The negative impact of noises is inevitable in the learning and control processes of redundant manipulators, which may degrade the performance. To mitigate challenges posed by noises, this paper proposes an integral-enhanced hierarchical control and kinematics learning (IHCKL) algorithm. This algorithm comprises two components: an integral-enhanced kinematics learning (IKL) model that incorporates an integral feedback term to reduce the influence of noises during kinematics learning, and an integral-enhanced hierarchical control (IHC) model that combines neural dynamics with hierarchical control to improve the control accuracy and noise resistance in noisy environments. The proposed algorithm accurately learns the kinematics in noisy environments, while achieving multi-task execution with priorities. Different from existing state-of-the-art algorithms that are difficult to achieve multi-task executions under unknown kinematics and noisy conditions, the IHCKL algorithm integrates both kinematics learning and hierarchical control with noise resistance, exhibiting enhanced robustness and accuracy. Theoretical analyses demonstrate that the IHCKL algorithm guarantees the error convergence and noise resistance under varying noise conditions. Simulations and experiments confirm that the IHCKL algorithm offers improvements in the multi-task execution, kinematics learning, and noise resistance in noisy environments.

In pursuit of safe and efficient distributed cooperative control of multi-robot systems (MRSs), a logic-adaptive discrete neural dynamics (LADND)-based minimum infinity norm (MIN) strategy is introduced in this paper. The MIN strategy is employed to address critical safety concerns caused by excessively high velocity in the individual joint. To further improve the adaptivity of the neural dynamics solver, a fuzzy system is integrated to enable adaptive parameter adjustment based on the real-time behavior of MRSs. Specifically, the cooperative control problem is formulated as a linear program incorporating the MIN along with constraints associated with distributed network topology and orientation maintenance, thereby enhancing the safety and effectiveness of MRSs. To efficiently solve the proposed linear program, an LADND solver is developed, which adaptively adjusts its parameter in real time according to the trajectory tracking error and its derivative. Furthermore, theoretical analyses confirm the convergence and robustness of the proposed LADND solver. Simulative and experimental results validate the effectiveness of the proposed LADND-based MIN strategy in cooperative trajectory tracking tasks.

The accuracy of the kinematic information of a redundant robot directly influences the control performance of its end-effector. However, in practical applications, kinematic parameters may change. To address this challenge, this paper proposes a robust learning and fuzzy control (RLFC) model that possesses kinematic learning and simultaneous control capabilities, enabling the estimation of unknown kinematic parameters and achieving adaptive control for redundant robots. Specifically, the RLFC model comprises two components: an integral-enhanced recurrent neural dynamics (IERND) and a fuzzy-enhanced recurrent neural dynamics (FERND). The IERND is designed to enhance the noise tolerance in kinematic parameter learning. Based on the learned kinematic parameters, the FERND, which incorporates a fuzzy logic system for dynamically adjusting convergence parameters, achieves effective position and orientation tracking of the end-effector in the redundant robot. Theoretical analyses are provided to demonstrate the convergence of the RLFC model. Simulations and experiments validate the effectiveness of the RLFC model in parameter learning, noise tolerance, and kinematic control. The accompanying video can be accessed athttps://youtu.be/DS6k7Cu19sU.

The image-based visual servoing (IBVS) describes a vision-based robot control. It controls the motion of the robot through the feedback from the vision sensors assembled at the end-effector of the robot, so that the feature points of the object are imaged at specific pixel points. Considering camera assembly error, end-effector assembly error, and vibration-induced noise during robot operation may affect vision servo control. We propose a model-free IBVS control scheme, which introduces a data-driven learning strategy to achieve the learning of the robot and camera Jacobian matrices and precise control of robots with unknown structures. Meanwhile, a neural dynamics-based noise-tolerant solver is proposed to solve the problems caused by noises during the robot's operation on visual servocontrol, and related theoretical analyses are carried out. Finally, the effectiveness of the proposed scheme is verified by simulations and experiments. Its superiority is demonstrated by comparison with other IBVS schemes.

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

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.

With the expansion of applications for robots, merely considering position control is no longer sufficient to meet practical requirements. Hence, it becomes crucial to develop a control method that synchronizes position and orientation for redundant manipulators. Over time, motion control schemes based on the quadratic programming (QP) have inevitably led to excessive joint movements. In this article, position and orientation control is modeled as a sparse optimization problem from a sparsity perspective. Meanwhile, a collective fuzzy gradient descent (CFGD) solver is designed to address the challenge of sparse position and orientation control for redundant manipulators. Theoretical analyses, simulations, and experiments demonstrate the effectiveness and superiority of the proposed method. The method is expected to provide a precise and efficient control strategy for redundant manipulators in complex tasks by reducing unnecessary joint movements and enhancing the overall performance.

The prosthetic finger demands an impedance controller with outstanding control performance to satisfy the tracking tasks’ requirements in complicated surroundings. For this purpose, suppressing the disturbances caused by the internal and external environments is the main concern for enhancing the universality of forming the impedance controller. This article presents a noise-tolerant zeroing neural network (NTZNN)-based impedance learning controller, which aims to strengthen the anti-noise performance and calculation accuracy of the prosthesis finger controller under noise pollution. Besides, the proposed impedance learning controller consists of an NTZNN model for calculating the actual trajectories in noisy circumstances, an adaptive learning law for improving the convergence property, and an interactive control term to enhance the transient performance. Furthermore, the stability and convergence performances are verified with a candidate Lyapunov function. In addition, the simulative and experimental results showcase the cutting-edge noise-tolerant, high calculation accuracy, and excellent long-term control property of the proposed controller under the noise pollution, which achieves the accuracy at the order of 10-5rad for position level and at the order of 10-3rad/s for velocity level. Eventually, in the noise environment, the accuracy of root-mean-square error (RMSE) andL2-norm in position and velocity levels for utilizing the NTZNN-based learning impedance learning controller achieves 0.0056 rad, 0.0564 rad/s, 0.2217 rad, and 2.5216 rad/s, respectively.

The insufficient generalization of adaptive moment estimation (Adam) has hindered its broader application. Recent studies have shown that flat minima in loss landscapes are highly associated with improved generalization. Inspired by the filtering effect of integration operations on high-frequency signals, we propose multiple integral Adam (MIAdam), a novel optimizer that integrates a multiple integral term into Adam. This multiple integral term effectively filters out sharp minima encountered during optimization, guiding the optimizer towards flatter regions and thereby enhancing generalization capability. We provide a theoretical explanation for the improvement in generalization through the diffusion theory framework and analyze the impact of the multiple integral term on the optimizer's convergence. Experimental results demonstrate that MIAdam not only enhances generalization and robustness against label noise but also maintains the rapid convergence characteristic of Adam, outperforming Adam and its variants in state-of-the-art benchmarks.

We introduce Dynamic Retrieval-Augmented Expert Networks (DRAE), a groundbreaking architecture that addresses the challenges of lifelong learning, catastrophic forgetting, and task adaptation by combining the dynamic routing capabilities of Mixture-of-Experts (MoE); leveraging the knowledge-enhancement power of Retrieval-Augmented Generation (RAG); incorporating a novel hierarchical reinforcement learning (RL) framework; and coordinating through ReflexNet-SchemaPlanner-HyperOptima (RSHO).DRAE dynamically routes expert models via a sparse MoE gating mechanism, enabling efficient resource allocation while leveraging external knowledge through parametric retrieval (P-RAG) to augment the learning process. We propose a new RL framework with ReflexNet for low-level task execution, SchemaPlanner for symbolic reasoning, and HyperOptima for long-term context modeling, ensuring continuous adaptation and memory retention. Experimental results show that DRAE significantly outperforms baseline approaches in long-term task retention and knowledge reuse, achieving an average task success rate of 82.5% across a set of dynamic robotic manipulation tasks, compared to 74.2% for traditional MoE models. Furthermore, DRAE maintains an extremely low forgetting rate, outperforming state-of-the-art methods in catastrophic forgetting mitigation. These results demonstrate the effectiveness of our approach in enabling flexible, scalable, and efficient lifelong learning for robotics.

Redundant manipulators are explored and utilized across a wide range of domains. Investigating effective trajectory tracking of redundant manipulators is pivotal for their practical applications. This paper constructs a model predictive control of position and orientation (MPCPO) scheme, which controls the position and orientation of the end-effector simultaneously while minimizing norms of the tracking error, joint velocity, and joint acceleration. Additionally, the MPCPO scheme addresses different levels of physical constraints while preserving the feasible region of decision variables. Moreover, an integration enhanced gradient-based recurrent neural network (IEGRNN) model is designed to solve the MPCPO scheme in noisy environments. Theoretical analyses demonstrate the convergence and robustness of the IEGRNN model. The effectiveness, accuracy, flexibility, and noise tolerance of the MPCPO scheme solved by the IEGRNN model are illustrated through simulations and experiments.

This paper develops a robust neural dynamics method for the distributed time-varying optimization problem with time-varying constraints. First, instead of assuming the objective functions and constraints to be static like a majority of the existing research, we consider distributed optimization from a time-varying perspective. Second, by employing the Lagrangian framework, we transform constraints and the concerned objective function that takes the summation of all local functions into a dynamic error function. Third, the robust neural dynamics method is capable of utilizing the time-varying information while solving constrained distributed optimization problems, and meanwhile handling disturbances purely based on its structure, thus lightening the communication and privacy burden. We provide proof of the convergence of the proposed method with activation functions under different disturbances. The comparative results on both illustrative examples and applications validate the efficiency. Note to Practitioners—The highlight of this paper lies in the co-design of time-varying computation and noise-tolerant ability for the proposed distributed optimization method, which could be beneficial to real-world scenarios. Different from existing methods focusing on static objective functions and constraints, we investigate how to find the trajectory formed by the time-varying optimal solutions even with the perturbation of noises. Besides, saturated or even nonconvex activation functions mimicking the synapses of the brain are incorporated into the proposed optimization methods to help accelerate the convergence and counteract the instability induced by noises, without heavily adding to the system’s burden. We also provide theoretical proof to not only guarantee its capability but also guide how to set the involved parameters. This paper proposes a noise-tolerant method for accurately solving distributed time-varying optimization problems and validates its performance on a multi-robot system, which could be suitable for plenty of real-world distributed optimization problems.

Model uncertainty, exogenous disturbance, and time-dependent computing are significant issues in constrained nonlinear optimization and related practical problems. This paper highlights two limitations of current methods for time-dependent nonlinear optimization, i.e., disturbance handling and restrictions on the objective function and constraints. First, a novel robust neural differential (RND) solution is proposed for solving equality-and inequality-constrained time-dependent nonlinear optimization (EIC-TDNO) problems involving the suppression of nonspecific disturbances. Second, the dynamic vector-valued error equation equivalent to the EIC-TDNO method is derived. Theoretical proofs ensure that the proposed RND solution converges to zero at an exponential rate, eliminates polynomial noise, and effectively reduces the time-varying disturbance. Finally, through simulation and applications to 2-D filter design and robot motion planning, the RND solution is verified to exhibit rapid convergence, high precision, strong robustness, and versatility in comparison with the existing models.Note to Practitioners—The primary impetus behind this paper is the disadvantage of current optimization methods when solving real-world application problems. First, most of the existing optimization methods consider time-invariant objective functions and constraints. Additionally, the latest time-varying optimization methods limit their application to unconstrained or equality-constrained situations and are capable of handling disturbances of only specific types and within specific numerical ranges. Note that the interplay between modules may be introduced if other components, such as filters, are used to handle disturbances. Therefore, in this paper, an optimization approach is intrinsically designed for time-dependent optimization with its own ability to stabilize the whole system while being perturbed by various types of time-varying disturbances, which could reduce large lagged errors and system complexity. Theoretical analysis provides performance guarantees as well as guidance on parameter tuning to ensure solution accuracy and robustness. This paper primarily investigates and verifies how the proposed robust neural differential solution solves constrained time-dependent nonlinear optimization problems with the presence of different time-varying disturbances; this approach can be applied to numerous practical engineering problems, such as robot control, energy dispatch, and image processing.

The joint drift problem may result in the omnidirectional mobile manipulator (OMM) failing to perform its tasks or even causing damage in practical applications. However, the coefficients for eliminating joint drift are coupled with the equation constraints in Cartesian space under the existing scheme, which theoretically results in a paradox between zero joint drift and zero positional error in Cartesian space. To address the joint drift, a joint drift-free repetitive motion programme with position error feedback (JDF-RMPPEF) is presented and analyzed. The JDF-RMPPEF scheme decouples the joint error and position error, which enables the OMM to accurately perform the trajectory tracking and repetitive motion tasks. In addition, to suppress the disturbances and solve the JDF-RMPPEF problem accurately, an allowed nonconvex noise-resistant neural network (ANNRNN) model is proposed, which allows for a nonconvex activation function with noise suppression properties. Theoretical analysis demonstrates that the ANNRNN model exhibits global convergence and strong robustness in the presence of interference. Through examples and comparisons, the effectiveness and superiority of the JDF-RMPPEF scheme synthesized by the ANNRNN model are validated.

Redundant robots may undergo structural changes due to factors such as modifications, which pose challenges to their precise control and obstacle avoidance. To resolve this issue, this article proposes a data-driven obstacle avoidance (DDOA) scheme for redundant robots with unknown structures, which integrates obstacle avoidance control and structure learning. To ensure collision-free operations, an obstacle avoidance method for redundant robots is devised to maintain a safe distance from obstacles. Simultaneously, a data-driven learning equation is developed to estimate two Jacobian matrices of robots for obstacle avoidance and motion planning. A recurrent neural network (RNN) is then established to find the optimal solution to the DDOA scheme with theoretical analyses. Furthermore, we demonstrate the learning and control capabilities of the proposed RNN by providing illustrative simulations and experiments on a Franka Emika Panda robot. The results exhibit significant collision avoidance and learning performance of the proposed method with tiny errors.

There may be obstacles in the workspace of redundant manipulators, which generally pose a hidden danger to the safety execution. How to avoid obstacles reasonably is one of the goals of this article. To this end, a modified obstacle avoidance (MOA) method is proposed, which creates a larger feasible space for the escape velocity of redundant manipulators in a more concise form than the existing methods. Equipped with the MOA method, a trajectory-tracking and modified-obstacle-avoidance (TT-MOA) scheme for redundant manipulators is constructed. On the other hand, ubiquitous noises also influence the operation of redundant manipulators. Therefore, a noise-tolerant gradient neural dynamics (NTGND) model is proposed to tolerate noises when solving the TT-MOA scheme. Rigorous theoretical analyses prove the convergence and robustness of the NTGND model, and computer simulations and physical experiments demonstrate the practicability and superiority of the proposed methods compared with the existing techniques.

Increasing complex driving scenarios inevitably expose autonomous vehicles to intricate nonconvex challenges, which are usually simplified or even ignored by current research, leading to accuracy compromises. In this regard, this paper newly constructs a collaborative physics-informed neural dynamics (CPIND) approach to simultaneously tackle the trajectory tracking and safety-critical control problems in autonomous vehicles. Specifically, the proposed CPIND approach consists of a linear quadratic regulator to provide global control inputs for the trajectory tracking task and a safety-critical optimization control scheme with newly established control barrier functions. The constructed optimization control scheme is essentially nonconvex with respect to decision variables to update the local control inputs for the obstacle avoidance task with the highest priority. A theorem is provided to substantiate the convergence of the proposed CPIND approach. At last, a comparative example, an example on the CarSim-Simulink co-simulation platform, and an experiment on the AgileX autonomous driving platform are conducted to verify the effectiveness and preponderance of the proposed CPIND approach. Overall, the proposed CPIND approach enables autonomous vehicles to follow a collision-free trajectory effectively and accurately, offering a promising solution for enhancing the safety and reliability of autonomous vehicles.

Theoretical and empirical evidence highlights a positive correlation between the flatness of loss landscapes around minima and generalization. However, most current approaches that seek to find flat minima either incur high computational costs or struggle to balance generalization, training stability, and convergence. This work proposes reshaping the loss landscape to induce the optimizer toward flat regions, an approach that has negligible computational costs and does not compromise training stability, convergence, or efficiency. We focus on nonlinear, loss-dependent reshaping functions underpinned by theoretical insights to reshape the loss landscape. To design these functions, we first identify where and how these functions should be applied. With the aid of recently developed tools in stochastic optimization, theoretical analysis shows that steepening the low-loss landscape improves the rate of sharp minimum escape while flattening the high- and ultralow-loss landscapes enhances training stability and optimization performance, respectively. Simulations and experiments reveal that the subtly designed reshaping functions not only induce optimizers to find flat minima and improve generalization performance but also stabilize training, promote optimization, and keep efficiency. Our approach is evaluated on image classification, adversarial robustness, and natural language processing (NLP) tasks and achieves significant improvement in generalization performance with negligible computational cost. We believe that the new perspective introduced in this work will broadly impact the field of deep neural network training. The code is available at https://github.com/LongJin-lab/LLR.

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.

As a competitive strategy, thek-winners-take-all (kWTA) operation is capable of selectingkwinners fromnelements (such as neurons or input signals) to be activated, while the remaining elements are suppressed as losers to be inactivated. In a dynamic task allocation on a multirobot system, the relevant information can be subtly estimated through communications among robots. However, the interference in the communication process and the time-delayed problem caused by data processing are unavoidable. Therefore, a time-delayedkWTA network considering communication interference (TDCI-kWTA) is established in this article. Different from existingkWTA networks, the TDCI-kWTA network allows robots both directed and undirected communication while eliminating communication interference. Besides, the time-delayed problem is taken into account by the TDCI-kWTA network, and the maximum delay allowed is derived from theorems. By modeling thekWTA operation as a nonlinear equation, lagging errors that exist in the solving process are eliminated due to the consideration of dynamic parameters. Theoretical analyses are given to demonstrate the convergence and robustness of the TDCI-kWTA network. Besides, simulations and experiments are further given to validate the effectiveness of the proposed network.

Since distributed control strategies can effectively reduce the operating load of the central processor, they have become a prominent research direction in the field of controlling multiple manipulators. However, existing distributed approaches predominantly rely on fixed topologies, overlooking the dynamic nature of task requirements. To address this limitation, this article proposes a distributed collaboration scheme that incorporates switching topologies. The distributed control problem is further formulated as a game-theoretic framework involving multiple manipulators. A dynamic neural network solver is then developed to approximate the optimal Nash equilibrium strategy, with its convergence and stability proven through theoretical analysis. The effectiveness of the proposed scheme and solver is validated through a series of physical experiments.

Remote center of motion (RCM) describes a robot with a rod-like end-effector operating through a hole in the interface separating the internal space from the external space. Considering that the control of RCM may be influenced by perturbations (noises) and that the end-effector is frequently replaced to complete different tasks, the structural information related to the robot manipulator and its rod-like end-effector may contain errors. This paper proposes an acceleration-level remote center of cyclic motion (ARC2M) control scheme, which takes into account the cyclic motion index and the physical limitations of robot manipulators to achieve repetitive motion planning and RCM control at the acceleration level. Additionally, a parameter calculation method is proposed to compute unknown parameters of the end-effector under the influence of noise. Kalman filter and a neural dynamics-based method are employed to address noises effects, and related theoretical analyses are given. To validate the proposed ARC2M scheme, simulations and physical experiments are carried out. The source code is available at https://github.com/LongJin-lab/ARCM.

This paper introduces a neural-dynamics-based active steering control (NDASC) scheme developed under artificial systems, computational experiments, and parallel execution (ACP) framework, aimed at enhancing the stability and reliability of autonomous vehicles in noisy environments. Based on the Taylor expansion theorem, noises can be represented in the form of polynomials for the desired accuracy, and therefore polynomial noises can be viewed as a more generalized representation of noises. Then, the proposed NDASC scheme includes a model predictive active steering control (MPASC) strategy solved by a polynomial noise resilience neural dynamics (PNRND) model. Computational experiments parallelly implemented upon the CarSim-Simulink platform substantiate the effectiveness and robustness of the proposed NDASC scheme, providing significant theoretical and practical insights for control strategies of autonomous vehicles under various noisy environments.

Sea ice plays a pivotal role in ocean-related research, necessitating the development of highly accurate and robust techniques for its extraction from diverse satellite remote sensing imagery. However, conventional learning methods face limitations due to the soaring cost and time associated with manually collecting sufficient sea ice data for model training. This paper introduces an innovative approach where Neural Dynamics (ND) algorithms are seamlessly integrated with a recurrent neural network, resulting in a Transfer-Learning-Like Neural Dynamics (TLLND) algorithm specifically tailored for sea ice extraction. Firstly, given the susceptibility of the image extraction process to noise in practical scenarios, an ND algorithm with noise tolerance and high extraction accuracy is proposed to address this challenge. Secondly, The internal coefficients of the ND algorithm are determined using a parametric method. Subsequently, the ND algorithm is formulated as a decoupled dynamical system. This enables the coefficients trained on a linear equation problem dataset to be directly generalized to solve the sea ice extraction challenges. Theoretical analysis ensures that the effectiveness of the proposed TLLND algorithm remains unaffected by the specific characteristics of various dataset. To validate its efficacy, robustness, and generalization performance, several comparative experiments are conducted using diverse Arctic sea ice satellite imagery with varying levels of noise. The outcomes of these experiments affirm the competence of the proposed TLLND algorithm in addressing the complexities associated with sea ice extraction.

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.

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.

Redundant manipulators, as mechanical equipments imitating human arms, have been applied to various areas in recent years from the perspective of control. Different from pure control technologies, the motion capability of a human arm is achieved by a complex and efficient neural system, with the cerebellum playing a pivotal role. Motivated by this fact, we design a cerebellum model based on an echo state network (ESN) for the learning and control of redundant manipulators. In addition, to simulate the skillful control ability of the cerebellum over movements of human arms, the proposed model is constructed at the joint velocity level. Furthermore, to improve the accuracy and applicability, we propose an ESN-based Kalman-filter-incorporated and cerebellum-inspired (KFICI) scheme for the learning and control of redundant manipulators with Kalman filter incorporated. The proposed scheme enables a redundant manipulator to track the desired trajectory at the velocity level and tolerate noises. Finally, simulations and experiments based on a physical redundant manipulator are performed to verify the effectiveness of the proposed control scheme.

The tracking control of redundant manipulators plays a crucial role in robotics research and generally requires accurate knowledge of models of redundant manipulators. When the model information of a redundant manipulator is unknown, the trajectory-tracking control with model-based methods may fail to complete a given task. To this end, this article proposes a data-driven neural dynamics-based model predictive control (NDMPC) algorithm, which consists of a model predictive control (MPC) scheme, a neural dynamics (ND) solver, and a discrete-time Jacobian matrix (DTJM) updating law. With the help of the DTJM updating law, the future output of the model-unknown redundant manipulator is predicted, and the MPC scheme for trajectory tracking is constructed. The ND solver is designed to solve the MPC scheme to generate control input driving the redundant manipulator. The convergence of the proposed data-driven NDMPC algorithm is proven via theoretical analyses, and its feasibility and superiority are demonstrated via simulations and experiments on a redundant manipulator. Under the drive of the proposed algorithm, the redundant manipulator successfully carries out the trajectory-tracking task without the need for its kinematics model.

This study focuses on exploring the solution to coordination in multirobot systems faced with competitive states, where the competition behavior can be described as a$k$-winner-take-all ($k$WTA) operation. To address the$k$WTA problem, a fuzzy$k$WTA (F-$k$WTA) network is proposed, which incorporates a fuzzy mechanism into the network that adapts the convergence rate of the F-$k$WTA network based on the error, leading to exceptional convergence behavior. In addition, a set of activation functions are provided to further enhance the capabilities of the F-$k$WTA network. In addition, the proposed network demonstrates remarkable convergence performance, as illustrated through both theorems and simulations. Finally, the practical application value of the F-$k$WTA network is demonstrated on a multirobot system.

In real-world robotics applications, kinematic parameters of redundant manipulators may need to be changed, thus creating difficulties in achieving precise control. To address this issue, this article proposes a fuzzy neural controller to learn kinematic parameters online and synchronously achieve the model-free control of redundant manipulators. Specifically, this controller consists of a gradient-based fuzzy (GBF) subsystem and a neural dynamics (ND) subsystem. On the one hand, the GBF subsystem is designed to achieve online learning of kinematic parameters, considering additional noise and a fuzzy parameter. Notably, the fuzzy parameter can drive the GBF subsystem to automatically terminate the learning process and convert the acquired information into usable structural knowledge once the kinematic parameters are precisely learned. On the other hand, based on the learned kinematic parameters, the ND subsystem is employed to solve a quadratic programming scheme for the kinematic control of manipulators. Such a scheme implements functions of orientation maintenance, trajectory tracking, and joint constraints in a model-free manner. Theoretical analyses confirm the effectiveness of the proposed controller's learning and control abilities. Finally, simulations, experiments, and comparisons demonstrate the feasibility and superiority of the fuzzy neural controller in controlling manipulators with unknown kinematic parameters.

A noise-tolerant$k$-winners-take-all ($k$-WTA) model injecting a summation item of error is constructed and applied to execute a$k$-WTA operation in this article. Then, theoretical analyses and proofs on the convergence of the noise-tolerant$k$-WTA model with different noise disturbances are carried out. In addition, numerical experiments synthesized by the noise-tolerant$k$-WTA model and other existing$k$-WTA models are provided to conduct comparisons to demonstrate the superior robustness and stability of the proposed model. Finally, tracking task experiments of a multirobot system with noise considered are operated to further illustrate the advantages of the proposed$k$-WTA model over the existing ones.

Time-variant quadratic programming (TVQP) has widespread applications and often involves equality, inequality, and bound constraints. An effective solver for TVQP problems is zeroing neural network (ZNN), and nonlinear complementary problem function-based ZNN (NCP-ZNN) is a state-of-the-art ZNN solver that can handle equality and inequality constraints. However, when dealing with bound constraints, NCP-ZNN expands the dimension of the matrix and then introduces twice the number of Lagrange multipliers. To overcome this deficiency, this article develops a modified NCP-ZNN solver by introducing the first-order optimality conditions. Numerical validation is performed to substantiate the superior solving efficiency of the modified NCP-ZNN solver, which can achieve the same or lower order of residual errors compared with the original NCP-ZNN. Then, the modified NCP-ZNN solver is applied to the pose control of a redundant manipulator, demonstrating its superiority in solving practical problems.

Manipulability optimization plays a crucial role in the kinematic control of redundant manipulators, as it reduces their risks of entering a singular state. However, manipulability is a nonlinear and nonconvex function with respect to joint angles. The existing kinematic schemes either do not consider the manipulability optimization or require transforming the nonconvex problem into a convex one, which may affect achieving the optimal value of manipulability. Furthermore, obstacle avoidance is rarely considered in the existing manipulability optimization methods. To address these limitations, this article proposes a manipulability optimization with obstacle avoidance constraints (MOOAC) scheme. Subsequently, a metaheuristic-based recurrent neural network (MRNN) model is constructed, which can directly handle a nonlinear and nonconvex problem with constraints and ensure achieving the global optimal with probability 1. In addition, the proposed MOOAC scheme is solved by the MRNN model at the joint angle level, which can handle the limits of joint angle and joint velocity without reducing the feasible region of decision variables. Computer simulations and physical experiments are provided to demonstrate the accuracy and superiority of the proposed scheme.

Motion-force control is one of the critical technologies for a manipulator to accomplish some tasks, such as polishing and burring. Some optimization-based and kinematics-related methods for motion-force control of redundant manipulators have good performance but exist some shortcomings. First, these methods utilize transformation techniques to deal with different levels of joint limits, such as joint angle, velocity, or acceleration limits, which reduces the feasible region of decision variables. Second, these methods require the direction for the end-effector of the manipulator to be perpendicular to the contact surface and thus are not applicable to some scenarios. In response to these shortcomings, this article proposes a noise-resilient neural-dynamics-based planning (NRNDP) scheme, which includes a model predictive motion-force control (MPMFC) strategy and a discrete-time noise-resilient neural dynamics solver. The proposed NRNDP scheme directly handles three levels of joint limits without reducing the feasible region. Meanwhile, it can achieve the desired force with the end-effector of the manipulator being at any suitable angle to the work surface. Moreover, it can reduce the impact of noise and thus improve the control accuracy and operational stability of redundant manipulators. Besides, the MPMFC strategy is improved to achieve motion-force control of pose-varying workpieces. Simulations, comparisons, and experiments demonstrate the effectiveness and superiority of the proposed scheme.

In consideration of the limitation of the communication and the possibility that redundant robots might deliver information at different power levels, cases under weight-unbalanced directed graphs from the network topology perspective are in larger accordance with those in multiple redundant robot systems. By moving forward along this direction, a distributed controller is proposed in this article to handle circumstances of collaborative control of multiple redundant robots under weight-unbalanced directed graphs. This kind of control problem is modeled into generalized quadratic programming (QP) problems with equality and inequality constraints. Then, the above QP problems are solved by a proposed neural-dynamics-based method, whose stability and convergence are theoretically proved subsequently. Besides, several experimental examples are conducted, and related comparisons are provided to demonstrate the feasibility of the proposed controller.

Underwater acoustic localization is a crucial technique for most underwater applications. However, in highly dynamic marine environments, underwater acoustic localization faces many challenges, such as the stratification effect, the clock asynchronization, the node drift, and environmental noises. Concerning above problems, we propose a new underwater localization algorithm for mobile underwater acoustic sensor networks (UASNs). At first, the measurement biases are modeled as the combination of constant biases and random biases according to the physical mechanism of their generation and distribution characteristics in measured data. Then, an error-summation-incorporated Newton iteration (ESINI) algorithm is designed to compute the localization result along the direction of constant biases decrease, and a Taylor expansion is used to approach the actual localization result along the direction of random biases decrease. Subsequently, a simplified Kalman filter (SKF) fuses the two localization results and enhances the localization accuracy. In this way, the proposed algorithm effectively increases the accuracy of localization results without adding extra measurement. Finally, theoretical analyses, simulations, and lake experiments are provided to verify the proposed algorithm's effectiveness and noise resistance performance.

Enlightened by competitive and collaborative coordination behaviors widely observed in natural swarm systems, this work emphasizes these coordinating modes in multirobot systems and optimizes system stability along with resource utilization. Then, schemes are constructed to describe and model these two modes, where a$k$-winner-take-all concept is introduced as the driving principle of multirobot competition. In addition, a distributed coordination approach is established to effectively handle the above schemes aided with optimality theory, which is developed by a fusion of a recurrent neural dynamics solver and a distributed solver. The former is a single-layer neural dynamics model with a simple structure, and the latter transforms the involved global information to a distributed type via consensus. Both of them are carried out in the discrete-time domain to fit the actual application. Finally, the convergence and stability of the proposed coordination approach are proved via theoretical analysis and further demonstrated through simulations and experiments.

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

For nonconvex optimization problems, a routine is to assume that there is no perturbation when executing the solution task. Nevertheless, dealing with the perturbation in advance may increase the burden on the system and take up extra time. To remedy this weakness, we propose a robust coevolutionary neural-based optimization algorithm with inherent robustness based on the hybridization between the particle swarm optimization and a class of robust neural dynamics (RND). In this framework, every neural agent guided by the RND supersedes the place of the particle, mutually searches for the optimal solution, and stabilizes itself from different perturbations. The theoretical analysis ensures that the proposed algorithm is globally convergent with probability one. Besides, the effectiveness and robustness of the proposed approach are illustrated by illustrative examples compared with the existing methods. We further apply this proposed algorithm to the source localization and manipulability optimization of the redundant manipulator, simultaneously disposing of perturbation from the internal and exogenous system with satisfactory performance.

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 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.

In industrial applications where computational resources are finite and data noises are prevalent, the representation power of deep neural networks (DNNs) is crucial. Traditional network structures often require a significant increase in the parameter amount to enhance the representation power, making it difficult to achieve effective representation under parameter amount constraints. In order to alleviate this problem, this work leverages the ordinary differential equation (ODE) interpretation of deep residual networks, elucidating the relationship between the fine-grained connectivity modes of blocks in DNNs and the representation power. We build a bridge from the order of numerical methods and the order of ODEs to the representation power of DNNs. Besides, we show that higher-order ODEs can be approximated by k-step methods incorporating trainable coefficients. Empirically, we validate our theoretical insights by demonstrating the superior representation power of our proposed network structures through enhanced performance on industrial tasks, such as surface defect detection, critical temperature prediction of superconductors, and image classification under noises. The proposed method provides a new approach to the design of network structures for robust and accurate DNNs, enhancing the representation power with a negligible number of additional parameters. The code is publicly available athttps://github.com/LongJin-lab/Order-and-Representation-Power.

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.

rgb0.00,0.00,0.00 In recent years, the discrete-time recurrent neural network (DTRNN) model has received growing attention. This fully benefits from the recurrent neural networks (RNNs) that not only have plenty of advantages for solving computing problems in the real-time tracking control but also have the remarkable potential of parallel processing and nonlinear processing. However, there is a general lack of research on the applicability of DTRNN model to handle parallel robot. In addition, the precision is always an important point in real-time tracking control, and most of existing studies generally lack the elaborate researches on the precision analyses. In this article, the corresponding DTRNN model (i.e., general five-instant discretization (FID) formula DTRNN model) with parameter selection method is established. As one of the important theoretical contributions, the dominant term of truncation error of discretization formula and the conditions of maintaining precision of corresponding DTRNN model are proved from the mathematical view strictly. Besides, the influence of the selected parameter for the precision of such a DTRNN model is also analyzed. Finally, the above theoretical analyses are verified in the tracking control experiments of the Stewart platform, which is a widely used and representative parallel robot.

For the image-based visual servoing (IBVS) of a manipulator with an unknown structure, the unavailability of the robot Jacobian matrix impedes the accurate control of the manipulator. To solve this issue, this article proposes a data-driven IBVS (DDIBVS) scheme combining model-free learning, matrix inversion estimation, feature tracking, and joint limits. On the one hand, a data-driven learning algorithm is designed, which enables an estimated end-effector velocity to approach the real one and outputs an estimated robot Jacobian matrix. On the other hand, we consider the desired velocity information of the visual feature to improve the tracking accuracy and design an auxiliary parameter to estimate the inversion operation and address the singularity problem. On this basis, a neural dynamic controller (NDC) is developed, which possesses learning, estimation, and control capabilities. Subsequently, the effectiveness, practicability, and superiority of the proposed method are evaluated through simulations and experiments conducted on a 7-degree-of-freedom (DOF) manipulator for visual servoing tasks.

In recent years, quadratic optimizations have become increasingly popular in engineering. However, conventional methods that investigate this problem from the perspective of a canonical form with linear constraints are not effective in dealing with the significant challenges posed by quadratic constraints in practice. This paper proposes a solution framework for the quadratic optimization with quadratic constraints (QOQC) based on innovative artificial societies, computational experiments, and parallel execution (ACP) framework. Then, a gradient projection differential neural solution (GPDNS) is proposed to address this. To illustrate the effectiveness of the GPDNS model in solving the QOQC system, numerical simulations are provided. Overall, this paper presents the potential of innovative approaches like the ACP framework to enhance our capabilities in addressing challenging optimization systems.

Motion-force control of redundant manipulators is universally regarded as a pivotal issue in industrial manufacturing, especially for the processing of precision instruments. This paper proposes a kinematics-based motion-force control (KBMFC) scheme for redundant manipulators, which is driven by joint velocity commands and different from the dynamics-based methods. Specifically, the force and motion are modeled and decoupled in the end-effector frame with the help of a stiffness coefficient. To control the orientation of the force, a quaternion control equation is designed by combining the rotation matrix and neural dynamics method. Different from traditional motion-force control methods, the proposed scheme is constructed as quadratic programming with the corresponding recurrent neural network (RNN) solver derived, which considers the kinematic optimization index and joint constraints. According to the generated control signals, a redundant manipulator is able to accurately fulfill the hybrid control of motion and force with the desired quaternion, which is intuitively confirmed by simulations and experiments.Note to Practitioners—This paper is motivated by the deficiencies that restrict the real-world applications of the motion-force control of redundant manipulators. On the one hand, most existing motion-force control schemes are implemented under the framework of dynamics, which inevitably leads to some kinematics-related defects. On the other hand, the latest kinematics-based techniques introduce an admittance control to achieve motion-force control. However, they model the force in the Z-axis of the base coordinate while the motion planning is limited in the X-Y plane, which dramatically reduces real-world applications. In this paper, the deformation force is designed in the end-effector frame, and a quaternion control technology of the end-effector is developed. Such a scheme can realize the real-time control of the orientation and magnitude of the force while ensuring trajectory tracking. In addition, the introduction of optimization indexes and joint constraints dramatically improves the functionality of the proposed scheme. Finally, the contributions of this paper are verified through simulations, experiments and comparisons. This work proposes a feasible framework for the motion-force control and orientation control of redundant manipulators.

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, a distributed and time-delayed k-winner-take-all (DT-kWTA) network is established and analyzed for competitively coordinated task assignment of a multirobot system. It is considered and designed from the following three aspects. First, a network is built based on a k-winner-take-all (kWTA) competitive algorithm that selects k maximum values from the inputs. Second, a distributed control strategy is used to improve the network in terms of communication load and computational burden. Third, the time-delayed problem prevalent in arbitrary causal systems (especially, in networks) is taken into account in the proposed network. This work combines distributed kWTA competition network with time delay for the first time, thus enabling it to better handle realistic applications than previous work. In addition, it theoretically derives the maximum delay allowed by the network and proves the convergence and robustness of the network. The results are applied to a multirobot system to conduct its robots' competitive coordination to complete the given task.

This article develops a fuzzy-neural controller for the kinematic and collaborative control of multimanipulator systems. The entire control scheme is designed based on quadratic programming and implemented by a constructed fuzzy-neural controller. A hybrid minimum joint velocity-acceleration index is introduced to adjust the operating performance of each manipulator and reduce the kinetic energy consumption of the system. Besides, a simple but effective set of membership functions and rules are used to describe the variation of controller parameters caused by the operational complexity and vagueness during task executions. The stability and robustness of the controller are verified through theoretical analysis. Finally, simulations and experimental studies of the multimanipulator system are carried out supporting the practicality of our findings.

The existing discrete-time neural dynamics methods for solving the multilinear tensor equation (MTE) with$\mathcal {M}$-tensor are all derived from the continuous-time one and depend on the Euler difference formula, which cannot be applied to essentially discrete problems and have low solution accuracy. Moreover, these methods all focus on static problems rather than time-varying ones, and thus may have unsatisfactory performance in applications with time-varying parameters. Additionally, most of these methods fail to handle the MTE with$\mathcal {M}$-tensor under noisy conditions. To remedy these issues, a high-order robust discrete-time neural dynamics (HRDND) method with a directly discrete approach is proposed for solving the time-varying MTE (TMTE) with$\mathcal {M}$-tensor in this article. Theoretical analyses on convergence and robustness are provided to prove that the proposed HRDND method is feasible and effective. Finally, simulative experiments on four time-varying numerical examples and an application derived from the Bellman equation solved by the proposed HRDND method and other four methods are given, whose results illustrate the superiority of the proposed HRDND method.

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.

This article proposes an improved general zeroing neural network model to suppress noise and to enhance the real-time performance of solving TVQP problems. The proposed model allows nonconvex activation functions and has noise suppression characteristics, i.e., the NCNSZNN model. Theoretical analyses show that the developed NCNSZNN model converges globally to an accurate solution to the TVQP problem and is robust in the case of MN. Illustrative examples and comparisons are supplied to verify the validity and superiority of the proposed model for online solving TVQP constrained by EAI with MN.

Deep neural networks often suffer from poor performance or even training failure due to the ill-conditioned problem, the vanishing/exploding gradient problem, and the saddle point problem. In this article, a novel method by acting the gradient activation function (GAF) on the gradient is proposed to handle these challenges. Intuitively, the GAF enlarges the tiny gradients and restricts the large gradient. Theoretically, this article gives conditions that the GAF needs to meet and, on this basis, proves that the GAF alleviates the problems mentioned above. In addition, this article proves that the convergence rate of SGD with the GAF is faster than that without the GAF under some assumptions. Furthermore, experiments on CIFAR, ImageNet, and PASCAL visual object classes confirm the GAF's effectiveness. The experimental results also demonstrate that the proposed method is able to be adopted in various deep neural networks to improve their performance. The source code is publicly available at https://github.com/LongJin-lab/Activated-Gradients-for-Deep-Neural-Networks.

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.

Position and orientation of the end-effector of redundant manipulators perform a core role in various complex tasks. However, most quadratic programming (QP)-based robot control approaches merely take the position of the end-effector into account, which is relatively inadequate and impractical. Driven by this significant deficiency, this article develops a control method for end-effector orientation representations by analyzing a rotation matrix. Specifically, it is formulated as an equality constraint and applied to control issues of Euler angles and axis-angle representation. On this basis, a QP-based position and orientation control (POC) scheme is proposed for the kinematic control of redundant manipulators. To handle such a POC problem, a dynamic neural network (DNN) is designed with rigorous theoretical analyses. Simulation results show that the POC scheme can accurately control the orientation representations and position of the end-effector. Experimental results and comparisons with state-of-the-art approaches highlight the feasibility and superiority of the proposed method.

The question of what kind of convolutional neural network (CNN) structure performs well is fascinating. In this work, we move toward the answer with one more step by connecting zero stability and model performance. Specifically, we found that if a discrete solver of an ordinary differential equation is zero stable, the CNN corresponding to that solver performs well. We first give the interpretation of zero stability in the context of deep learning and then investigate the performance of existing first- and second-order CNNs under different zero-stable circumstances. Based on the preliminary observation, we provide a higher-order discretization to construct CNNs and then propose a zero-stable network (ZeroSNet). To guarantee zero stability of the ZeroSNet, we first deduce a structure that meets consistency conditions and then give a zero stable region of a training-free parameter. By analyzing the roots of a characteristic equation, we theoretically obtain the optimal coefficients of feature maps. Empirically, we present our results from three aspects: We provide extensive empirical evidence of different depth on different datasets to show that the moduli of the characteristic equation's roots are the keys for the performance of CNNs that require historical features; Our experiments show that ZeroSNet outperforms existing CNNs which is based on high-order discretization; ZeroSNets show better robustness against noises on the input. The source code is available at https://github.com/logichen/ZeroSNet.

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.

Symmetric high-dimensional and sparse (SHiDS) networks are frequently found in various industrial applications. A symmetric non-negative latent factor (SNLF) model can acquire essential features from them precisely, yet it suffers from slow convergence. To address this issue, this article integrates a generalized momentum method into a symmetric, single latent factor-dependent, non-negative and multiplicative update (S2LF-NMU) algorithm, thereby achieving amomentum-incorporated,symmetric,single-latent-factor-dependentnon-negative-multiplicative-update (MS2N) algorithm. Based on an MS2N algorithm, momentum-incorporated symmetric non-negative latent factor (MSNLF) models are proposed for an SHiDS network, which ensures fast convergence as well as high representative learning ability. Empirical studies on four SHiDS networks from industrial applications demonstrate that compared with state-of-the-art models, the proposed MSNLF models have significantly higher computational efficiency and representative learning ability.

Online fountain codes (OFCs) have many advantages, such as low overhead, online feedback and optimal encoding, due to the feedback of the instantaneous decoding state. This paper analyzes the characteristics of underwater acoustic networks (UANs) as well as the issues of existing OFCs applied in UANs. Aiming at these issues, two optimization objectives of OFCs are put forward for UANs. In addition, a recursive OFC with limited feedback (ROFC-LF) is presented for UANs. The ROFC-LF reduces the consumption of bandwidth and energy caused by the transmission of useless coding packets. Through limited feedback, the problem of low channel utilization in UANs with half-duplex communication is solved. Furthermore, a data transmission mechanism based on the ROFC-LF for UANs is presented. The theoretical analysis and simulation results show that the proposed transmission mechanism based on the ROFC-LF scheme outperforms the existing OFC schemes in terms of overhead, computational complexity, coding efficiency and energy consumption. Consequently, the ROFC-LF is suitable for UANs with constrained resources.

In this article, a robust k -winner-take-all ( k -WTA) neural network employing the saturation-allowed activation functions is designed and investigated to perform a k -WTA operation, and is shown to possess enhanced robustness to disturbance compared to existing k -WTA neural networks. Global convergence and robustness of the proposed k -WTA neural network are demonstrated through analysis and simulations. An application studied in detail is competitive multiagent coordination and dynamic task allocation, in which k active agents [among ] are allocated to execute a tracking task with the static m-k ones. This is implemented by adopting a distributed k -WTA network with limited communication, aided with a consensus filter. Simulation results demonstrating the system's efficacy and feasibility are presented.

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

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.

Community detection is a popular yet thorny issue in social network analysis. A symmetric and nonnegative matrix factorization (SNMF) model based on a nonnegative multiplicative update (NMU) scheme is frequently adopted to address it. Current research mainly focuses on integrating additional information into it without considering the effects of a learning scheme. This study aims to implement highly accurate community detectors via the connections between an SNMF-based community detector's detection accuracy and an NMU scheme's scaling factor. The main idea is to adjust such scaling factor via a linear or nonlinear strategy, thereby innovatively implementing several scaling-factor-adjusted NMU schemes. They are applied to SNMF and graph-regularized SNMF models to achieve four novel SNMF-based community detectors. Theoretical studies indicate that with the proposed schemes and proper hyperparameter settings, each model can: 1) keep its loss function nonincreasing during its training process and 2) converge to a stationary point. Empirical studies on eight social networks show that they achieve significant accuracy gain in community detection over the state-of-the-art community detectors.

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

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.

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

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

Many complex nonlinear optimization or control issues can be transformed into the solving of time-varying nonlinear equations (TVNEs), playing a fundamental role in the control and management of complex systems. As a result, a robust and high-precision online solution method is significant for TVNE. However, there are three main challenges for handling TVNE via the existing methods: First, short-time invariance assumption frequently leveraged in the existing methods leads to lagging errors that are difficult to eliminate. Second, it is difficult in dealing with unknown noise disturbance during the solution process, which causes low solution accuracy or solution failure. Third, existing continuous-time methods are hard to be implemented on digital equipments. In this article, an anti-noise discrete-time neural dynamics (DTND) is designed and studied to overcome the above issues systematically. The theoretical analysis and numerical simulations demonstrate that the proposed model effectively eliminates the lagging errors and achieves the accurate solution of the TVNE in a noisy environment. Moreover, to verify the superior numerical computational property of the DTND model, the intention recognition of lower limbs is explored from the artificial systems, computational experiments, and parallel execution (ACP) framework. Specifically, a nonlinear artificial dynamic system (NADS) concerning the human surface electromyogram (sEMG) signals and joint information is established, which performs in parallel with the actual human lower limb physical experiments. Simulation results illustrate that, within the acceptable range of the digital computer, the controller designed by the DTND model can well guide the NADS to accurately recognize the motion intention of the human lower limb.

Up to date, the existing methods for nonlinear optimization with time-dependent parameters can be classified into two types: 1) static methods are capable of handling inequality constraints but may generate large lagging errors in the solution of the intrinsically time-dependent constrained nonlinear optimization (TDCNO) problem due to the hypothesis of short-time invariance and 2) time-variant methods, e.g., zeroing neural networks, are able to remedy the lagging error but fail to solve the TDCNO problem under inequality constraints. To resolve this contradiction, a noise-suppressing neural dynamics (NSND) model is proposed to solve the TDCNO problem subject to both equality and inequality constraints via the nonlinear complementary problem (NCP) function. The proposed method allows inequality constraints for unknown variables, removes the short-time invariance hypothesis, and further eliminates lagging errors during the solving process in the presence of noises. Besides, the rapid convergence, global stability, and noise processing of the NSND model are verified by the theoretical analyses. Simulation results of illustrative examples, including dimensionality reduction on principal component analyses (PCA) and a robot motion control, show that the NSND model outperforms the existing models for the TDCNO problem.

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.

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

Aiming at time-variant problems solving, a special type of recurrent neural networks, termed zeroing neural network (ZNN), has been proposed, developed, and validated since 2001. Although equality-constrained time-variant quadratic programming (TVQP) has been well solved using the ZNN approach, TVQP problems with inequality constraints involved have not been satisfactorily handled by the existing ZNN models. To overcome this issue, this paper designs a ZNN model with exponential convergence for solving equality- and inequality-constrained TVQP problems. Considering a fast convergence is preferred in some time-critical applications in practice, a predefined-time stabilizer is for the first time utilized to endow the ZNN model with predefined-time convergence, leading to a predefined-time convergent ZNN (PTCZNN) model that exhibits an antecedently- and explicitly-defined convergence time. Theoretical analysis is performed with the convergence of the two ZNN models including the predefined-time convergence of the PTCZNN model rigorously proved. Validations are comparatively conducted to verify the effectiveness and superiority of the PTCZNN model in terms of convergence performance. To demonstrate the potential applications, the PTCZNN model is applied to image fusion and kinematic control of two robotic arms with joint limits considered. The efficacy and applicability of the PTCZNN model are validated by the illustrative examples. This is the first time to develop a ZNN model working as a quadratic programming solver that is applicable to kinematic control of robotic arms with joint constraints handled since the emergence of ZNNs.

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.

Nonlinear optimization problems with dynamical parameters are widely arising in many practical scientific and engineering applications, and various computational models are presented for solving them under the hypothesis of short-time invariance. To eliminate the large lagging error in the solution of the inherently dynamic nonlinear optimization problem, the only way is to estimate the future unknown information by using the present and previous data during the solving process, which is termed the future dynamic nonlinear optimization (FDNO) problem. In this paper, to suppress noises and improve the accuracy in solving FDNO problems, a novel noise-tolerant neural (NTN) algorithm based on zeroing neural dynamics is proposed and investigated. In addition, for reducing algorithm complexity, the quasi-Newton Broyden-Fletcher-Goldfarb-Shanno (BFGS) method is employed to eliminate the intensively computational burden for matrix inversion, termed NTN-BFGS algorithm. Moreover, theoretical analyses are conducted, which show that the proposed algorithms are able to globally converge to a tiny error bound with or without the pollution of noises. Finally, numerical experiments are conducted to validate the superiority of the proposed NTN and NTN-BFGS algorithms for the online solution of FDNO problems.

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.

A latent factor (LF) model can implement efficient analysis for a high-dimensional and sparse (HiDS) matrix from recommender systems (RSs). However, an LF model's representation learning ability to a targeted HiDS matrix is heavily proportional to its known data density. Unfortunately, an HiDS matrix's known data are limited due to users' activity limitations in RSs. Motivated by this observation, this paper proposes a Prediction-sampling-based Multilayer-structured Latent Factor (PMLF) model. Following the principle of Deep Forest [1], PMLF implements a loosely-connected multilayered LF structure, where each layer generates synthetic ratings to enrich the input for the next layer. Such an injection process is carefully monitored through a random sampling process and nonlinear activations to avoid overfitting. Thus, PMLF's representation learning ability to an HiDS matrix is significantly enhanced owing to the carefully injected estimates and its generalized multilayer-structure. Experimental results on four HiDS matrices from industrial RSs indicate that compared with six state-of-the-art LF-based and deep neural networks-based models, PMLF well balances the prediction accuracy and computational efficiency, making it satisfy demands of fast and accurate industrial applications.

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

In this article, a neural dynamics model is constructed and investigated for solving time-dependent Sylvester equation with matrix inversion involved in the solving process. Besides, to eliminate the matrix inversion in the model, the quasi-Newton Broyden-Fletcher-Goldfarb-Shanno method is leveraged to construct a new model. Moreover, the global convergence performance and the effectiveness of the two discrete computational models are testified by providing theoretical analyses and numerical experiments with comparisons to the existing solutions, respectively. Two applications to robotics and the multiple-input multiple-output system are given to elucidate the feasibility of the proposed models for solving time-dependent Sylvester equation.

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

In order to leverage the unique advantages of redundant manipulators, avoiding the singularity during motion planning and control should be considered as a fundamental issue to handle. In this article, a distributed scheme is proposed to improve the manipulability of redundant manipulators in a group. To this end, the manipulability index is incorporated into the cooperative control of multiple manipulators in a distributed network, which is used to guide manipulators to adjust to the optimal spatial position. Moreover, from the perspective of game theory, this article formulates the problem into a Nash equilibrium. Then, a neural network with anti-noise ability is constructed to seek and approximate the optimal strategy profile of the Nash equilibrium problem with time-varying parameters. Theoretical analyses show that the neural network model has the superior global convergence and noise immunity. Finally, simulation results demonstrate that the neural network is effective in real-time cooperative motion generation of multiple redundant manipulators under perturbations in distributed networks.

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.

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.

Neural networks have been generally deemed as important tools to handle kinds of online computing problems in recent decades, which have plenty of applications in science and electronics fields. This paper proposes a novel recurrent neural network (RNN) to handle the perturbed time-varying underdetermined linear system with double bound limits on residual errors and state variables. Beyond that, the bound-limited underdetermined linear system is converted into a time-varying system that consists of linear and nonlinear formulas through constructing a nonnegative time-varying variable. Then, theoretical analyses are conducted to verify the superior convergence performance of the proposed RNN model. Furthermore, numerical experiment results and computer simulations demonstrate the superiority and effectiveness of the proposed RNN model for handling the time-varying underdetermined linear system with double bound limits. Finally, the proposed RNN model is applied to the physically limited PUMA560 robot to show its satisfactory applicabilities.

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 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.

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.

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.

We study unsupervised learning by developing a generative model built from progressively learned deep convolutional neural networks. The resulting generator is additionally a discriminator, capable of "introspection" in a sense - being able to self-evaluate the difference between its generated samples and the given training data. Through repeated discriminative learning, desirable properties of modern discriminative classifiers are directly inherited by the generator. Specifically, our model learns a sequence of CNN classifiers using a synthesis-by-classification algorithm. In the experiments, we observe encouraging results on a number of applications including texture modeling, artistic style transferring, face modeling, and unsupervised feature learning.

In this paper, to achieve the fault-tolerant capability for redundant manipulators, a dimension-reduction method is presented and investigated at the joint-acceleration level. By incorporating such a dimension-reduction method and the limits of joint angle, joint velocity as well as joint acceleration (i.e., the physical constraints on joints), an acceleration fault-tolerant scheme for redundant manipulator motion planning and control (or say, motion-planning-and-control, MPaC) is thus proposed and investigated. The scheme is then reformulated as a quadratic program (QP) subject to equality and bound constraints. For the online solution of the proposed scheme, the PLPE (piecewise-linear projection equation) oriented numerical algorithm is adopted to obtain the final QP solver. The derived QP resulting from the proposed scheme combines the abilities of fault tolerance, joints limits avoidance and repetitive motion, which can achieve the repetitive motion before and after the fault tolerance.

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.

We propose introspective convolutional networks (ICN) that emphasize the importance of having convolutional neural networks empowered with generative capabilities. We employ a reclassification-by-synthesis algorithm to perform training using a formulation stemmed from the Bayes theory. Our ICN tries to iteratively: (1) synthesize pseudo-negative samples; and (2) enhance itself by improving the classification. The single CNN classifier learned is at the same time generative --- being able to directly synthesize new samples within its own discriminative model. We conduct experiments on benchmark datasets including MNIST, CIFAR-10, and SVHN using state-of-the-art CNN architectures, and observe improved classification results.

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.

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.

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.

In this paper, a new Taylor-type numerical differentiation formula is first presented to discretize the continuous-time Zhang neural network (ZNN), and obtain higher computational accuracy. Based on the Taylor-type formula, two Taylor-type discrete-time ZNN models (termed Taylor-type discrete-time ZNNK and Taylor-type discrete-time ZNNU models) are then proposed and discussed to perform online dynamic equality-constrained quadratic programming. For comparison, Euler-type discrete-time ZNN models (called Euler-type discrete-time ZNNK and Euler-type discrete-time ZNNU models) and Newton iteration, with interesting links being found, are also presented. It is proved herein that the steady-state residual errors of the proposed Taylor-type discrete-time ZNN models, Euler-type discrete-time ZNN models, and Newton iteration have the patterns of O(h(3)), O(h(2)), and O(h), respectively, with h denoting the sampling gap. Numerical experiments, including the application examples, are carried out, of which the results further substantiate the theoretical findings and the efficacy of Taylor-type discrete-time ZNN models. Finally, the comparisons with Taylor-type discrete-time derivative model and other Lagrange-type discrete-time ZNN models for dynamic equality-constrained quadratic programming substantiate the superiority of the proposed Taylor-type discrete-time ZNN models once again.

In this paper, to remedy the joint-angle drift phenomenon for manipulation of two redundant robot arms, a novel scheme for simultaneous repetitive motion planning and control (SRMPC) at the joint-acceleration level is proposed, which consists of two subschemes. To do so, the performance index of each SRMPC subscheme is derived and designed by employing the gradient dynamics twice, of which a convergence theorem and its proof are presented. In addition, for improving the accuracy of the motion planning and control, position error, and velocity, error feedbacks are incorporated into the forward kinematics equation and analyzed via Zhang neural-dynamics method. Then the two subschemes are simultaneously reformulated as two quadratic programs (QPs), which are finally unified into one QP problem. Furthermore, a piecewise-linear projection equation-based neural network (PLPENN) is used to solve the unified QP problem, which can handle the strictly convex QP problem in an inverse-free manner. More importantly, via such a unified QP formulation and the corresponding PLPENN solver, the synchronism of two redundant robot arms is guaranteed. Finally, two given tasks are fulfilled by 2 three-link and 2 five-link planar robot arms, respectively. Computer-simulation results validate the efficacy and accuracy of the SRMPC scheme and the corresponding PLPENN solver for synchronous manipulation of two redundant robot arms.

In this brief, a discrete-time Zhang neural network (DTZNN) model is first proposed, developed, and investigated for online time-varying nonlinear optimization (OTVNO). Then, Newton iteration is shown to be derived from the proposed DTZNN model. In addition, to eliminate the explicit matrix-inversion operation, the quasi-Newton Broyden-Fletcher-Goldfarb-Shanno (BFGS) method is introduced, which can effectively approximate the inverse of Hessian matrix. A DTZNN-BFGS model is thus proposed and investigated for OTVNO, which is the combination of the DTZNN model and the quasi-Newton BFGS method. In addition, theoretical analyses show that, with step-size h=1 and/or with zero initial error, the maximal residual error of the DTZNN model has an O(τ(2)) pattern, whereas the maximal residual error of the Newton iteration has an O(τ) pattern, with τ denoting the sampling gap. Besides, when h ≠ 1 and h ∈ (0,2) , the maximal steady-state residual error of the DTZNN model has an O(τ(2)) pattern. Finally, an illustrative numerical experiment and an application example to manipulator motion generation are provided and analyzed to substantiate the efficacy of the proposed DTZNN and DTZNN-BFGS models for OTVNO.

This paper proposes a novel multi-input Bernoulli-polynomial neuronet (MIBPN) on the basis of function approximation theory. The MIBPN is trained by a weights-and-structure-determination (WASD) algorithm with twice pruning (TP). The WASD algorithm can obtain the optimal weights and structure for the MIBPN, and overcome the weaknesses of conventional BP (back-propagation) neuronets such as slow training speed and local minima. With the TP technique, the neurons of less importance in the MIBPN are pruned for less computational complexity. Furthermore, this MIBPN can be extended to a multiple input multiple output Bernoulli-polynomial neuronet (MIMOBPN), which can be applied as an important tool for classification. Numerical experiment results show that the MIBPN has outstanding performance in data approximation and generalization. Besides, experiment results based on the real-world classification data-sets substantiate the high accuracy and strong robustness of the MIMOBPN equipped with the proposed WASD algorithm for classification. Finally, the twice-pruning aided WASD neuronet of Bernoulli-polynomial type in the forms of MIBPN and MIMOBPN is established, together with the effective extension to robust classification.