Graph Neural Networks (GNNs) are known to be prone to adversarial attacks, among which backdoor attack is a major security threat. By injecting backdoor triggers into a graph and assigning a target class label to nodes attached to the triggers, the attacker can mislead the GNN model trained on the poisoned graph to classify test nodes attached with a trigger to the target class. To defend against backdoor attacks, existing defense methods rely on anomaly detection in feature distribution or label transformation. However, these approaches are incapable of detecting in-distribution triggers or clean-label attacks that do not alter the class label of target nodes. To tackle these threats, we empirically analyze triggers from a multidimensional aspect, and our analysis shows that there are clear distinctions between trigger nodes and normal ones in terms of node feature values, node embeddings, and class prediction probabilities. Based on these findings, we propose a Multidimensional Anomaly Detection framework (MAD) that can effectively minimize the impact of triggers by pruning away anomalous nodes and edges. Extensive experiments show that at the cost of slight loss in clean classification accuracy, MAD achieves considerably lower attack success rate as compared to state-of-the-art backdoor defense methods.

Repetitive motion control (RMC) for redundant manipulators has been extensively studied from the kinematic perspective, whereas security concerns under malicious adversaries have received limited attention. In network-controlled manipulators, when control commands sent from the control center to the remote manipulator are subject to false data injection attacks (FDIAs), serious incidents and potential harm to individuals can occur. This paper proposes a novel resilient controller such that the manipulator can successfully complete motion tracking tasks and address the non-repetitive motion problem, even in the presence of FDIAs. The problem is first reformulated as a convex optimization problem with an unknown parameter relative to FDIAs, where the RMC criteria serves as the objective function and physical limitations are incorporated as inequality constraints. A recurrent neural network (RNN) is then introduced to solve the problem, improving computational efficiency. Additionally, a detection mechanism is integrated to estimate the unknown attack parameter, allowing the RNN to find the optimal control command. Simulations and experiments are conducted on an RM65-B manipulator to validate the efficacy of the proposed method, and comparisons with existing approaches highlight its superior performance.

This paper investigates the problem of optimal consensus of high-order nonlinear multi-agent systems under privacy constraints. To address the potential privacy leakage during inter-agent communication, the Paillier homomorphic encryption scheme is incorporated into the consensus control protocol. Two privacy-preserving mechanisms are proposed, based on direct state difference and weighted state difference, respectively. These mechanisms enable effective encrypted information exchange without disclosing the agents’ actual states. Theoretical analysis is conducted to evaluate the system’s privacy properties, proving that neither curious-but-honest agents within the system nor external eavesdroppers can infer the initial states of other agents. Simulation results verify the effectiveness and advantages of the proposed method.

Average consensus is a fundamental problem in multi-agent systems, but traditional consensus algorithms relying on explicit state exchange are unsuitable for privacy-sensitive scenarios. Although various privacy-preserving approaches have been proposed to address this issue, most of them significantly degrade convergence speed, computational efficiency, or accuracy. In this paper, we propose a computationally efficient average consensus algorithm based on one-step perturbation. Each agent injects random perturbation into transmitted state information only in the first step, then follows the standard protocol. This design preserves the privacy of initial states of agents while maintaining fast and accurate average consensus. Simulations confirm the effectiveness of the proposed algorithm and its advantages in convergence, accuracy, and computational efficiency.

Tasks allocation plays a pivotal role in cooperative robotics. This study proposes a novel fully distributed task allocation method for target tracking, by which mobile robots only need to share state information with communication neighbors. The proposed method adopts a distributed k winners-take-all (k-WTA) network to select the k mobile robots closest to the moving target to perform the target tracking task. In addition, an innovative robot control law is designed, incorporating speed feedback and nonlinear activation functions to achieve finite-time error convergence. Unlike previous approaches, our distributed task allocation method yields finite-time error convergence, does not rely on consensus filters, and eliminates the need for a central computing unit to get the k-WTA result during the control process. We demonstrate the effectiveness of the proposed method through theoretical analysis and simulations. Compared to traditional methods, our method leads to smaller total moving distances and speed norms, which underscores the significance of our method in enhancing the efficiency and performance of mobile robots in dynamic task allocation.

Time-dependent matrix inversion (TDMI) is popularly utilized in scientific fields. Considering the low computing costs and simplified structure, this brief puts forward a Frobenius norm-based dynamic neural network (FNBDNN) model to address a TDMI problem for the first time, which achieves convergence within finite time and ensures strong robustness without using integral operations and element-wise nonlinear activation functions. Moreover, precise theoretical analyses are provided to display the property of finite-time convergence of the FNBDNN model in dealing with the TDMI problem. Simulation experiments are further conducted to verify the validity and preponderance of the FNBDNN model. Finally, an application of the devised FNBDNN model to the precise motion control of a two-axis manipulator is introduced.

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

Various recurrent neural network (RNN) models, especially zeroing neutral network (ZNN) models, have been investigated to solve time-varying linear inequalities (TVLI) and applied to different important fields. Existing ZNN models can solve TVLI in finite time by using complicated elementwise nonlinear functions, which brings a concern about cost for hardware implementation. To achieve a balance between implementation cost and convergence performance, this article explores a new RNN model based on ZNN by using a two-norm method for solving TVLI, which is called norm-based ZNN (NBZNN), and the proposed model can achieve finite-time convergence without the assistance of elementwise nonlinear activation functions. Strict theoretical analysis is given on convergence properties of the proposed model, showing its global finite-time convergence, which is preserved under a class of bounded noises. For the first time, our work shows that a finite-time convergent RNN model can be designed for solving TVLI without using elementwise nonlinear activation functions. Computer simulation results further verify the effectiveness and superiority of the proposed NBZNN model for solving TVLI. An application to robotics further demonstrates the efficacy of the proposed NBZNN model.

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

Dynamic neural networks are considered as an effective method in the field of scientific computing, among which gradient neural networks (GNNs) are an efficient method for solving static problems. However, when solving dynamic problems, the current GNNs are often subject to lagging errors. In this article, we develop a finite-time convergent GNN (FTCGNN) model for solving static and time-varying systems of linear equations. Different from zeroing neural networks (ZNNs) dedicated to time-varying problem solving, the FTCGNN model has finite-time convergence regardless of the existence of time-varying noises. Simulation results show that the FTCGNN model is effective, among which the comparisons with existing GNNs and ZNNs validate the advantages of the FTCGNN model.

The k-winners-take-all (k-WTA) network is a model based on competition. The extant literature on k-WTA models only deals with static undirected connected graphs. In the actual application scenario, the static undirected connection graph cannot adapt to the complex and changing communication conditions. Thus, in this paper we find a distributed k-WTA network that can be applied to dynamic undirected connected graphs. Our experimental simulation results demonstrate that the network efficiently identify the top k largest inputs from n inputs in dynamic undirected connected graphs. Furthermore, we apply this network to a distributed multi-robot target tracking task assignment scenario. Our proposed algorithm shows promising results in this application, indicating its potential in real-world scenarios.

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

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

In an acceleration-based Secure Device Pairing (SDP) scheme, two unauthenticated devices continuously measure their own acceleration. If the similarity of their measurements are sufficiently high, the devices will build a secure communication channel assume that it is hard for any attacker to estimate their measurements in real-time. This paper demonstrates that the assumption does not hold and further proposes an effective Man-in-the-Middle (MitM) attack on acceleration-based SDP schemes. That is to say, an MitM adversary is able to quickly estimate the acceleration measurements of the target devices with automatic visual tracking technologies, and then compromise the device’s communication channel by impersonating the target devices with the estimated measurements. The present attack is extensively evaluated on acceleration-based SDP schemes in indoor and outdoor environments. The evaluation results show that the device’s acceleration can be estimated with high accuracy in real time. Thus, the present MitM attack is practical to defeat the acceleration-based SDP schemes.

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

Finding dynamic Moore-Penrose inverses (DMPIs) in real-time is a challenging problem due to the time-varying nature of the inverse. Traditional numerical methods for static Moore-Penrose inverse are not efficient for calculating DMPIs and are restricted by serial processing. The current state-of-the-art method for finding DMPIs is called the zeroing neural network (ZNN) method, which requires that the time derivative of the associated matrix is available all the time during the solution process. However, in practice, the time derivative of the associated dynamic matrix may not be available in a real-time manner or be subject to noises caused by differentiators. In this article, we propose a novel gradient-based neural network (GNN) method for computing DMPIs, which does not need the time derivative of the associated dynamic matrix. In particular, the neural state matrix of the proposed GNN converges to the theoretical DMPI in finite time. The finite-time convergence is kept by simply setting a large parameter when there are additive noises in the implementation of the GNN model. Simulation results demonstrate the efficacy and superiority of the proposed GNN method.

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

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

In this paper, we propose novel distributed near-optimal consensus protocols for input-constrained double-integrator multi-agent systems with an undirected connected communication topology. The design of the consensus protocols is based on the optimization of an integral-type performance index. By using the Taylor expansion and projection neural networks, we realize the optimization of the performance indices subject to the input constraints of the agents. The performance of the proposed consensus protocols is demonstrated via computer simulations.

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

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

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

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

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

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

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

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

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

The solving of nonlinear equation systems (e.g., complex transcendental dispersion equation systems in waveguide systems) is a fundamental topic in science and engineering. Davidenko method has been used by electromagnetism researchers to solve time-invariant nonlinear equation systems (e.g., the aforementioned transcendental dispersion equation systems). Meanwhile, Zhang dynamics (ZD), which is a special class of neural dynamics, has been substantiated as an effective and accurate method for solving nonlinear equation systems, particularly time-varying nonlinear equation systems. In this paper, Davidenko method is compared with ZD in terms of efficiency and accuracy in solving time-invariant and time-varying nonlinear equation systems. Results reveal that ZD is a more competent approach than Davidenko method. Moreover, discrete-time ZD models, corresponding block diagrams, and circuit schematics are presented to facilitate the convenient implementation of ZD by researchers and engineers for solving time-invariant and time-varying nonlinear equation systems online. The theoretical analysis and results on Davidenko method, ZD, and discrete-time ZD models are also discussed in relation to solving time-varying nonlinear equation systems.