicates that the proposed strategy is successful in reducing risks and increasing rewards.

Sports intelligence receives constant attention, especially with the development of information technology. Existing tennis-launching machines, a kind of device launching tennis balls from a fixed point, have shortcomings such as limited launching height and low control accuracy, which are lack of considerable flexibility when applied in a practical situation. In this article, a tennis-training robot based on a redundant manipulator cooperated with a tennis-launching structure is presented to realize a high-precision and flexible ball-launching task. In order to construct a control scheme of the robotic system, the physical situation of tennis launching is modeled, and further transformed into a quadratic programming problem. Then, a recurrent neural network (RNN) is built to obtain the optimal solution. Furthermore, simulative experiments based on the CoppeliaSim platform using a FRANKA EMIKA manipulator are carried out to demonstrate the realizability of the designed application scenarios.

Abstract Redundancy manipulators need favorable redundancy resolution to obtain suitable control actions to guarantee accurate kinematic control. Among numerous kinematic control applications, some specific tasks such as minimally invasive manipulation/surgery require the distal link of a manipulator to translate along such fixed point. Such a point is known as remote center of motion (RCM) to constrain motion planning and kinematic control of manipulators. Recurrent neural network (RNN) which possesses parallel processing ability, is a powerful alternative and has achieved success in conventional redundancy resolution and kinematic control with physical constraints of joint limits. However, up to now, there still is few related works on the RNNs for redundancy resolution and kinematic control of manipulators with RCM constraints considered yet. In this paper, for the first time, an RNN-based approach with a simplified neural network architecture is proposed to solve the redundancy resolution issue with RCM constraints, with a new and general dynamic optimization formulation containing the RCM constraints investigated. Theoretical results analyze and convergence properties of the proposed simplified RNN for redundancy resolution of manipulators with RCM constraints. Simulation results further demonstrate the efficiency of the proposed method in end-effector path tracking control under RCM constraints based on a redundant manipulator.

This paper investigates a distributed competition behavior in multi-robot coordination under variable communication topology and switching one. In terms of multi-robot competition-based coordination, a winner-take-all (WTA) strategy is leveraged to address this issue with inevitable environmental barriers incorporated. Moreover, an innovative control theory stimulated gradient neural network (CTSGNN) algorithm is proposed to realize the WTA with prominent robustness and convergence over the traditional ones. Besides, to adapt to diversified local communication modes among multi-robot systems, fast variable and low switching topologies are constructed to establish two dynamic consensus estimators, accompanied by the proposed distributed control schemes. Traditional algorithms are introduced and served as a contrast. Afterward, the global convergence of the proposed algorithm in dealing with multi-robot competitive coordination, the universality of the application scenario, as well as the weaknesses of traditional methods are substantiated theoretically. The effectiveness and superiority of the proposed CTSGNN algorithm and the resultant distributed control schemes by integrating consensus estimators are further sustained via simulations. Note to Practitioners—The motivation of this paper is the coordination operation of multi-robot systems, but it is also applicable to other fields adopting multi-agent systems. Most of the existing researches on multi-robot coordination only exploit their collaborative behavior, which usually leads to the system redundancy and overflow of control costs. To this end, an innovative control algorithm is proposed for this competitive coordination and remains to be perfect in terms of stability and accuracy. Then, this paper establishes new distributed control schemes for multi-robot systems to compete for optimal dynamic task allocation. In this sense, under the premise of ensuring a successful task execution, only a few individuals with strong abilities and advantages are assigned. It is promising to maximize resource utilization, increase efficiency, and be extended to multi-objective scenarios. Note that the design of this scheme takes into account the environmental constraints and physical constraints of the robot itself. Theoretical analysis and preliminary simulation experiments prove the high efficiency of the control scheme. In ongoing research, the competitive coordination tasks of the mobile robot systems and communication delays or fault in control scheme design are explored to expand the operation scope and system extensibility.

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.

The measurement algebraic connectivity plays an important role in many graph theory-based investigations, such as cooperative control of multiagent systems. In general, the measurement is considered to be centralized. In this article, a distributed model is proposed to estimate the algebraic connectivity (i.e., the second smallest eigenvalue of the corresponding Laplacian matrix) by the approach of distributed estimation via high-pass consensus filters. The global asymptotic convergence of the proposed model is theoretically guaranteed. Numerical examples are shown to verify the theoretical results and the superiority of the proposed distributed model.

In this article, we propose a novel learning and near-optimal control approach for underactuated surface (USV) vessels with unknown mismatched periodic external disturbances and unknown hydrodynamic parameters. Given a prior knowledge of the periods of the disturbances, an analytical near-optimal control law is derived through the approximation of the integral-type quadratic performance index with respect to the tracking error, where the equivalent unknown parameters are generated online by an auxiliary system that can learn the dynamics of the controlled system. It is proved that the state differences between the auxiliary system and the corresponding controlled USV vessel are globally asymptotically convergent to zero. Besides, the approach theoretically guarantees asymptotic optimality of the performance index. The efficacy of the method is demonstrated via simulations based on the real parameters of an USV vessel.

Redundant manipulators play a critical role in industry and academia, which can be controlled from the kinematic or dynamic perspective. The motion-force control of redundant manipulators is a core problem in robot control, especially for the task requiring keeping contact with objectives, such as cutting, polishing, deburring, etc. However, when a manipulator’s model structure is unknown, it is challenging to take motion-force control of redundant manipulators. This article proposes a data-driven-based motion-force control scheme, which solves the motion-force control problem from the kinematic perspective. The scheme can take effect and estimate the structure information, i.e., the model parameters involved in the forward kinematics when the structure of the manipulator is incomplete or unknown. A recurrent neural network is devised to find the solution to the scheme. Besides, the theoretical analysis is presented to prove the correctness of the scheme. Simulations and physical experiments running on seven degrees of freedom redundant manipulators illustrate the superb performance and practicability of the scheme intuitively. The key contribution of this article is that, for the first time, a motion-force control scheme aided with data-driven technology is proposed from a kinematic perspective for the redundant manipulators.

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.

In this brief, the problem of synchronization control is investigated for a class of fractional-order chaotic systems with unknown dynamics and disturbance. The controller is constructed using neural approximation and disturbance estimation where the system uncertainty is modeled by neural network (NN) and the time-varying disturbance is handled using disturbance observer (DOB). To evaluate the estimation performance quantitatively, the serial-parallel estimation model is constructed based on the compound uncertainty estimation derived from NN and DOB. Then, the prediction error is constructed and employed to design the composite fractional-order updating law. The boundedness of the system signals is analyzed. The simulation results show that the proposed new design scheme can achieve higher synchronization accuracy and better estimation performance.

It is generally considered that controlling a robot precisely becomes tough on the condition of unknown structure information. Applying a data-driven approach to the robot control with the unknown structure implies a novel feasible research direction. Therefore, in this article, as a combination of the structural learning and robot control, an acceleration-level data-driven repetitive motion planning (DDRMP) scheme is proposed with the corresponding recurrent neural network (RNN) constructed. Then, theoretical analyses on the learning and control abilities are provided. Moreover, simulative experiments on employing the acceleration-level DDRMP scheme as well as the corresponding RNN to control a Sawyer robot and a Baxter robot with unknown structure information are performed. Accordingly, simulation results validate the feasibility of the proposed method and comparisons among the existing repetitive motion planning (RMP) schemes indicate the superiority of the proposed method. This work offers sufficient theoretical and simulative solutions for the acceleration-level redundancy problem of redundant robots with unknown structure and joint limits considered.

Dual-arm robotic systems have great advantages over the single-arm robotic system, for the arms can either run independently or cooperate to finish the task. In this paper, minimum kinetic energy (MKE) is concerned as a performance index for the planning and control of a dual-arm robotic system. First, two sub schemes are formulated on the left arm and right arm of the robot, which are constructed on velocity level with consideration of manipulators' physical constraints. Then, the two sub schemes are unified into one scheme, which is finally transformed into a quadratic program (QP) problem. For solving the formulated QP problem, a recurrent neural network (RNN) is devised based on the Lagrange multiplier method. At last, the simulations and simulative experiments on a dual-arm redundant robotic system named Baxter are carried out. The simulation results reveal that the devised RNN model has a good performance for solving the presented MKE scheme applying to the dual-arm robotic system.

Non-negativity is vital for a latent factor (LF)-based model to preserve the important feature of a high-dimensional and sparse (HiDS) matrix in recommender systems, i.e., none of its entries is negative. Current non-negative models rely on constraints-combined training schemes. However, they lack flexibility, scalability, or compatibility with general training schemes. This work aims to perform unconstrained non-negative latent factor analysis (UNLFA) on HiDS matrices. To do so, we innovatively transfer the non-negativity constraints from the decision parameters to the output LFs, and connect them through a single-element-dependent mapping function. Then we theoretically prove that by making a mapping function fulfill specific conditions, the resultant model is able to represent the original one precisely. We subsequently design highly efficient UNLFA algorithms for recommender systems. Experimental results on four industrial-size HiDS matrices demonstrate that compared with four state-of-the-art non-negative models, a UNLFA-based model obtains advantage in prediction accuracy for missing data and computational efficiency. Moreover, such high performance is achieved through its unconstrained training process which is compatible with various general training schemes, on the premise of fulfilling non-negativity constraints. Hence, UNLFA algorithms are highly valuable for industrial applications with the need of performing non-negative latent factor analysis on HiDS matrices.

This article investigates the composite learning fuzzy control for a class of stochastic nonlinear strict-feedback systems subject to dynamics uncertainty. The fuzzy logic system is built to model the unknown system nonlinearity. The highlight is that different from previous studies using only tracking error for fuzzy weight updating, the accuracy of fuzzy learning is emphasized in this study. The serial-parallel estimation model with fuzzy approximation and gain compensation is constructed to acquire the prediction error such that the composite fuzzy updating law is designed with more accurate feedback information. The stochastic stability analysis ensures the uniformly ultimate boundedness of the system signals in mean square. Through the simulation tests on a numerical example with different stochastic disturbances and one-link manipulator dynamics, it is proved that the proposed composite learning scheme can solve the system uncertainty effectively and make the closed-loop system track the reference command with satisfactory accuracy.

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.

Joint-drift problems could result in failures in executing task or even damage robots in actual applications and different schemes have been presented to deal with such a knotty problem. However, in these existing schemes, there exists the coupling in coefficients for eliminating the drift in the joint space and the equality constraint for completing the given task in the Cartesian space, thereby, theoretically, leading to a paradox in achieving zero joint drift in the joint space and zero position error in the Cartesian space simultaneously. A novel joint-drift-free (JDF) scheme synthesized by a projected zeroing neural network (PZNN) model for the motion generation and control of redundant robot manipulators perturbed by disturbances is proposed and analyzed in this article. Besides, the PZNN model could adopt saturated or even nonconvex projection functions. The proposed scheme completely decouples the interferences of joint errors in the joint space and position errors in the Cartesian space for the first time. Beyond that, theoretical analysis is conducted in order to validate that the PZNN model is of global convergence to the theoretical kinematics solution to the motion generation of robots, and that the joint-drift problems are thus remedied. Moreover, several simulations and physical experiments on the strength of different robot manipulators are carried out to confirm the superiority, efficiency, and accuracy of the proposed JDF scheme synthesized by the PZNN model for remedying joint-drift problems of redundant robot manipulators in noisy environments.

Non-negative latent factor (NLF) models can efficiently acquire useful knowledge from high-dimensional and sparse (HiDS) matrices filled with non-negative data. Single latent factor-dependent, non-negative and multiplicative update (SLF-NMU) is an efficient algorithm for building an NLF model on an HiDS matrix, yet it suffers slow convergence. A momentum method is frequently adopted to accelerate a learning algorithm, but it is incompatible with those implicitly adopting gradients like SLF-NMU. To build a fast NLF (FNLF) model, we propose a generalized momentum method compatible with SLF-NMU. With it, we further propose a single latent factor-dependent non-negative, multiplicative and momentum-incorporated update algorithm, thereby achieving an FNLF model. Empirical studies on six HiDS matrices from industrial application indicate that an FNLF model outperforms an NLF model in terms of both convergence rate and prediction accuracy for missing data. Hence, compared with an NLF model, an FNLF model is more practical in industrial applications.

This article focuses on the research of a general time-varying nonlinear optimization (TVNO) problem solving especially in a noise-disturbance environment. For addressing this problem more efficiently, a new noise-enduring and finite-time convergent design formula is suggested to establish a novel zeroing neural network (NZNN). In contrast to the initial zeroing neural network or the noising-enduring zeroing neural network, which either only achieves finite-time convergence or only suppresses external disturbances, the merit of the proposed NZNN model is able to find an error-free optimal solution in a finite time under various different types of external noises. In addition, the detailed mathematical analyses about finite-time convergence and noise endurance are given to prove the excellent characteristics of the NZNN model. Numerical comparative results are provided to demonstrate the accuracy, efficiency, and advantages of the NZNN model for TVNO under various types of external disturbances. Robotic tracking example further validates the applicability of the NZNN model especially in a noise-disturbance environment.

The communication cost is generally higher for the consensus of high-order multiagent systems than that for low-order multiagent systems. In this paper, two novel distributed protocols are proposed to address the consensus of high-order discrete-time multiagent systems. By the proposed consensus protocols, each agent only needs to transmit the value of a variable to neighbor agents regardless of the order of agent dynamics. Theoretical analysis shows that the proposed protocols guarantee asymptotic consensus of the agent states in different cases of communication graphs, including jointly connected ones. Simulative examples verify the theoretical results and the efficacy of the proposed protocols.

In this paper, a multi-level simultaneous minimization (MLSM) scheme is proposed and investigated to remedy the joint-angle drift (JAD) and non-zero final joint-velocity (NZFJV) phenomena as well as to prevent the occurrence of high joint variables of redundant robot manipulators. The proposed scheme is novelly designed within multiple levels and finally resolved at the jerk level for a jerk-bounded robot motion, which is desirable for engineering applications. More importantly, the correctness of the proposed MLSM scheme is guaranteed by the corresponding theorems. Then, the MLSM scheme is formulated as a dynamical quadratic program (DQP) that is solved by a piecewise linear projection equation neural network (PLPENN). Furthermore, the path-tracking simulations based on a 6-degrees-of-freedom (DOF) robot manipulator substantiate the effectiveness and advantage of the MLSM scheme. Comparisons between the MLSM scheme and the minimum jerk norm (MJN) scheme illustrate that the proposed scheme is superior and more applicable. Finally, the additional validation on the KUKA robot in the virtual robot experimentation platform (V-REP) is provided for reproducible engineering applications by researchers and practitioners.Note to Practitioners—This paper is motivated by the inverse kinematics problem of jerk-bounded redundant robot manipulators in practical applications. Note that the joint-angle drift (JAD) and non-zero final joint-velocity (NZFJV) phenomena as well as the occurrence of high joint variables always encountered in the traditional norm-based scheme for robot manipulators, which is not suitable for the real-time control of robots. Besides, it would be appealing and desirable to resolve the robot redundancy at the jerk level for industrial robots in engineering. Therefore, an effective, flexible, and stable solution for such robot manipulators is significant for practitioners. This paper proposes a multi-level simultaneous minimization (MLSM) scheme for practitioners interested in robot kinematics to remedy the JAD and NZFJV phenomena as well as to prevent the occurrence of high joint variables of redundant robot manipulators. Unlike traditional single-level schemes, such as the minimum jerk norm (MJN) scheme, the proposed scheme is designed within multiple levels with distinct physical nature and finally resolved at the jerk level to achieve a desirable performance for the jerk-bounded redundant robot manipulators. Besides, for better understanding of practitioners, the corresponding block diagram and principle interpretation of the MLSM scheme are presented. Simulation studies and comparisons are designed and conducted on a 6-degrees-of-freedom (DOF) robot manipulator to substantiate the effectiveness and superiority of the proposed scheme. Extensive tests with different weighting factors fully verify the flexibility and stable performance of the proposed MLSM scheme. For reproducible engineering applications by researchers and practitioners, the additional validation on the KUKA robot in the virtual robot experimentation platform (V-REP) is further presented.

In this article, we computationally model the social behavior of beetles and apply it to the tracking control of manipulators. The beetles demonstrate excellent skills to forage food in a previously unknown environment by merely using their olfactory senses. The goal of the beetle is to search the region with the maximum smell. Therefore, the actions of the beetle can be characterized as an optimization algorithm. This article mathematically models this behavior in the form of a recurrent neural network (RNN) with a temporal-feedback connection. We apply the formulated RNN controller for the redundancy resolution and tracking control of the redundant manipulators with an unknown kinematic model. Most of the industrial robots have redundant manipulators, and kinematic trajectory tracking is a fundamental problem for any industrial task. The behavior of the beetle allows us to formulate a position-level controller without relying on the manipulation of the Jacobian matrix. It is in contrast with the conventional velocity-level controllers, which require an accurate kinematic model of the manipulator and calculation of pseudoinverse of Jacobian, a computationally expensive task. The proposed algorithm, called Beetle Antennae Olfactory Recurrent Neural Network (BAORNN) algorithm, is capable of driving the manipulator by only using the feedback from the position and orientation sensors. The stability and convergence of the proposed algorithm are theoretically proved, and the simulations results using a seven-degree-of-freedom (DOF) industrial robotic arm, KUKA LBR IIWA14, are presented to demonstrate the performance of the proposed algorithm.

Parallel robots are usually required to perform real-time tracking control tasks in the presence of external disturbances in the complex environment. Conventional zeroing neural-dynamics (ZNDs) provide an alternative solution for the real-time tracking control of parallel robots due to its capacity of parallel processing and nonlinearity handling. However, it is still a challenge for the solution in a unified framework of the ZND to deal with the external disturbances, and simultaneously possess a finite-time convergence property. In this paper, a novel ZND model by exploring the super-twisting (ST) algorithm, named ST-ZND model, is proposed. The theoretical analyses on the global stability, finite-time convergence, as well as the robustness against the external disturbances are rigorously presented. Finally, the effectiveness and superiority of the ST-ZND model for the real-time tracking control of parallel robots are demonstrated by two illustrative examples, comparisons, and convergence tests.

High-dimensional and sparse (HiDS) matrices are commonly seen in big-data-related industrial applications like recommender systems. Latent factor (LF) models have proven to be accurate and efficient in extracting hidden knowledge from them. However, they mostly fail to fulfill the non-negativity constraints that describe the non-negative nature of many industrial data. Moreover, existing models suffer from slow convergence rate. An alternating-direction-method of multipliers-based non-negative LF (AMNLF) model decomposes the task of non-negative LF analysis on an HiDS matrix into small subtasks, where each task is solved based on the latest solutions to the previously solved ones, thereby achieving fast convergence and high prediction accuracy for its missing data. This paper theoretically analyzes the characteristics of an AMNLF model, and presents detailed empirical studies regarding its performance on nine HiDS matrices from industrial applications currently in use. Therefore, its capability of addressing HiDS matrices is justified in both theory and practice.

Due to the property of multiple solutions, redundant robot manipulators are usually required to simultaneously achieve multiple objectives in complex applications. The research of robustness for scheme formulation and optimization becomes an increasingly important issue for motion planning of redundant robot manipulators. From the perspective of optimization, a robust hybrid multiobjective (RHMO) scheme with a new disturbance rejection constraint is proposed in this article to achieve simultaneously four objectives together with the suppression of external time-varying disturbances. Theoretical results on the property of disturbance rejection are shown to confirm the effectiveness and robustness of the proposed RHMO scheme with a new disturbance rejection constraint. The RHMO scheme is then reformulated as dynamical quadratic programming with its solution found via the piecewise-linear projection equation neural network. Numerical experiments, tests, and comparisons on the basis of a PA10 manipulator verify the effectiveness, robustness, and superiority of the RHMO scheme with the new constraint for the motion planning and optimization of redundant robot manipulators against time-varying disturbances.

The Zhang neural network (ZNN) has recently realized remarkable success in solving time-varying problems. Harmonic noise widely exists in industrial applications and can severely affect the solution computed by ZNN models. This article attempts to solve the aforementioned limitations by providing the first ZNN design with an inherent capability to prohibit harmonic noise. Moreover, it opens new opportunities to shift the research on ZNNs in ideal situations to that with theoretical consideration on nonideal working environments. We establish a modified ZNN design formula in a noisy environment by incorporating the dynamics of harmonic signals. Theoretical analysis shows the convergence of the proposed ZNN design. An application case study for the new ZNN model verifies its effectiveness for time-varying matrix inversion in the presence of harmonic noise. The simulation further substantiates the effectiveness, superiority, and application prospects of the proposed ZNN design.

In this article, we present a metaheuristic-based control framework, called beetle antennae olfactory recurrent neural network, for simultaneous tracking control and obstacle avoidance of a redundant manipulator. The ability to avoid obstacles while tracking a predefined reference path is critical for any industrial manipulator. The formulated control framework unifies the tracking control and obstacle avoidance into a single constrained optimization problem by introducing a penalty term into the objective function, which actively rewards the optimizer for avoiding the obstacles. One of the significant features of the proposed framework is the way that the penalty term is formulated following a straightforward principle: maximize the minimum distance between a manipulator and an obstacle. The distance calculations are based on Gilbert–Johnson–Keerthi algorithm, which calculates the distance between a manipulator and an obstacle by directly using their three-dimensional geometries, which also implies that our algorithm works for a manipulator and an arbitrarily shaped obstacle. Theoretical treatment proves the stability and convergence, and simulations results using an LBR IIWA seven-DOF manipulator are presented to analyze the performance of the proposed framework.

Nowadays, industrial redundant manipulators have been playing important roles in manufacturing fields, such as welding and assembling, by performing repetitive and dull work. Such long-term industrial operations usually require redundant manipulators to keep good working conditions and maintain steadiness of joint actuation. However, some joints of redundant manipulators may fall into fault status after enduring long-period heavy manipulations, causing that the desired industrial tasks cannot be accomplished accurately. In this article, we propose a novel fault-tolerant method with simultaneous fault-diagnose function for motion planning and control of industrial redundant manipulators. The proposed approach is able to adaptively localize which joints run away from the normal state to be fault, and it can guarantee to finish the desired path tracking control even when these fault joints lose their velocity to actuate. Simulation and experiment results on a Kuka LBR iiwa manipulator demonstrate the efficiency of the proposed fault-tolerant method for motion control of the redundant manipulator.

In this article, a real-time moment of inertia identification technique using Petri probabilistic fuzzy neural network with an asymmetric membership function (PPFNN-AMF) for an interior permanent magnet synchronous motor (IPMSM) servo drive is proposed. The estimated moment of inertia will be used in the online design of an integral–proportional (IP) speed controller to achieve the gains autotuning of the IPMSM servo drive. In the proposed method, the dynamic analysis of a field-oriented control IPMSM servo drive system with an IP speed controller is constructed first. Then, a heuristic approach using the PPFNN-AMF is proposed for the real-time identification of the moment of inertia of the IPMSM servo drive system. Moreover, the network structure and the convergence analysis of the PPFNN-AMF are devised and derivated. Furthermore, an IPMSM servo drive based on a high-performance digital signal processor is developed. Finally, from the experimental results, the gains of the IP speed controller can be tuned online effectively at different operating conditions with robust control characteristics.

Most traditional methods for solving the kinematic control problem of redundant manipulators are designed from a signal processing perspective. However, such a perspective may make the resultant design difficult for practitioners to understand. If the problem is addressed from an energy perspective, the resultant design may be more comprehensive, because energy is a universal concept and can be used to describe complex large-scale industrial systems. Passivity is a property of engineering systems, which is characterized through energy transformation. In this paper, a passivity-based approach is proposed for the kinematic control of redundant manipulators, where the joint velocity limit of manipulators is also considered. The performance of the approach is theoretically guaranteed. In addition, simulative examples are presented to validate the efficacy of the approach and the theoretical results.

This paper addresses the problem of adaptive neural output-feedback decentralized control for a class of strongly interconnected nonlinear systems suffering stochastic disturbances. An state observer is designed to approximate the unmeasurable state signals. Using the approximation capability of radial basis function neural networks (NNs) and employing classic adaptive control strategy, an observer-based adaptive backstepping decentralized controller is developed. In the control design process, NNs are applied to model the uncertain nonlinear functions, and adaptive control and backstepping are combined to construct the controller. The developed control scheme can guarantee that all signals in the closed-loop systems are semiglobally uniformly ultimately bounded in fourth-moment. The simulation results demonstrate the effectiveness of the presented control scheme.

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.

The efficient driving control of MEMS gyroscopes is an attractive way to improve the precision without hardware redesign. This paper investigates the sliding mode control (SMC) for the dynamics of MEMS gyroscopes using neural networks (NNs). Considering the existence of the dynamics uncertainty, the composite neural learning is constructed to obtain higher tracking precision using the serial-parallel estimation model (SPEM). Furthermore, the nonsingular terminal SMC (NTSMC) is proposed to achieve finite-time convergence. To obtain the prescribed performance, a time-varying barrier Lyapunov function (BLF) is introduced to the control scheme. Through simulation tests, it is observed that under the BLF-based NTSMC with composite learning design, the tracking precision of MEMS gyroscopes is highly improved.

Computing time-varying linear systems is widely encountered in engineering practice and scientific computation. Dynamic neural networks, as a class of modeling approaches, have been intensively explored in recent decades for solving linear equations. The time-varying nature of this problem and the noisy workspace for many engineering practice require two features of practical design: 1) fast convergence in time and 2) robustness against noises and disturbance. Existing solutions usually decouple the problem into two steps by designing a fast-convergent neural controller and then topped with an additional low-pass filter to reach noise robustness. However, due to the interplay of the mentioned two dynamical parts, the overall system may lose stability if the parameters are not well tuned. In this paper, we establish the first dynamical neural model for simultaneously achieving fast-convergence, particularly finite-time convergence, and noise-robustness, with the capability to reject the unknown noise when it is constant or varies slowly. To do so, a superior design formula activated by noise-tolerant nonlinear functions is proposed to enhance the capability of zeroing neural networks (ZNNs), achieving denoising and finite-time convergence in a unified design. According to this design formula, a novel recurrent neural network (RNN) with finite-time convergence and inherently noise-suppression performance [thus termed the finite-time robust RNN (FTRRNN)] is developed and applied to robotic motion tracking illustrated via time-varying linear equation system solving. Furthermore, theoretical analyses on the global stability, the finite-time convergence and the denoising ability of the proposed design formula and the corresponding FTRRNN model are presented in details. The upper bound on the convergence time is also analytically derived. A numerical example is supplied to verify the superior property of the FTRRNN model to the ZNN model according to the results of computing time-varying linear equation system in the presence of additive noises. Finally, an application to robotic motion tracking is presented to show that the presented FTRRNN model can successfully realize the ellipse-path tracking control of a planar two-link manipulator in front of the external disturbances, while the conventional ZNN model fails under the same conditions.

Hashing methods have attracted much attention due to their superior time and storage properties for image retrieval. To learn similarity-preserving hash function, most existing methods are designed for the centralized setting. However, the current data storage systems are distributed to increase scalability. Obviously, it is infeasible to aggregate all the data into a fusion center because of the prohibitively expensive communication and computation overhead. Motivated by this, some methods are proposed to achieve hashing for distributed data. However, these methods mostly focus on extending one specific hashing to a distributed model without considering the generality. In this letter, we propose a novel general distributed hash learning model, which can be viewed as an effective distributed model of most hashing methods. The proposed model can achieve up to 15.2% accuracy gains over state-of-the-art distributed hashing methods, while the communication cost is independent on the data size.

Input disturbances and physical constraints are important issues in the kinematic control of redundant manipulators. In this paper, we propose a novel recurrent neural network to simultaneously address the periodic input disturbance, joint angle constraint, and joint velocity constraint, and optimize a general quadratic performance index. The proposed recurrent neural network applies to both regulation and tracking tasks. Theoretical analysis shows that, with the proposed neural network, the end-effector tracking and regulation errors asymptotically converge to zero in the presence of both input disturbance and the two constraints. Simulation examples and comparisons with an existing controller are also presented to validate the effectiveness and superiority of the proposed controller.

Oil spill at the Gulf of Mexico a few years ago sets great hazardous to environments. The runtime monitoring and tracking of plume pose challenges to research community. Robot-based approaches have been proposed in previous work to solve this problem in environments with known physical parameters and measurable currents. However, practical implementation of this type of control laws may require additional sensors and the sensing error may significantly impact the convergence. This paper extends previous work by overcoming the challenge to establish a new control law by integrating interactive estimation and control in a unified loop. With a deliberate design, the parameters can be estimated online and the control can be achieved at the same time with provable convergence of the overall system, despite of the interplay of the two parts. An auxiliary system is constructed for efficient estimation of unknown parameters and set projection is incorporated to further improve the transient performance, making the system work well in both slow and fast time-varying environments. Theories of convergence, stability, and transient state are presented to guarantee the performance of plume front tracking. Validation experiments verify the theoretical results and substantiate the efficacy of the proposed scheme for plume tracking in unknown environments.

It has been found that there exists an essential similarity between solving equations and controlling dynamic systems: Both errors are expected to decrease to zero (or an acceptably tiny value) as soon as possible. By exploiting such a similarity, researchers have presented and investigated continuous-time recurrent neural network models for solving time-varying problems. To be compatible with digital computers, it is desirable to develop discrete-time neural algorithms from the control perspective for performance improvement. In this paper, a discrete-time zeroing neural algorithm is proposed for the solving system of linear equations with the aid of control techniques. To lay a basis for theoretical analyses, the proposed zeroing neural algorithm with nonlinearity is converted into a second-order linear system plus a residual term, and then, analyzed using the control theory. Theoretical results and numerical experiments are provided, which illustrate that the proposed neural algorithm possesses an improved performance compared to the existing solutions.

Recently, Recurrent Neural Network (RNN) control schemes for redundant manipulators have been extensively studied. These control schemes demonstrate superior computational efficiency, control precision, and control robustness. However, they lack planning completeness. This paper explains why RNN control schemes suffer from the problem. Based on the analysis, this work presents a new random RNN control scheme, which 1) introduces randomness into RNN to address the planning completeness problem, 2) improves control precision with a new optimization target, 3) improves planning efficiency through learning from exploration. Theoretical analyses are used to prove the global stability, the planning completeness, and the computational complexity of the proposed method. Software simulation is provided to demonstrate the improved robustness against noise, the planning completeness and the improved planning efficiency of the proposed method over benchmark RNN control schemes. Real-world experiments are presented to demonstrate the application of the proposed method.

Zeroing neural dynamics (ZND) can be seen as an effective controller to solve various challenging scientific and engineering problems. Computing Lyapunov equation is a kind of important issue in nonlinear systems for stability analysis in control. This paper presents a systematic and constructive procedure on using ZND to design control laws based on the efficient solution of dynamic Lyapunov equation. We particularly address three important aspects in the design: 1) the global stability of ZND, to guarantee the effectiveness of the solution; 2) the robustness against additive noises, to ensure the capability of ZND for using in harsh environments; and 3) the finite-time convergence of ZND, to endow ZND for real-time solution of dynamical problems. To do so, a novel formula is first designed in a unified manner of ZND. Differing from the conventional formula appearing in ZND, the proposed formula simultaneously has finite-time convergence and noise robustness property. According to this novel formula, a novel control law (termed nonlinear neural dynamics, NND) is established to compute dynamic Lyapunov equation in the presence of various additive noises. Both theoretical and simulative results ensure the finite-time convergence and noise robustness property of the NND model for computing dynamic Lyapunov equation in front of various additive noises. As compared to the conventional ZND model for computing dynamic Lyapunov, the superior property of the NND model is further demonstrated.

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.

Recurrent neural networks (RNNs) have found a great variety of application areas. As a special type of RNNs, zeroing neural network (ZNN), or termed Zhang neural network, has been reported to have powerful abilities to address various nonstationary problems. To overcome drawbacks and improve the performance of existing ZNN models, several modified ZNN models are proposed in this paper, which allow nonconvex activation functions and possess accelerated finite-time convergence property. Theoretical analyses suggest that the developed ZNN models are equipped with the global convergence property and the convergence-accelerated models are verified by the estimated upper bounds of convergence time. Finally, comparative and illustrative simulation results, including a verification on a mobile manipulator, are presented to illustrate the effectiveness and superiority of proposed ZNN models to existing models for solving nonstationary Sylvester equations.

In a reconfigurable battery pack, the connections among cells can be changed during operation to form different configurations. This can lead a battery, a passive two-terminal device, to a smart battery that can reconfigure itself according to the requirement to enhance operational performance. Several hardware architectures with different levels of complexities have been proposed. Some researchers have used existing hardware and demonstrated improved performance on the basis of novel optimization and scheduling algorithms. The possibility of software techniques to benefit the energy storage systems is exciting, and it is the perfect time for such methods as the need for high-performance and long-lasting batteries is on the rise. This novel field requires new understanding, principles, and evaluation metrics of proposed schemes. In this article, we systematically discuss and critically review the state of the art. This is the first effort to compare the existing hardware topologies in terms of flexibility and functionality. We provide a comprehensive review that encompasses all existing research works, starting from the details of the individual battery including modeling and properties as well as fixed-topology traditional battery packs. To stimulate further research in this area, we highlight key challenges and open problems in this domain.

Redundancy resolution is a critical problem in the control of manipulators. The dual neural network, as a special type of recurrent neural networks that are inherently parallel processing models, is widely investigated in past decades to control manipulators. However, to the best of our knowledge, existing dual neural networks require a full knowledge about manipulator parameters for efficient control. We make progress along this direction in this paper by proposing a novel model-free dual neural network, which is able to address the learning and control of manipulators simultaneously in a unified framework. Different from pure learning problems, the interplay of the control part and the learning part allows us to inject an additive noise into the control channel to increase the richness of signals for the purpose of efficient learning. Due to a deliberate design, the learning error is guaranteed for convergence to zero despite the existence of additive noise for stimulation. Theoretical analysis reveals the global stability of the proposed neural network control system. Simulation results verify the effectiveness of the proposed control scheme for redundancy resolution of a PUMA 560 manipulator.

Two novel nonlinearly activated recurrent neural networks (RNNs) with finite-time convergence [called finite-time RNNs (FTRNNs)] are proposed and analyzed to solve efficiently time-varying systems of nonlinear equations (SoNEs). Compared with previously presented neural networks for solving such a SoNE, the FTRNNs are activated by new nonlinear activation functions and thus possess a better finite-time convergence property. In addition, theoretical analyses about FTRNNs are presented to determine the upper bounds of convergence time under the context of using such two novel nonlinear activation functions. Computer simulations based on a numerical example validate the preponderance of the proposed FTRNNs for time-varying SoNE, as compared to the recently proposed Zhang neural network and its improved version. Finally, an engineering practical example to motion tracking of a robot manipulator demonstrates the feasibility and applicability of the FTRNNs.

Recurrent Neural Networks (RNNs) demonstrated advantages on control precision, system robustness and computational efficiency, and have been widely applied to redundant manipulator control optimization. Existing RNN control schemes locally optimize trajectories and are efficient and reliable on obstacle avoidance. However, for motion planning, they suffer from local minimum and do not have planning completeness. This work explained the cause of the planning incompleteness and addressed the problem with a novel RNN control scheme. The paper presented the proposed method in detail and analyzed the global stability and the planning completeness in theory. The proposed method was compared with other three control schemes on the precision, the robustness and the planning completeness in software simulation and the results shows the proposed method has improved precision and robustness, and planning completeness.

Non-negative latent factor (NLF) models can efficiently acquire useful knowledge from high-dimensional and sparse (HiDS) matrices filled with non-negative data. Single latent factor-dependent, non-negative and multiplicative update (SLF-NMU) is an efficient algorithm for building an NLF model on an HiDS matrix, yet it suffers slow convergence. On the other hand, a momentum method is frequently adopted to accelerate a learning algorithm explicitly depending on gradients, yet it is incompatible with learning algorithms implicitly depending on gradients, like SLF-NMU. To build a fast NLF model, we firstly propose a generalized momentum method compatible with SLF-NMU. With it, we propose the single latent factor-dependent, non-negative, multiplicative and momentum-integrated update (SLF-NM2U) algorithm for accelerating the building process of an NLF model, thereby achieving a fast non-negative latent factor (FNLF) model. Empirical studies on six HiDS matrices from industrial application indicate that with the incorporated momentum effects, FNLF outperforms NLF in terms of both convergence rate and prediction accuracy for missing data. Hence, compare with an NLF model, an FNLF model is more practical in industrial applications.

Generating highly accurate predictions for missing quality-of-service (QoS) data is an important issue. Latent factor (LF)-based QoS-predictors have proven to be effective in dealing with it. However, they are based on first-order solvers that cannot well address their target problem that is inherently bilinear and nonconvex, thereby leaving a significant opportunity for accuracy improvement. This paper proposes to incorporate an efficient second-order solver into them to raise their accuracy. To do so, we adopt the principle of Hessian-free optimization and successfully avoid the direct manipulation of a Hessian matrix, by employing the efficiently obtainable product between its Gauss-Newton approximation and an arbitrary vector. Thus, the second-order information is innovatively integrated into them. Experimental results on two industrial QoS datasets indicate that compared with the state-of-the-art predictors, the newly proposed one achieves significantly higher prediction accuracy at the expense of affordable computational burden. Hence, it is especially suitable for industrial applications requiring high prediction accuracy of unknown QoS data.

Tracking control of robot manipulators is a fundamental and significant problem in robotic industry. As a conventional solution, the Jacobian-matrix-pseudo-inverse (JMPI) method suffers from two major limitations: one is the requirement on known information of the robot model such as parameter and structure; the other is the position error accumulation phenomenon caused by the open-loop nature. To overcome such two limitations, this paper proposes a novel Jacobian-matrix-adaption (JMA) method for the tracking control of robot manipulators via the zeroing dynamics. Unlike existing works requiring the information of the known robot model, the proposed JMA method uses only the input-output information to control the robot with unknown model. The solution based on the JMA method transforms the internal, implicit, and unmeasurable model information to the external, explicit, and measurable input-output information. Moreover, simulation studies including comparisons and tests substantiate the efficacy and superiority of the proposed JMA method for the tracking control of robot manipulators subject to unknown models.

In this paper, the existing recurrent neural network (RNN) models for solving zero-finding (e.g., matrix inversion) with time-varying parameters are revisited from the perspective of control and unified into a control-theoretical framework. Then, limitations on the activated functions of existing RNN models are pointed out and remedied with the aid of control-theoretical techniques. In addition, gradient-based RNNs, as the classical method for zero-finding, have been remolded to solve dynamic problems in manners free of errors and matrix inversions. Finally, computer simulations are conducted and analyzed to illustrate the efficacy and superiority of the modified RNN models designed from the perspective of control. The main contribution of this paper lies in the removal of the convex restriction and the elimination of the matrix inversion in existing RNN models for the dynamic matrix inversion. This work provides a systematic approach on exploiting control techniques to design RNN models for robustly and accurately solving algebraic equations.

In this paper, a neural-dynamic distributed scheme is proposed for the cooperative control of multiple redundant manipulators with limited communications. It is guaranteed that, with the communication network being connected, all manipulators can jointly reach the same desired motion. The proposed distributed scheme is rearranged as a time-varying quadratic program and solved online by a Zhang neural network. Then, theoretical analyses show that, without noise, the proposed distributed scheme is able to execute a given task with exponentially convergent position errors. Moreover, an explicit bound relationship between the control input noise and the end-effector position error is analytically derived. Furthermore, numerical comparisons substantiate the superiority, effectiveness, and accuracy of the proposed distributed scheme.

Improvement of the real-time performance of tracking control is increasingly desirable. It is a routine for most conventional algorithms that the control input at current time instant is to track the current desired output. However, lagging errors resulting from computational time and the fluctuation of the desired output exist for the tracking control. Different from conventional algorithms, a look-ahead scheme of zeroing dynamics (ZD) is established in this paper to achieve the real-time tracking control of both serial and parallel manipulators. With the exploitation of data at current time and that in history, the control inputs generated by the proposed ZD algorithms never lead to lagging errors with the source from the inevitable computational time. To tackle prediction errors for ZD algorithms, a new high-precision discretization formula, as an essential part of ZD algorithms, is presented to confine the prediction error in an ignorable range in comparison with lagging errors.

High-dimensional and sparse (HiDS) matrices are commonly encountered in many big-data-related and industrial applications like recommender systems. When acquiring useful patterns from them, nonnegative matrix factorization (NMF) models have proven to be highly effective owing to their fine representativeness of the nonnegative data. However, current NMF techniques suffer from: 1) inefficiency in addressing HiDS matrices; and 2) constraints in their training schemes. To address these issues, this paper proposes to extract nonnegative latent factors (NLFs) from HiDS matrices via a novel inherently NLF (INLF) model. It bridges the output factors and decision variables via a single-element-dependent mapping function, thereby making the parameter training unconstrained and compatible with general training schemes on the premise of maintaining the nonnegativity constraints. Experimental results on six HiDS matrices arising from industrial applications indicate that INLF is able to acquire NLFs from them more efficiently than any existing method does.

The Lyapunov equation is widely employed in the engineering field to analyze stability of dynamic systems. In this paper, based on a new evolution formula, a novel finite-time recurrent neural network (termed finite-time Zhang neural network, FTZNN) is proposed and studied for solving a nonstationary Lyapunov equation. In comparison with the original Zhang neural network (ZNN) model for a nonstationary Lyapunov equation, the convergence performance has a remarkable improvement for the proposed FTZNN model and can be accelerated to finite time. Besides, by solving the differential inequality, the time upper bound of the FTZNN model is computed theoretically and analytically. Simulations are conducted and compared to validate the superiority of the FTZNN model to the original ZNN model for solving the nonstationary Lyapunov equation. At last, the FTZNN model is successfully applied to online tracking control of a wheeled mobile manipulator.

Manipulators are subject to physical constraints at different levels, i.e., joint angle limits, joint velocity limits, and acceleration limits. Effective resolution of redundant manipulators with compliance to the physical constraints is a fundamental issue for safe operation. Existing results generally resolve the manipulator redundancy either at the velocity level or the acceleration level. On the one hand, the velocity-level redundancy resolution scheme is able to deal with the joint angle and joint velocity limits successfully but cannot address the joint acceleration limit. On the other hand, although the existing acceleration-level redundancy resolution scheme is able to overcome the failure of the velocity-level one in complying with acceleration constraints, it is at the cost of making the system equation more complicated, e.g., the dependence on the time derivative of the Jacobian matrix. Whether it is possible to conduct redundancy resolution at the velocity level but with the compliance to joint angle constraints, joint velocity constraints, and joint acceleration constraints remains an open problem in past decades. This paper gives a positive answer to this pending problem by providing a novel scheme. In the proposed scheme, the redundancy resolution problem is formulated as a quadratic program subject to joint angle, velocity, and acceleration constraints with the joint velocity being the decision variable and joint velocity norm as the performance index, which is widely adopted and closely related to the energy consumption. Then, a projection neural network is designed and proposed to online solve the problem with the joint acceleration constraint handled. Theoretical analysis is performed to guarantee the global convergence of the proposed projection neural network to the optimal solution to the redundancy resolution problem. Besides, simulation results based on a PUMA 560 industrial manipulator are presented and compared to verify the theoretical result and substantiate the efficacy and superiority of the proposed scheme.

In this paper, we propose a novel recurrent neural network to resolve the redundancy of manipulators for efficient kinematic control in the presence of noises in a polynomial type. Leveraging the high-order derivative properties of polynomial noises, a deliberately devised neural network is proposed to eliminate the impact of noises and recover the accurate tracking of desired trajectories in workspace. Rigorous analysis shows that the proposed neural law stabilizes the system dynamics and the position tracking error converges to zero in the presence of noises. Extensive simulations verify the theoretical results. Numerical comparisons show that existing dual neural solutions lose stability when exposed to large constant noises or time-varying noises. In contrast, the proposed approach works well and has a low tracking error comparable to noise-free situations.

In recent decades, primal-dual neural networks, as a special type of recurrent neural networks, have received great success in real-time manipulator control. However, noises are usually ignored when neural controllers are designed based on them, and thus, they may fail to perform well in the presence of intensive noises. Harmonic noises widely exist in real applications and can severely affect the control accuracy. This work proposes a novel primal-dual neural network design that directly takes noise control into account. By taking advantage of the fact that the unknown amplitude and phase information of a harmonic signal can be eliminated from its dynamics, our deliberately designed neural controller is able to reach the accurate tracking of reference trajectories in a noisy environment. Theoretical analysis and extensive simulations show that the proposed controller stabilizes the control system polluted by harmonic noises and converges the position tracking error to zero. Comparisons show that our proposed solution consistently and significantly outperforms the existing primal-dual neural solutions as well as feedforward neural one and adaptive neural one for redundancy resolution of manipulators.

This paper presents the development of an adaptive neural controller for a class of nonlinear systems with unmodeled dynamics and immeasurable states. An observer is designed to estimate system states. The structure consistency of virtual control signals and the variable partition technique are combined to overcome the difficulties appearing in a nonlower triangular form. An adaptive neural output-feedback controller is developed based on the backstepping technique and the universal approximation property of the radial basis function (RBF) neural networks. By using the Lyapunov stability analysis, the semiglobally and uniformly ultimate boundedness of all signals within the closed-loop system is guaranteed. The simulation results show that the controlled system converges quickly, and all the signals are bounded. This paper is novel at least in the two aspects: 1) an output-feedback control strategy is developed for a class of nonlower triangular nonlinear systems with unmodeled dynamics and 2) the nonlinear disturbances and their bounds are the functions of all states, which is in a more general form than existing results.

Main issues in visual servoing of manipulators mainly include rapid convergence of feature errors to zero and the safety of joints regarding joint physical limits. To address the two issues, in this paper, an image-based visual servoing scheme is proposed for manipulators with an eye-in-hand configuration. Compared with existing schemes, the proposed one does not require performing pseudoinversion for the image Jacobian matrix or inversion for the Jacobian matrix associated with the forward kinematics of the manipulators. Theoretical analysis shows that the proposed scheme not only guarantees the asymptotic convergence of feature errors to zero but also the compliance with joint angle and velocity limits of the manipulators. Besides, simulation results based on a PUMA560 manipulator with a camera mounted on the end effector verify the theoretical conclusions and the efficacy of the proposed scheme.

In this paper, the receding horizon near-optimal tracking control problem about a class of continuous-time nonlinear systems with fully unknown dynamics is considered. The main challenges of this problem lie in two aspects: 1) most existing systems only restrict their considerations to the state feedback part while the input channel parameters are assumed to be known. This paper considers fully unknown system dynamics in both the state feedback channel and the input channel and 2) the optimal control of nonlinear systems requires the solution of nonlinear Hamilton-Jacobi-Bellman equations. Up to date, there are no systematic approaches in the existing literature to solve it accurately. A novel model-free adaptive near-optimal control method is proposed to solve this problem via utilizing the Taylor expansion-based problem relaxation, the universal approximation property of sigmoid neural networks, and the concept of sliding mode control. By making approximation for the performance index, it is first relaxed to a quadratic program, and then, a linear algebraic equation with unknown terms. An auxiliary system is designed to reconstruct the input-to-output property of the control systems with unknown dynamics, so as to tackle the difficulty caused by the unknown terms. Then, by considering the property of the sliding-mode surface, an explicit adaptive near-optimal control law is derived from the linear algebraic equation. Theoretical analysis shows that the auxiliary system is convergent, the resultant closed-loop system is asymptotically stable, and the performance index asymptomatically converges to optimal. An illustrative example and experimental results are presented, which substantiate the efficacy of the proposed method and verify the theoretical results.

In this paper, a distributed scheme is proposed for the cooperative motion generation in a distributed network of multiple redundant manipulators. The proposed scheme can simultaneously achieve the specified primary task to reach global cooperation under limited communications among manipulators and optimality in terms of a specified optimization index of redundant robot manipulators. The proposed distributed scheme is reformulated as a quadratic program (QP). To inherently suppress noises originating from communication interferences or computational errors, a noise-tolerant zeroing neural network (NTZNN) is constructed to solve the QP problem online. Then, theoretical analyses show that, without noise, the proposed distributed scheme is able to execute a given task with exponentially convergent position errors. Moreover, in the presence of noise, the proposed distributed scheme with the aid of NTZNN model has a satisfactory performance. Furthermore, simulations and comparisons based on PUMA560 redundant robot manipulators substantiate the effectiveness and accuracy of the proposed distributed scheme with the aid of NTZNN model.

The problem of dynamic task allocation in a distributed network of redundant robot manipulators for pathtracking with limited communications is investigated in this paper, where k fittest ones in a group of n redundant robot manipulators with n k are allocated to execute an object tracking task. The problem is essentially challenging in view of the interplay of manipulator kinematics and the dynamic competition for activation among manipulators. To handle such an intricate problem, a distributed coordination control law is developed for the dynamic task allocation among multiple redundant robot manipulators with limited communications and with the aid of a consensus filter. In addition, a theorem and its proof are presented for guaranteeing the convergence and stability of the proposed distributed control law. Finally, an illustrative example is provided and analyzed to substantiate the efficacy of the proposed control law.

In this paper, a time-scale expansion-based scheme is proposed for approximately solving the optimal control problem of continuous-time underactuated nonlinear systems subject to input constraints and system dynamics. By time-scale Taylor approximation of the original performance index, the optimal control problem is relaxed into an approximated optimal control problem. Based on the system dynamics, the problem is further reformulated as a quadratic programming problem, which is solved by a projection neural network. Theoretical analysis on the closed-loop system synthesized by the controlled system and the projection neural network is conducted, which reveals that, under certain conditions, the closed-loop system possesses exponential stability and the original performance index converges to zero as time tends to infinity. In addition, two illustrative examples, which are based on a flexible joint manipulator and an underactuacted ship, are provided to validate the theoretical results and demonstrate the efficacy and superiority of the proposed control scheme.

This paper investigates the distributed motion planning of multiple robot arms with limited communications in the presence of noises. To do this, a nonlinearly-activated noise-tolerant zeroing neural network (NANTZNN) is designed and presented for the first time for solving the presented distributed scheme online. Theoretical analyses and simulation results show the effectiveness and accuracy of the presented distributed scheme with the aid of NANTZNN model.

The speed control of permanent magnet brushed (PMB) DC motors at low speeds is difficult due to the nonlinearity caused by various types of frictions. Under parameter uncertainty, the speed control becomes more difficult. In this paper, to handle the parameter uncertainty, we propose a dynamic neural network to adaptively reconstruct or learn the dynamics of PMB DC motors. Then, based on the parameters of the neural dynamic model, a near-optimal dynamic neural controller is designed and proposed for the speed control of PMB DC motors with frictions considered under parameter uncertainty. Simulations substantiate the efficacy of the proposed dynamic neural model and adaptive near-optimal controller for PMB DC motors with fully unknown parameters.

Surgical robot research is driven by the desire of improving surgical outcomes. This paper proposed a Recurrent Neural Network based controller to address two problems: 1) improving control precision, 2) increasing adaptiveness for robot motion (explained in Section I). RNN was adopted in this work mainly because 1) the problem formulation naturally matches RNN structure, 2) RNN has advantages as an biologically inspired method. The proposed method was explained in detail and analysis shows that the proposed method is able to dynamically regulate outputs to increase the adaptiveness and the control precision. This paper uses Raven II surgical robot as an example to show the application of the proposed method, and the numeral simulation results from the proposed method and three other controllers show that the proposed method has improved precision, improved high robustness against noise and increased movement smoothness, and it keeps the manipulator links as far away as possible from physical boundaries, which potentially increases surgical safety and leads to improved surgical outcomes.

The charging power supply for batteries may be variable under many circumstances, e.g., when using solar panels or air-driven generators as the energy source. The mismatch between the voltages of the power supply and the battery may cause significant charging inefficiency. In this paper, we use reconfigurable batteries to solve this voltage mismatch problem. We develop algorithms to dynamically decide the battery connections, to both minimize the voltage mismatch and maintain SOC balancing among difference batteries. We build a hardware prototype to implement and validate our method and use simulation experiments to empirically evaluate its performance.

Using neural networks to handle intractability problems and solve complex computation equations is becoming common practices in academia and industry. It has been shown that, although complicated, these problems can be formulated as a set of equations and the key is to find the zeros of them. Zeroing neural networks (ZNN), as a class of neural networks particularly dedicated to find zeros of equations, have played an indispensable role in the online solution of time-varying problem in the past years and many fruitful research outcomes have been reported in the literatures. The aim of this paper is to provide a comprehensive survey of the research on ZNNs, including continuous-time and discrete-time ZNN models for various problems solving as well as their applications in motion planning and control of redundant manipulators, tracking control of chaotic systems, or even populations control in mathematical biosciences. By considering the fact that real-time performance is highly demanded for time-varying problems in practice, stability and convergence analyses of different continuous-time ZNN models are reviewed in detail in a unified way. For the case of discrete-time problems solving, the procedures on how to discretize a continuous-time ZNN model and the techniques on how to obtain an accuracy solution are summarized. Concluding remarks and future directions of ZNN are pointed out and discussed.

In this paper, backstepping for a class of block strict-feedback nonlinear systems is considered. Since the input function could be zero for each backstepping step, the backstepping technique cannot be applied directly. Based on the assumption that nonlinear systems are polynomials, for each backstepping step, Lypunov function can be constructed in a polynomial form by sum of square (SOS) technique. The virtual control can be obtained by the Sontag feedback formula, which is equivalent to an optimal control-the solution of a Hamilton-Jacobi-Bellman equation. Thus, approximate dynamic programming (ADP) could be used to estimate value functions (Lyapunov functions) instead of SOS. Through backstepping technique, the control Lyapunov function (CLF) of the full system is constructed finally making use of the strict-feedback structure and a stabilizable controller can be obtained through the constructed CLF. The contributions of the proposed method are twofold. On one hand, introducing ADP into backstepping can broaden the application of the backstepping technique. A class of block strict-feedback systems can be dealt by the proposed method and the requirement of nonzero input function for each backstepping step can be relaxed. On the other hand, backstepping with surface dynamic control actually reduces the computation complexity of ADP through constructing one part of the CLF by solving semidefinite programming using SOS. Simulation results verify contributions of the proposed method.

Protein-protein interactions (PPIs) play a central role in many biological processes. Although a large amount of human PPI data has been generated by high-throughput experimental techniques, they are very limited compared to the estimated 130 000 protein interactions in humans. Hence, automatic methods for human PPI-detection are highly desired. This work proposes a novel framework, i.e., Low-rank approximation-kernel Extreme Learning Machine (LELM), for detecting human PPI from a protein's primary sequences automatically. It has three main steps: 1) mapping each protein sequence into a matrix built on all kinds of adjacent amino acids; 2) applying the low-rank approximation model to the obtained matrix to solve its lowest rank representation, which reflects its true subspace structures; and 3) utilizing a powerful kernel extreme learning machine to predict the probability for PPI based on this lowest rank representation. Experimental results on a large-scale human PPI dataset demonstrate that the proposed LELM has significant advantages in accuracy and efficiency over the state-of-art approaches. Hence, this work establishes a new and effective way for the automatic detection of PPI.

We propose a cyber-physical system of unmanned quadcopters to locate air pollution sources in a timely manner. The system consists of a physical part and a cyber part. The physical part includes unmanned quadcopters equipped with multiple sensors. The cyber part carries out control laws. We simplify the control laws by decoupling the quadcopters’ horizontal-plane motion control from vertical motion control. To control the quadcopter’s horizontal-plane motions, we propose a controller that combines pollutant dynamics with quadcopter physics. To control the quadcopter’s vertical motions, we adopt an anti-windup proportional-integral (PI) controller. We further extend the horizontal-plane control laws from a single quadcopter to multiple quadcopters. The multi-quadcopter control laws are distributed and convergent. We implement a prototype quadcopter and carry out experiments to verify the vertical control laws. We also carry out simulations to evaluate the horizontal-plane control laws. With quadcopter parameters set commensurate with our prototype implementation’s, our simulations show that the control laws can drive quadcopters to locate pollution source(s) in a timely way.

Undirected, high-dimensional, and sparse (HiDS) networks are frequently encountered in industrial applications. They contain rich knowledge regarding various useful patterns. Nonnegative latent factor (NLF) models are effective and efficient in extracting useful knowledge from directed networks. However, they cannot describe the symmetry of an undirected network. For addressing this issue, this paper analyzes the extraction process of NLFs on asymmetric and symmetric matrices, respectively, thereby innovatively achieving the symmetric and nonnegative latent factor (SNLF) models for undirected, HiDS networks. The proposed SNLF models are equipped with: 1) high efficiency; 2) nonnegativity; and 3) symmetry. Experimental results on real networks show that the SNLF models are able to: 1) describe the symmetry of the target network rigorously; 2) ensure the nonnegativity of resultant latent factors; and 3) achieve high computational efficiency when addressing data analysis tasks like missing data estimation.

The charging and discharging procedure of a battery is a typical electrochemical process, which can be modeled as a dynamic system. State of charge (SoC) is a commonly used measure to quantify the charge stored in the battery in relation to its full capacity. Recent efforts of optimizing battery performance require more accurate SoC information. The noise in sensor readings makes the estimation even more challenging, especially in battery-operated systems where the supply voltage of the sensor keeps changing. Traditionally used methods of Coulomb counting and extended Kalman filter suffer from the accumulation of noise and common phenomenon of biased noise, respectively. The traditional approach of dealing with ever-increasing demand for accuracy is to develop more complicated and sophisticated solutions, which generally require special models. A key challenge in the adoption of such systems is the inherent requirement of specialized knowledge and hit-and-trial-based tuning. In this paper, we explore a new dimension from the perspective of a self-tuning algorithm, which can provide accurate SoC estimation without error accumulation by creating a negative feedback loop and enhancing its strength to penalize the estimation error. Specifically, we propose a novel method, which uses a battery model and a conservative filter with a strong feedback, which guarantees that worst-case amplification of noise is minimized. We capitalize on the battery model for data fusion of current and voltage signals for SoC estimation. To compute the best parameters, we formulate the linear matrix inequality conditions, which are optimally solved using open-source tools. This approach also features a low computational expense during estimation, which can be used in real-time applications. Thorough mathematical proofs, as well as detailed experimental results, are provided, which highlight the advantages of the proposed method over traditional techniques.

This paper considers cooperative kinematic control of multiple manipulators using distributed recurrent neural networks and provides a tractable way to extend existing results on individual manipulator control using recurrent neural networks to the scenario with the coordination of multiple manipulators. The problem is formulated as a constrained game, where energy consumptions for each manipulator, saturations of control input, and the topological constraints imposed by the communication graph are considered. An implicit form of the Nash equilibrium for the game is obtained by converting the problem into its dual space. Then, a distributed dynamic controller based on recurrent neural networks is devised to drive the system toward the desired Nash equilibrium to seek the optimal solution of the cooperative control. Global stability and solution optimality of the proposed neural networks are proved in the theory. Simulations demonstrate the effectiveness of the proposed method.

Redundancy resolution is a critical problem in the control of robotic manipulators. Recurrent neural networks (RNNs), as inherently parallel processing models for time-sequence processing, are potentially applicable for the motion control of manipulators. However, the development of neural models for high-accuracy and real-time control is a challenging problem. This paper identifies two limitations of the existing RNN solutions for manipulator control, i.e., position error accumulation and the convex restriction on the projection set, and overcomes them by proposing two modified neural network models. Our method allows nonconvex sets for projection operations, and control error does not accumulate over time in the presence of noise. Unlike most works in which RNNs are used to process time sequences, the proposed approach is model-based and training-free, which makes it possible to achieve fast tracking of reference signals with superior robustness and accuracy. Theoretical analysis reveals the global stability of a system under the control of the proposed neural networks. Simulation results confirm the effectiveness of the proposed control method in both the position regulation and tracking control of redundant PUMA 560 manipulators.

In this paper, a unified framework is proposed for designing distributed control laws to achieve the consensus of linear and nonlinear multiagent systems. The consensus problem is formulated as a receding-horizon dynamic optimization problem with an integral-type performance index subject to the dynamics of the considered multiagent system. Different from conventional optimal control that solves Hamilton-Jacobian-Bellman equation numerically in high dimensions, we present a suboptimal solution with analytical expressions by utilizing Taylor expansion for prediction along time and give the corresponding distributed control law in an explicit form. Theoretical analysis shows that the proposed control laws can guarantee exponential and asymptotical stability of the multiagent systems. It is also proved that the proposed suboptimal control laws tend to be optimal with time. Illustrative examples are also presented to validate the efficacy of the proposed distributed control laws and the theoretical results.

This paper presents an overview of recent trends in Battery System Management Architectures (BSMAs). After introducing the main characteristics of large battery packs, the state of the art in BSMAs is discussed. Two emerging concepts are in the focus of this contribution. On the one hand, there is a development from centralized battery management architectures with a single control entity towards decentralized management where the computational resources are distributed across the battery pack and, hence, move closer to the individual battery cells. This enables a more scalable and modular battery system architecture, while, at the same time, posing challenges regarding hardware and management algorithm design. On the other hand, the static setup of the series- and parallel-connected cells forming the battery pack may be developed towards a reconfigurable architecture such that the electrical topology of the pack can be adaptively changed. Such reconfigurability could increase the reliability of battery packs and reduce management efforts such as cell balancing. At the same time, limited energy efficiency of the additional hardware poses a challenge. We give an outlook how these two trends could be combined into distributed reconfigurable BSMAs. This introduces a set of challenges which have to be solved in order to benefit from the increased scalability, reliability and safety such designs could offer.

High-dimensional and sparse (HiDS) matrices are commonly encountered in many big data-related industrial applications like recommender systems. When acquiring useful patterns from them, non-negative matrix factorization (NMF) models have proven to be highly effective because of their fine representativeness of non-negative data. However, current NMF techniques suffer from a) inefficiency in addressing HiDS matrices, and b) constrained training schemes lack of flexibility, extensibility and adaptability. To address these issues, this work proposes to factorize industrial-size sparse matrices via a novel Inherently Non-negative Latent Factor (INLF) model. It connects the output factors and decision variables via a single-element-dependent sigmoid function, thereby innovatively removing the non-negativity constraints from its training process without impacting the solution accuracy. Hence, its training process is unconstrained, highly flexible and compatible with general learning schemes. Experimental results on five HiDS matrices generated by industrial applications indicate that INLF is able to acquire non-negative latent factors from them in a more efficient manner than any existing method does.

With the exploration of the World Wide Web, more and more entities are involved in various online applications, e.g., recommender systems and social network services. In such context, high-dimensional sparse matrices describing the relationships among them are frequently encountered. It is highly important to develop efficient non-negative latent factor (NLF) models for these high-dimensional sparse relationships because of a) their ability to extract useful knowledge from them; b) their fulfillment of the non-negativity constraints for representing most non-negative industrial data; and c) their high computational and storage efficiency on high-dimensional sparse matrices. However, due to the imbalanced distribution of known data in such a matrix, it is necessary to investigate the regularization effect in NLF models. We first review the NLF model briefly. Then we propose to integrate the frequency-weight on each involved entity into its Tikhonov regularization terms, for representing the imbalanced data from a high-dimensional sparse matrix. Experimental results on industrial-size matrices indicate that the proposed scheme is effective in improving the performance of the NLF model in missing-data-estimation.

In this article, we propose formation control of nonholonomic mobile robots avoiding obstacles in a distributed manner for cluttered environments. The introduction of a virtual robot restructures the formation control problem into a tracking control problem between the virtual reference robot and follower robots. A novel obstacle avoidance approach is proposed based upon the scaling of whole (partial) formation corresponding to a centralized (distributed) framework. For the distributed environment with limited communication, our approach utilized proportional-integral average consensus estimators, whereby information from each robot diffuses through the communication network. The theoretical contribution is to determine the time constant involved in the diffusion process, which can affect overall system performance. The asymptotic convergence of follower robots to the position and orientation of the reference robot is ensured using the Lyapunov function. The new technique is tested with complete, limited, and no information availability. Several simulation results are provided that demonstrate the formation control and obstacle avoidance for multirobots using the proposed scheme.

Collaborative filtering (CF)-based recommenders are achieved by matrix factorization (MF) to obtain high prediction accuracy and scalability. Most current MF-based models, however, are static ones that cannot adapt to incremental user feedbacks. This work aims to develop a general, incremental- and-static-combined scheme for MF-based CF to obtain highly accurate and computationally affordable incremental recommenders. With it, a recommender is designed to consist of two components, i.e., a static one built on static rating data, and an incremental one built on a sub-matrix related to rating-variations only. Highly reliable predictions are thus generated by fusing their results. The experiments on large industrial datasets show that desired accuracy and acceptable computational complexity are achieved by the resulting recommender with the proposed scheme.

Networked robotics are a typical cyber–physical system (CPS). This paper presents the cyber physical interaction model to perform formation control and tracking in the presence of other robots and static obstacles. It discusses how such a model can be effectively utilized to deal with kinodynamic and operation range constraints. The cyber system is also responsible for feasible trajectory generation based upon regional path segments and to ensure that all the robots maneuver through obstacles in a safe manner. The introduction of virtual robot restructures the formation control problem into a tracking control problem between virtual reference robot and follower robots. A novel obstacle avoidance approach is proposed based upon the scaling of whole (partial) formation corresponding to centralized (distributed) framework. The involved CPS has network structure preserving properties that are key to effective distributed decision making. The novel formation control, obstacle avoidance, and trajectory tracking approaches facilitate networked robots to be effectively controlled through the cyber system. We also discuss efficient and optimal implementation of the proposed trajectory generator using computer-aided design for CPSs. Evaluation of the proposed approach is provided that demonstrate the formation control, trajectory tracking, and obstacle avoidance for multirobots using the proposed scheme.

The extreme learning machine (ELM) has drawn insensitive research attentions due to its effectiveness in solving many machine learning problems. However, the matrix inversion operation involved in the algorithm is computational prohibitive and limits the wide applications of ELM in many scenarios. To overcome this problem, in this paper, we propose an inverse-free ELM to incrementally increase the number of hidden nodes, and update the connection weights progressively and optimally. Theoretical analysis proves the monotonic decrease of the training error with the proposed updating procedure and also proves the optimality in every updating step. Extensive numerical experiments show the effectiveness and accuracy of the proposed algorithm.

Redundancy resolution is a critical problem in the control of parallel Stewart platform. The redundancy endows us with extra design degree to improve system performance. In this paper, the kinematic control problem of Stewart platforms is formulated to a constrained quadratic programming. The Karush-Kuhn-Tucker conditions of the problem is obtained by considering the problem in its dual space, and then a dynamic neural network is designed to solve the optimization problem recurrently. Theoretical analysis reveals the global convergence of the employed dynamic neural network to the optimal solution in terms of the defined criteria. Simulation results verify the effectiveness in the tracking control of the Stewart platform for dynamic motions.

Matrix inversion often arises in the fields of science and engineering. Many models for matrix inversion usually assume that the solving process is free of noises or that the denoising has been conducted before the computation. However, time is precious for the real-time-varying matrix inversion in practice, and any preprocessing for noise reduction may consume extra time, possibly violating the requirement of real-time computation. Therefore, a new model for time-varying matrix inversion that is able to handle simultaneously the noises is urgently needed. In this paper, an integration-enhanced Zhang neural network (IEZNN) model is first proposed and investigated for real-time-varying matrix inversion. Then, the conventional ZNN model and the gradient neural network model are presented and employed for comparison. In addition, theoretical analyses show that the proposed IEZNN model has the global exponential convergence property. Moreover, in the presence of various kinds of noises, the proposed IEZNN model is proven to have an improved performance. That is, the proposed IEZNN model converges to the theoretical solution of the time-varying matrix inversion problem no matter how large the matrix-form constant noise is, and the residual errors of the proposed IEZNN model can be arbitrarily small for time-varying noises and random noises. Finally, three illustrative simulation examples, including an application to the inverse kinematic motion planning of a robot manipulator, are provided and analyzed to substantiate the efficacy and superiority of the proposed IEZNN model for real-time-varying matrix inversion.

Nonnegative matrix factorization (NMF)-based models possess fine representativeness of a target matrix, which is critically important in collaborative filtering (CF)-based recommender systems. However, current NMF-based CF recommenders suffer from the problem of high computational and storage complexity, as well as slow convergence rate, which prevents them from industrial usage in context of big data. To address these issues, this paper proposes an alternating direction method (ADM)-based nonnegative latent factor (ANLF) model. The main idea is to implement the ADM-based optimization with regard to each single feature, to obtain high convergence rate as well as low complexity. Both computational and storage costs of ANLF are linear with the size of given data in the target matrix, which ensures high efficiency when dealing with extremely sparse matrices usually seen in CF problems. As demonstrated by the experiments on large, real data sets, ANLF also ensures fast convergence and high prediction accuracy, as well as the maintenance of nonnegativity constraints. Moreover, it is simple and easy to implement for real applications of learning systems.

With the emergence of many commercial-off-the-shelf (COTS) and/or open-source hardware and software, we can now build cheap Unmanned Aerial Vehicles (UAVs). This will enable a broad spectrum of potential UAV based mobile applications. In this work, we propose a simple open UAV platform: Ard-μ-copter. Ard-μ-copter is a quadcopter built upon the open source ArduPilot [1] infrastructure library and hardware. Comparing to the many existing commercial quadcopters platforms and open source quadcopter platforms, Ard-μ-copter platform is fully open source, simple (i.e. what the "μ" stands for), and with good documentations.

Recommender systems are an important kind of learning systems, which can be achieved by latent-factor (LF)-based collaborative filtering (CF) with high efficiency and scalability. LF-based CF models rely on an optimization process with respect to some desired latent features; however, most of them employ first-order optimization algorithms, e.g., gradient decent schemes, to conduct their optimization task, thereby failing in discovering patterns reflected by higher order information. This work proposes to build a new LF-based CF model via second-order optimization to achieve higher accuracy. We first investigate a Hessian-free optimization framework, and employ its principle to avoid direct usage of the Hessian matrix by computing its product with an arbitrary vector. We then propose the Hessian-free optimization-based LF model, which is able to extract latent factors from the given incomplete matrices via a second-order optimization process. Compared with LF models based on first-order optimization algorithms, experimental results on two industrial datasets show that the proposed one can offer higher prediction accuracy with reasonable computational efficiency. Hence, it is a promising model for implementing high-performance recommenders.

Protein-protein interactions (PPIs) play crucial roles in the execution of various cellular processes. Almost every cellular process relies on transient or permanent physical bindings of proteins. Unfortunately, the experimental methods for identifying PPIs are both time-consuming and expensive. Therefore, it is important to develop computational approaches for predicting PPIs. In this study, a novel approach is presented to predict PPIs using only the information of protein sequences. This method is developed based on learning algorithm-Extreme Learning Machine (ELM) combined with the concept of Chous Pseudo-Amino Acid Composition (PseAAC) composition. PseAAC is a combination of a set of discrete sequence correlation factors and the 20 components of the conventional amino acid composition, so this method can observe a remarkable improvement in prediction quality. ELM classifier is selected as prediction engine, which is a kind of accurate and fast-learning innovative classification method based on the random generation of the input-to-hidden-units weights followed by the resolution of the linear equations to obtain the hidden-to-output weights. When performed on the PPIs data of Saccharomyces cerevisiae, the proposed method achieved 79.66% prediction accuracy with 79.16% sensitivity at the precision of 79.96%. Extensive experiments are performed to compare our method with state-of-the-art techniques Support Vector Machine (SVM). Achieved results show that the proposed approach is very promising for predicting PPIs, and it can be a helpful supplement for PPIs prediction.

The Sylvester equation is often encountered in mathematics and control theory. For the general time-invariant Sylvester equation problem, which is defined in the domain of complex numbers, the Bartels-Stewart algorithm and its extensions are effective and widely used with an O(n³) time complexity. When applied to solving the time-varying Sylvester equation, the computation burden increases intensively with the decrease of sampling period and cannot satisfy continuous realtime calculation requirements. For the special case of the general Sylvester equation problem defined in the domain of real numbers, gradient-based recurrent neural networks are able to solve the time-varying Sylvester equation in real time, but there always exists an estimation error while a recently proposed recurrent neural network by Zhang et al [this type of neural network is called Zhang neural network (ZNN)] converges to the solution ideally. The advancements in complex-valued neural networks cast light to extend the existing real-valued ZNN for solving the time-varying real-valued Sylvester equation to its counterpart in the domain of complex numbers. In this paper, a complex-valued ZNN for solving the complex-valued Sylvester equation problem is investigated and the global convergence of the neural network is proven with the proposed nonlinear complex-valued activation functions. Moreover, a special type of activation function with a core function, called sign-bi-power function, is proven to enable the ZNN to converge in finite time, which further enhances its advantage in online processing. In this case, the upper bound of the convergence time is also derived analytically. Simulations are performed to evaluate and compare the performance of the neural network with different parameters and activation functions. Both theoretical analysis and numerical simulations validate the effectiveness of the proposed method.

It is meaningful to design a strategy to roughly localize mobile phones without a GPS by exploiting existing conditions and devices especially in environments without GPS availability (e.g., tunnels, subway stations, etc.). The availability of Bluetooth devices for most phones and the existence of a number of GPS equipped phones in a crowd of phone users enable us to design a Bluetooth aided mobile phone localization strategy. With the position of GPS equipped phones as beacons, and with the Bluetooth connection between neighbor phones as proximity constraints, we formulate the problem into an inequality problem defined on the Bluetooth network. A recurrent neural network is developed to solve the problem distributively in real time. The convergence of the neural network and the solution feasibility to the defined problem are both theoretically proven. The hardware implementation architecture of the proposed neural network is also given in this article. As applications, rough localizations of drivers in a tunnel and localization of customers in a supermarket are explored and simulated. Simulations demonstrate the effectiveness of the proposed method.

Data association is a fundamental problem in multisensor fusion, tracking, and localization. The joint compatibility test is commonly regarded as the true solution to the problem. However, traditional joint compatibility tests are computationally expensive, are sensitive to linearization errors, and require the knowledge of the full covariance matrix of state variables. The paper proposes a posterior-based joint compatibility test scheme to conquer the three problems mentioned above. The posterior-based test naturally separates the test of state variables from the test of observations. Therefore, through the introduction of the robot movement and proper approximation, the joint test process is sequentialized to the sum of individual tests; therefore, the test has$O(n)$complexity (compared with$O(n^{2})$for traditional tests), where$n$denotes the total number of related observations. At the same time, the sequentialized test neither requires the knowledge to the full covariance matrix of state variables nor is sensitive to linearization errors caused by poor pose estimates. The paper also shows how to apply the proposed method to various simultaneous localization and mapping (SLAM) algorithms. Theoretical analysis and experiments on both simulated data and popular datasets show the proposed method outperforms some classical algorithms, including sequential compatibility nearest neighbor (SCNN), random sample consensus (RANSAC), and joint compatibility branch and bound (JCBB), on precision, efficiency, and robustness.

The winner-take-all (WTA) competition is widely observed in both inanimate and biological media and society. Many mathematical models are proposed to describe the phenomena discovered in different fields. These models are capable of demonstrating the WTA competition. However, they are often very complicated due to the compromise with experimental realities in the particular fields; it is often difficult to explain the underlying mechanism of such a competition from the perspective of feedback based on those sophisticate models. In this paper, we make steps in that direction and present a simple model, which produces the WTA competition by taking advantage of selective positive-negative feedback through the interaction of neurons via p-norm. Compared to existing models, this model has an explicit explanation of the competition mechanism. The ultimate convergence behavior of this model is proven analytically. The convergence rate is discussed and simulations are conducted in both static and dynamic competition scenarios. Both theoretical and numerical results validate the effectiveness of the dynamic equation in describing the nonlinear phenomena of WTA competition.

This paper presents a discrete-time neural network with a switching structure to solve a general quadratic programming problem in real time. Compared with existing ones for solving quadratic programming problems, the proposed neural network model has a simple architecture and uses a limited number of neurons to solve the problem, irrespective of the dimension of the decision variables or the number of constraints. The global convergence of the model is proven using contraction theory. Simulations are performed to demonstrate the effectiveness of the proposed method.

The fact that most mobile phones are equipped with short-range communication devices, such as Bluetooth, etc., and a portion of mobile phones have GPS embedded enables us to envision to roughly localize GPS-free phones recursively and progressively by exploiting the available information. With the position of GPS equipped phones as beacons, and with the Bluetooth connection between neighbor phones as proximity constraints, we formulate the problem as an inequality problem defined on the Bluetooth network. A recurrent neural network is developed to solve the problem distributively in real time. The convergence of the neural network and the solution feasibility to the defined problem are both theoretically proven. Two applications examples are considered and simulated. Simulations demonstrate the effectiveness of the proposed method.