ABSTRACT The vehicle routing problem (VRP) has garnered significant interest due to its central role in logistics and transportation systems. However, existing deep reinforcement learning (DRL) approaches often underexploit the structural information encoded in graph topologies, and tend to generate solution trajectories with limited diversity, restricting effective exploration of the solution space. To overcome these limitations, we present a Graph‐based Diverse Trajectory‐driven Attention Model (GDTAM) for solving VRPs across a range of scales and types. Built upon a transformer backbone, GDTAM operates directly on undirected graphs and integrates an edge‐driven graph attention block within the encoder, enabling the joint modeling of node‐ and edge‐level topological features. To enhance adaptability to dynamic environments, we introduce a feature integrator that bridges the encoder and decoder, enabling the fusion of real‐time state features with static graph representations. Moreover, GDTAM incorporates a multi‐decoder architecture with identical structures but independently network parameters, promoting the generation of diverse routing trajectories through a Jensen–Shannon divergence regularization term. We evaluate GDTAM on four canonical VRP variants, i.e., the traveling salesman problem (TSP), the capacitated VRP (CVRP), the orienteering problem (OP), and the asymmetric traveling salesman problem (ATSP). Experimental results demonstrate that GDTAM represents a meaningful advancement over mainstream heuristic and DRL‐based baselines, while exhibiting strong generalization across various problem scales, underscoring its effectiveness and robustness for real‐world routing applications.

ABSTRACT The multiple traveling salesman problem (mTSP) has attracted considerable attention due to its importance in logistics, robotics, and transportation systems. However, existing deep reinforcement learning (DRL) methods often rely on monolithic solution paradigms, which limit scalability, underutilize local graph structures, and hinder adaptability in dynamic decision‐making. To address these challenges, we propose a hierarchical divide‐and‐conquer neural approach (HDCN) for solving mTSPs in a scalable and principled manner. HDCN adopts a hierarchical architecture that decomposes the global problem into task allocation and route planning, which are jointly optimized within a unified framework. At the upper level, an affinity‐guided self‐organizing map is employed to generate structured task assignments by capturing latent spatial patterns. At the lower level, a neighborhood‐aware deep reinforcement learning model with a transformer‐inspired policy network constructs routing trajectories conditioned on the allocation results. To improve adaptability during sequential decision‐making, an integrator is introduced to fuse dynamic environmental states with static graph representations. Extensive experiments conducted on mTSP benchmarks with varying scales and spatial distributions demonstrate that HDCN consistently outperforms mainstream heuristic methods and DRL‐based baselines in terms of solution quality, scalability, and generalization performance, highlighting its effectiveness and robustness for large‐scale and complex mTSP scenarios.

This paper presents a novel Nesterov accelerated gradient-based fixed-time convergent actor-critic (NAG-FxT-AC) scheme for the optimal control of nonlinear systems. The proposed approach integrates the Nesterov accelerated gradient method with FxT concurrent learning to achieve rapid convergence while ensuring optimal performance. Actor-critic neural networks (NN) are employed to approximate the optimal value function and control policy, where the accelerated gradient mechanism introduces auxiliary variables to enhance learning efficiency. A FxT concurrent learning algorithm is developed to update the NN weights, guaranteeing convergence to bounded regions within fixed time independent of initial conditions. Lyapunov stability analysis proves that both the closed-loop system states and NN estimation errors are ultimately uniformly bounded with FxT NN weights convergence properties. Simulation results on a nonlinear system validate the effectiveness of the proposed control scheme. Compared to the baseline methods like FxT-ADP, the proposed NAG-FxT-AC reduces the state convergence time by up to 12% and the weight convergence time by 84%, demonstrating superior learning efficiency.

This paper presents EveryBrain, a method to generate electroencephalographic (EEG) signals of visual stimuli using images. Given that individuals exhibit distinct EEG responses to the same visual stimulus, EveryBrain is capable of capturing these individual characteristics during signal generation. The framework operates in two stages. By leveraging the temporal properties of EEG signals and the spatial features of images, EveryBrain presents a self-supervised framework that simultaneously reconstruct EEG signals and perform contrastive learning between image and EEG features. Furthermore, through additional training focused on individual EEG differences, Stage2 injects an ID number (representing a specific person) into image features via a cross-modal projector. The resulting personalized EEG latent codes, supervised by the Stage1 encoder, are then decoded into vivid, individualized EEG responses. Experiments validate the accuracy of EveryBrain in generating EEG signals for various individuals in response to visual stimuli. Overall, the proposed method tackles challenges in EEG generation from images, such as cross-modal alignment, individual variability, and waveform stability, yielding promising results. Additionally, the novel approach of of joint learning between images and EEG demonstrates positive effects on decoding visual neural representations. Both quantitative and qualitative evaluations demonstrate the effectiveness of methods, marking a significant step toward portable and cost-effective "image-to-thought".

This work investigates the formation tracking issue for multirobot manipulator end-effectors under input constraints. A distributed formation control law is designed to guarantee the finite-time boundedness of tracking errors within the framework. To estimate the significant bias of dynamics discovered during practical multirobot collaborative manipulation tasks, a bias radial basis function neural network (RBFNN) is integrated, along with a designed adaptive updating law for expeditious approximation. In addition, an anti-windup compensator within a finite-time framework is specifically introduced to mitigate the input saturation issue arising from torque limitations in joint actuators. Finally, the system’s semi-global practical finite-time boundedness (SGPFTB) is rigorously established through Lyapunov theory. Five planar manipulators are employed in comparative computational experiments to validate the feasibility of the presented control strategy.

ABSTRACT Recently, routing problems have made significant progress and exhibited remarkable performance across various domains. However, they still suffer from severe issues, including high computational complexity and path intersection phenomenon, which curtail their broader applicability. This study focuses on the challenging and practical Single Depot‐Multiple Traveling Salesman Problem (SD‐MTSP) with a min‐max objective, which aims to minimize the maximum tour length among all salesmen. To tackle these challenges, we propose a Hierarchical Self Organizing Map (HiSOM) based on a divide‐and‐conquer framework to decompose the complex scheduling of SD‐MTSP into task allocation and route planning subproblems, with a strong emphasis on reducing computational complexity. Specifically, in the task allocation stage, we introduce the concept of soft labels to precisely characterize the strength of association between salesmen and their traversal cities, and devise an SGD‐SOM framework to optimize the sum square error with smooth gradient descents. In the route planning stage, we design a TOSOM framework to generate a topologically ordered tour with minimal length, ensuring strict adherence to the convex hull property and effectively mitigating path intersection. Comprehensive experiments on both synthetic and real‐world datasets demonstrate that our proposed HiSOM outperforms numerous baseline methods by up to 6.91%.

This paper proposes a hierarchical safe reinforcement learning with prescribed performance control (HSRL-PPC) scheme to address the challenges of interconnected leader-follower systems operating in complex environments. The framework consists of two levels: at the higher level, the leader agent detects and avoids moving obstacles while planning optimal paths; at the lower level, the follower agent tracks the leader within strict prescribed performance bounds. We formulate the optimal prescribed performance safe control problem and solve it using the Hamilton-Jacobi-Bellman (HJB) equation. Due to system nonlinearity and obstacle complexity, we approximate the leader’s optimal value function using a state-following neural network that efficiently extrapolates training data to neighboring states, while employing a regular critic neural network for the follower’s value function approximation. Lyapunov stability analysis demonstrates the closed-loop system’s theoretical guarantees. Experimental results from two simulation examples and hardware tests with a quadcopter-vehicle system validate the effectiveness of the proposed approach in achieving safe navigation and precise tracking performance in dynamic environments. Note to Practitioners—Challenges exist in unpredictable obstacles and agent limitations for the interconnected leader-follower system. To provide a safe, efficient, and reliable control scheme, hierarchical safe reinforcement learning with prescribed performance control is proposed in this paper. The hierarchical structure is utilized to coordinate the leader and follower agents in the interconnected system, where the leader agent plans the optimal path and avoids obstacles, and the follower agent tracks the leader within prescribed performance bounds. Based on the proposed hierarchical structure, engineers can design efficient and safe control schemes for interconnected leader-follower systems with moving obstacles. In future work, we will address the problem of external disturbances and uncertainties in the interconnected leader-follower system.

Real-world applications of nonlinear systems tracking control are always challenging due to the existence of uncertainties and disturbances. To design a robust optimal tracking controller for uncertain nonlinear systems with disturbances and actuator saturation, this paper investigates the prescribed performance robust optimal tracking control problem. A prescribed performance mechanism is constructed to convert the dynamics of tracking error into transformed error dynamics, which keeps the system’s operating states within specific bounds, ensuring tracking with predefined error constraints. For the optimal tracking controller design, an optimal index is established to optimize the performance of tracking control, and a robust optimal index is established to optimize the disturbance effect on the tracking error. To achieve robust optimal tracking control that minimizes both optimal and robust optimal indexes, a Stackelberg game is constructed, which provides a hierarchical game structure for the optimal controller and the worst disturbance. The robust optimal controller is approximated online using reinforcement learning techniques. An actor-critic-identifier algorithm is designed to approximate the optimal value function, optimal controller, and drifted system parameters. Lyapunov theory is utilized to analyze the closed-loop system’s stability. To demonstrate the effectiveness of the proposed robust optimal control method, two numerical simulations and a hardware experiment on a quadcopter system are conducted. The experiment results demonstrate that our method successfully achieves prescribed performance tracking control when actuators are saturated and disturbances are present. Note to Practitioners—In this paper, the probelm of mixed$H_{2}/H_{\infty }$prescribed-performance optimal tracking control for nonlinear systems with input saturation is investigated. To constrain the operating states of the system within certain bounds, the prescribed performance transformation is designed to achieve tracking with predefined error constraints. For the optimal controller design, the$H_{2}$index is established to minimize the optimal tracking performance, and the$H_{\infty }$index is designed to minimize the disturbance effect on the tracking error. A Stackelberg-based non-zero sum game between the optimal controller and the worst disturbance is established to design the mixed$H_{2}/H_{\infty }$optimal tracking controller. The designed optimal controller is approximated online using reinforcement learning. Effectiveness of the proposed method is demonstrated by two numerical simulations and a hardware experiment on a quadcopter system. Based on the proposed high-performance controller, engineers can design a high-performance robust optimal tracking controller for uncertain nonlinear systems with extreme conditions of disturbances and actuator saturation.

The object detection of the substation is the key to ensuring the safety and reliable operation of the substation. The traditional image detection algorithms use the corresponding texture features of single-class objects and would not handle other different class objects easily. The object detection algorithm based on deep networks has generalization, and its sizeable complex backbone limits the application in the substation monitoring terminals with weak computing power. This article proposes a multitargets joint training lightweight model. The proposed model uses the feature maps of the complex model and the labels of objects in images as training multitargets. The feature maps have deeper feature information, and the feature maps of complex networks have higher information entropy than lightweight networks have. This article proposes the heat pixels method to improve the adequate object information because of the imbalance of the proportion between the foreground and the background. The heat pixels method is designed as a kind of reverse network calculation and reflects the object's position to the pixels of the feature maps. The temperature of the pixels indicates the probability of the existence of the objects in the locations. Three different lightweight networks use the complex model feature maps and the traditional tags as the training multitargets. The public dataset VOC and the substation equipment dataset are adopted in the experiments. The experimental results demonstrate that the proposed model can effectively improve object detection accuracy and reduce the time-consuming and calculation amount.

Multiagent formation tracking tasks in constrained space commonly require the formation to transform its pattern adaptively. Thus, the multiagent systems can effectively avoid spatial constraints and safely pass through the constrained region. Aiming to achieve such control objectives, a formation tracking control strategy based on the leader-following framework is designed in this article. An adaptive formation scaling mechanism called orientational scaling is first designed. A time-varying matrix introduces real-time information about the formation shape and obstacles into the formation tracking controller. With the action of the controller, the formation can perform an orientational scaling action on its pattern according to the constraints of the external space during the tracking of a given trajectory. Besides, a spatial receding control mechanism is also designed to handle possible collisions in scaling transformations in multiagent systems, reducing the collision risk and improving movement efficiency. The stability conditions of the system are given by adopting the Lyapunov stability theory. Finally, the effectiveness of the designed control strategy is illustrated by simulation results.

This article proposes single-objective/multiobjective cat swarm optimization clustering algorithms for data partition. The proposed methods use the cat swarm to search the optimal. The position of the cat tightly associates with the clustering centers and is updated by two submodes: the seeking mode and the tracing mode. The seeking mode uses the simulated annealing strategy to update the cat position at a probability. Inspired by the quantum theories, the tracing mode adopts the quantum model to update the cat position in the whole solution space. First, the single-objective method is proposed and adopts the cohesion of clustering as the objective function, in which the kernel method is applied. For considering more objective functions to reveal diverse aspects of data, the multiobjective method is proposed and adopts both the cohesion and the connectivity as the objective functions. The Pareto optimization method is applied to balance the objectives. In the experiments, three kinds of data sets are used to examine the effectiveness of the proposed methods, which are three synthetic data sets, four data sets from the UCI Machine Learning Repository, and a field data set. Experimental results verified that the proposed methods perform better than the traditional clustering algorithms, and the proposed multiobjective method has the highest accuracy. Note to Practitioners-This article presents single-objective/multiobjective cat swarm optimization clustering analysis methods for data partition. Through automatically extracting meaningful or useful classes, clustering analysis could help the practitioners or the intelligent devices find the specific meanings of data, natural data structure, the data relationships, or other characteristics. The proposed methods use the cat swarm to search the optimal clustering result. One or more criterion functions could be selected as the optimization objectives. The time complexity of the multiobjective type is higher than that of the single-objective type. Therefore, in the industrial field, engineers should choose the number of the optimization objectives based on the actual requirements. The proposed methods could be widely used into industrial applications to deal with complex data sets. Future research could consider some more progressive optimization schemes to improve the effectiveness.

Gas component perception plays an important role of robot for environment detection. The reinforced nonlinear model with update-driven is proposed for gas component perception. When new data are collected, the update-driven strategy constructs two concatenations to modify the proposed model without using the old data, where two concatenations are the loading matrices of the old model concatenated to new collected data. Considering the nonlinear characteristics between the independent variables and the dependent variables, there are two types of the proposed method (TypeI and TypeII). For TypeI, partial least squares (PLS) is performed on the concatenations, and the inner linear function of PLS is replaced by the neural network, where the radial basis function neural network (RBFNN) and the back propagation neural network (BPNN) are, respectively, employed for TypeI (TypeI-RBFNN and TypeI-BPNN). For TypeII, the radial basis function network extends the independent variables of the concatenations, and PLS is performed on the concatenations to extract the nonlinear principle components, which are the inputs of two feedforward neural networks. The residuals error matrices of the concatenations are, respectively, used as the outputs of two feedforward neural networks. Two real experimental data sets, which are gas-fired plant data set and coal-fired plant data set, are used for estimating the proposed method. The experimental results show that the proposed method can realize gas component perception and TypeI-RBFNN of the proposed method has a better prediction accuracy for different components. Note to Practitioners —For nonlinear characteristics being between the independent variables and the dependent variables, this paper proposes the reinforced nonlinear model with update-driven for gas component perception. Based on the measured absorption spectra, the proposed method can deal with the nonlinearity more effective due to the use of neural networks. The update-driven strategy is adopted for modifying model without using the old data, namely, the new collected data are combined with loading matrices of the old model to update model. The proposed method can improve the performance of the component prediction for the gas sensing system, which is usually equipped for the olfactory perception of robot. Moreover, the proposed method can support engineers to focus on any interest analyte based on the actual requirements, and the proposed method would be developed for multicomponent analysis.

Data-defect would affect the data quality and the analysis results of data mining. This paper presents a data-defect inspection method with kernel-neighbor-density-change outlier factor (KNDCOF). The definition of kernel neighbor density is proposed to represent the density of each object in database, and the ascending distance series (ADS) of each object is calculated based on the kernel distance between the object and its neighbors. Then, the average density fluctuation (ADF) of the object is established according to the weighted sum of the square of density difference between the object and others in ADS. Finally, the KNDCOF of the object is equal to the ratios of the ADF of the object and the average ADF of neighbors of the object. The degree of the object being an outlier is indicated by the KNDCOF value. The experiments are performed on three real data sets to evaluate the effectiveness of the proposed method. The experimental results verify that the proposed method has higher quality of data-defect inspection and does not increase the time complexity.

In this paper, we deal with the learning problem when using an adaptive filtering method. For the learning system in filtering, the knowledge is obtained and updated based on the newly acquired information that is extracted and learned from the sequential samples over time. Effective measurement on the informativeness of a sample and reasonable subsequent treatment on the sample will improve the learning performance. This paper proposes a sequential outlier criterion for sparsification of online adaptive filtering. The method is proposed to achieve effective informativeness measurement of online filtering to obtain a more accurate and more compact network in the learning process. In the proposed method, the measurement on the samples' informativeness is established based on the historical sequentially adjacent samples, and then the informative-measured samples are treated individually by the learning system based on whether the sample is informative, redundant, or abnormal. With our method, a more sensible learning process can be achieved with valid knowledge extracted, and the optimal network in the learning system can be obtained. Simulations based on static function estimation, Mackey-Glass time series prediction, and Lorenz chaotic time series prediction demonstrate that the proposed method can provide more effective classification on samples and more accurate networks in online adaptive filtering.

Accurate high-temperature measurement is very important for process monitoring of an industrial system. Infrared thermometers usually can handle no more than 1000 °C and should use some expensive accessories for higher temperature measurements. This paper proposes a low-cost pyrometry system with nonlinear multisense partial least squares (NMSPLS). The ordinary camera with different filters is designed to collect the images of hot object at different wavelengths, and the NMSPLS is presented for predicting the temperature of the hot object from the obtained images. For the proposed method, the obtained images are represented by the multisense tensor, where red, green, and blue are regarded as three different dimensions in a sense of the tensor, respectively. The proposed method integrates an outer model and a nonlinear inner model. For the outer model, the independent variables and the dependent variables are projected into a low-dimensional common latent subspace. The weight matrices are calculated from the independent variables by the tucker decomposition, and the single value decomposition is adopted for extracting the latent variables (Lvs) based on the covariance between the independent variables and the dependent variables. For the nonlinear inner model, the neural network is adopted and the extracted Lvs are used as the input and the output of the neural network, respectively. Two real experiments are performed for estimating the proposed method. The experimental results verify that the proposed method can be applied for pyrometry and have higher effectiveness.

For autonomous robots, the Fuzzy C-means algorithm (FCM) is used in the tasks like self-position estimation, path planning and environment navigation. This paper proposes a suspect point recheck method for fuzzy clustering algorithm. First, the proposed method works as the typical FCM to obtain an original clustering result. Then the method classifies all the data points into normal points and suspect points according to their memberships of each cluster. Finally, the method redistributes the suspect points according to the information of their nearby normal points. Three datasets from UCI Machine Learning Repository are used in the experiments. The experimental results verify that the proposed method has higher clustering capability.