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Due to the advantages of fast training speed and competitive performance, Broad Learning System (BLS) has been widely used for classification tasks across various domains. However, the random weight generation mechanism in BLS makes the model unstable, and the performance of BLS may be limited when dealing with some complex datasets. On the other hand, the instability of BLS brings diversity to ensemble learning, and ensemble methods can also reduce the variance and bias of the single BLS. Therefore, we propose an ensemble learning algorithm based on BLS, which includes three modules. To improve the stability and generalization ability of BLS, we utilize BLS as the base classifier in an AdaBoost framework first. Taking advantage of the incremental learning mechanism of BLS, we then propose a selective ensemble method to raise the accuracy and diversity of the BLS ensemble method. In addition, based on the former selective Adaboost framework, we suggest a hierarchical ensemble algorithm, which combines sample and feature dimensions to further improve the fitting ability of the ensemble BLS. Extensive experiments have demonstrated that the proposed method performs better than the original BLS and other state-of-the-art models, proving the effectiveness and versatility of our proposed approaches.

Imbalanced data poses a substantial challenge to conventional classification methods, which often disproportionately favor samples from the majority class. To mitigate this issue, various oversampling techniques have been deployed, but opportunities for optimizing data distributions remain underexplored. By exploiting the ability of metric learning to refine the sample distribution, we propose a novel approach, Imbalance Large Margin Nearest Neighbor (ILMNN). Initially, ILMNN is applied to establish a latent feature space, pulling intra-class samples closer and distancing inter-class samples, thereby amplifying the efficacy of oversampling techniques. Subsequently, we allocate varying weights to samples contingent upon their local distribution and relative class frequency, thereby equalizing contributions from minority and majority class samples. Lastly, we employ Kullback-Leibler (KL) divergence as a safeguard to maintain distributional similarity to the original dataset, mitigating severe intra-class imbalances. Comparative experiments on various class-imbalanced datasets verify that our ILMNN approach yields superior results.

Recently, rule-based classification on multivariate time series (MTS) data has gained lots of attention, which could improve the interpretability of classification. However, state-of-the-art approaches suffer from three major issues. 1) few existing studies consider temporal relations among features in a rule, which could not adequately express the essential characteristics of MTS data. 2) due to the concept drift and time warping of MTS data, traditional methods could not mine essential characteristics of MTS data. 3) existing online learning algorithms could not effectively update shapelet-based temporal association rules of MTS data due to its temporal relationships among features of different variables. To handle these issues, we propose an online learning method for temporal association rule on dynamically collected MTS data (OTARL). First, a new type of rule named temporal association rule is defined and mined to represent temporal relationships among features in a rule. Second, an online learning mechanism with a probability correlation-based evaluation criterion is proposed to realize the online learning of temporal association rules on dynamically collected MTS data. Finally, an ensemble classification approach based on maximum-likelihood estimation is advanced to further enhance the classification performance. We conduct experiments on ten real-world datasets to verify the effectiveness and efficiency of our approach.

Single Image Super-Resolution (SISR) aims to reconstruct a high-resolution image from its corresponding low-resolution input. A common technique to enhance the reconstruction quality is Non-Local Attention (NLA), which leverages self-similar texture patterns in images. However, we have made a novel finding that challenges the prevailing wisdom. Our research reveals that NLA can be detrimental to SISR and even produce severely distorted textures. For example, when dealing with severely degrade textures, NLA may generate unrealistic results due to the inconsistency of non-local texture patterns. This problem is overlooked by existing works, which only measure the average reconstruction quality of the whole image, without considering the potential risks of using NLA. To address this issue, we propose a new perspective for evaluating the reconstruction quality of NLA, by focusing on the sub-pixel level that matches the pixel-wise fusion manner of NLA. From this perspective, we provide the approximate reconstruction performance upper bound of NLA, which guides us to design a concise yet effective Texture-Fidelity Strategy (TFS) to mitigate the degradation caused by NLA. Moreover, the proposed TFS can be conveniently integrated into existing NLA-based SISR models as a general building block. Based on the TFS, we develop a Deep Texture-Fidelity Network (DTFN), which achieves state-of-the-art performance for SISR. Our code and a pre-trained DTFN are available on GitHub† for verification.

This article investigates the fixed-time attitude control problem of quadrotor unmanned aerial vehicles (QUAVs) subject to stochastic disturbances. A fixed-time stability criterion for stochastic systems, which can compress the upper bound of the convergence time compared with the fixed-time stable Lyapunov theorem commonly used in the existing works, is proposed and theoretically proofed. The impact of stochastic disturbances on a QUAV is considered and a stochastic model of the attitude system of a QUAV is established. Based on the proposed criterion, a novel fixed-time attitude tracking controller for QUAV is designed, which can theoretically ensure the stability of attitude tracking within a fixed-time frame. To demonstrate the effectiveness of the controller, a simulation example is presented. A simulation comparison of different methods is also conducted. By artificially adding stochastic disturbances to the attitude angular velocity signals from sensors, an experiment is carried out on the three-DoF QUAV experimental platform. The experimental results show the feasibility of the designed control method in practical application.

In this article, a proactive control strategy is developed for robots interacting with humans by integrating the estimation of human partner's motion intention. A human control model is used and a least square-based observer is employed to estimate the human control input without a force sensor. Using the estimate of the human intention, a neural network (NN)-enhanced robot controller is designed to make the robot actively follow the human trajectory. NNs are integrated into robot controller to approximate and compensate the system uncertainties, so that a tracking performance can be guaranteed. Rigorous analysis based on Lyapunov theory proves that all the error signals are uniformly ultimately bounded. Implementations show that the proposed control method has adaptive properties.

This article investigates the adaptive optimal tracking problem for a class of nonlinear affine systems with asymmetric Prandtl–Ishlinskii (PI) hysteresis nonlinearities based on actor-critic (A-C) learning mechanisms. Considering the huge obstacles arising from the uncertainty of hysteresis nonlinearity in actuators, we develop a scheme for the conflict between the construction of Hamilton functions and hysteresis nonlinearity. The actuator hysteresis forces the input into a hysteresis delay, thus preventing the Hamilton function from getting the current moment’s input instantly and thus making optimization impossible. In the first step, an inverse model is constructed to compensate for the hysteresis model with a shift factor. In the second step, we compensate for the control input by designing a feedback controller and incorporating the estimation and approximation errors into the Hamilton error. Optimal control, the other part of the actual control input, is obtained by taking partial derivatives of the Hamiltonian function after the nonlinearities have been circumvented. At the end, a simulation is given to validate the developed solution.

Broad learning system (BLS) with semi-supervised learning relieves label dependence and expands application. Despite some efforts and progress, the semi-supervised BLS still needs improvement, especially in handling imbalanced data or concept drift scenarios for self-training-based methods. To this extent, this article proposes a robust semi-supervised BLS guided by ensemble-based self-training (ESTSS-BLS). Distinctive to self-training that assigns the pseudo-label via a single classifier and confidence, the advocated ensemble-based self-training determines the pseudo-label according to the turnout of multiple BLSs. In addition, label purity is proposed to ensure the correctness and credibility of the auxiliary training data, which is a comprehensive evaluation of the voting. During iterative learning, a small portion of labeled data first trains multiple BLSs in parallel. Then, the system recursively updates its data, structure, and meta-parameters using label purity and a data-driven dynamic nodes mechanism that dynamically guides the network’s structural adjustments to solve the concept drift problem caused by a large amount of auxiliary training data. The experimental results demonstrate that ESTSS-BLS exhibits exceptional performance compared to existing methods, with the lowest-time consumption and the highest accuracy, precision, recall, F1 score, and AUC. Exhilaratingly, it achieves an accuracy of 87.84% with only 0.1% labeled data on MNIST, and with just 2% labeled data, it matches the performance of supervised learning using all training data on NORB. In addition, ESTSS-BLS also performs stably on medical or biological data, verifying its high adaptability.

Broad learning system (BLS), which emerges as a lightweight network paradigm, has recently attracted great attention for recognition problems due to its good balance between efficiency and accuracy. However, the supervision mechanism in BLS and its variants generally relies on the strict binary label matrix, which imposes limitations on approximation and fails to adequately align with the data distribution. To address this issue, in this article, two novel flexible label-induced BLS models with the manifold manner are proposed, whose notable characteristics are as follows. First, two proposed label relaxation strategies can both enlarge the margins between different categories and simultaneously enhance the diversity within labels. Second, the integration of manifold geometrical criterion enables the models to capture local feature structures, ensuring the obtained flexible labels align better with the similarity between samples. Third, the proposed models can be optimized efficiently with the alternating direction method of multipliers. Each iteration benefits from a closed-form solution, facilitating the optimization process. Extensive experiments and thorough theoretical analysis are intended to show the advantages of our proposed models compared to other state-of-the-art recognition algorithms.

Multiview multi-instance multilabel learning (M3L) is a popular research topic during the past few years in modeling complex real-world objects such as medical images and subtitled video. However, existing M3L methods suffer from relatively low accuracy and training efficiency for large datasets due to several issues: 1) the viewwise intercorrelation (i.e., the correlations of instances and/or bags between different views) are neglected; 2) the diverse correlations (e.g., viewwise intercorrelation, interinstance correlation, and interlabel correlation) are not jointly considered; and 3) high computation burden for training process over bags, instances, and labels across different views. To resolve these issues, a novel framework called fast broad M3L (FBM3L) is proposed with three innovations: 1) utilization of viewwise intercorrelation for better modeling of M3L tasks while existing M3L methods have not considered; 2) based on graph convolutional network (GCN) and broad learning system (BLS), a viewwise subnetwork is newly designed to achieve joint learning among the diverse correlations; and 3) under BLS platform, FBM3L can learn multiple subnetworks jointly across all views with significantly less training time. Experiments show that FBM3L is highly competitive (or even better than) in all evaluation metrics [up to 64% in average precision (AP)] and much faster than most M3L (or MIML) methods (up to 1030 times), especially on large multiview datasets (≥260 K objects).

This article investigates the event-driven finite-horizon optimal consensus control problem for multiagent systems with symmetric or asymmetric input constraints. Initially, in order to overcome the difficulty that the Hamilton–Jacobi–Bellman equation is time-varying in finite-horizon optimal control, a single critic neural network (NN) with time-varying activation function is applied to obtain the approximate optimal control. Meanwhile, for minimizing the terminal error to satisfy the terminal constraint of the value function, an augmented error vector containing the Bellman residual and the terminal error is constructed to update the weight of the NN. Furthermore, an improved learning law is proposed, which relaxes the tricky persistence excitation condition and eliminates the requirement of initial stability control. Moreover, a specific algorithm is designed to update the historical dataset, which can effectively accelerate the convergence rate of network weight. In addition, to improve the utilization rate of the communication resource, an effective dynamic event-triggering mechanism (DETM) composed of dynamic threshold parameters (DTPs) and auxiliary dynamic variables (ADVs) is designed, which is more flexible compared with the ADV-based DETM or DTP-based DETM. Finally, to support the effectiveness of the proposed method and the superiority of the designed DETM, a simulation example is provided.

In this article, we study the predefined-time adaptive control problem for a class of strict-feedback nonlinear systems with parametric uncertainties and disturbances. A new practical predefined time stable (PPTS) criterion is first presented as the theoretical basis of predefined time control design, and then a new nonlinear command filter is designed. Based on the established PPTS criterion and backstepping control design technique, a command filter-based predefined time adaptive backstepping control scheme is developed. The proposed control method can guarantee the control system to be PPTS and the tracking error converges to a small neighborhood around zero. Moreover, it can overcome the computational complexity and control singular problems. Finally, the simulation and comparisons are provided to verify the predefined time control performance.

Feature selection is a highly regarded research area in the field of data mining, as it significantly enhances the efficiency and performance of high-dimensional data analysis by eliminating redundant and irrelevant features. Despite the ease of data acquisition, labeling data remains a laborious and expensive task. To leverage the abundance of unlabeled data, researchers have proposed various feature selection methods that operate with limited labels, including semi-supervised feature selection and unsupervised feature selection. However, a comprehensive review encompassing a thorough overview of feature selection algorithms with limited labels is lacking. To bridge this gap, this paper conducts a comprehensive exploration of feature selection methods specifically tailored to limited-label scenarios. These methods are systematically classified into two primary categories: semi-supervised and unsupervised feature selection. Additionally, by introducing a novel taxonomy and discussing future challenges, this survey aims to provide researchers with a comprehensive and in-depth understanding of feature selection in limited-label scenarios. Moreover, it aims to offer valuable insights that can guide further research and development in this domain.

This paper investigates adaptive neural network filtering control for uncertain nonlinear systems with general model state and input quantization. The plants under consideration contain quantized states, quantized input, and unknown nonlinear system functions. A universal quantizer is established for both system states and control input. In the control design process, neural networks and the command filter are used to approximate the unknown nonlinear system functions and overcome the discontinuities of virtual control signals, respectively. A new command filtering-based control strategy is proposed using the backstepping design technique. It is testified that the proposed control approach can guarantee that the closed-loop signals are semi-global uniform ultimate boundedness. A simulation example is presented to further demonstrate our proposed scheme’s effectiveness. Note to Practitioners—This work is motivated by the quantized control problem for a class of nonlinear systems with state and input quantization. In modern control engineering applications, quantization plays a crucial role due to the prevalent use of digital processors that operate with finite precision arithmetic. It is valuable and inevitable to minimize information flow, reduce communication burden, and improve system security. However, quantization will introduce significant discontinuous characteristics and strong nonlinearity, which may decrease the system’s performance and even drive the closed-loop system to instability. This paper demonstrates how to use backstepping and adaptive control methods with command filter to complete controller design and deal with the quantization effects. Therefore, it provides a feasible approach for engineering applications.

Traditional partition-based clustering is very sensitive to the initialized centroids, which are easily stuck in the local minimum due to their nonconvex objectives. To this end, convex clustering is proposed by relaxing $K$ -means clustering or hierarchical clustering. As an emerging and excellent clustering technology, convex clustering can solve the instability problems of partition-based clustering methods. Generally, convex clustering objective consists of the fidelity and the shrinkage terms. The fidelity term encourages the cluster centroids to estimate the observations and the shrinkage term shrinks the cluster centroids matrix so that their observations share the same cluster centroid in the same category. Regularized by the $\ell _{p_{n}}$ -norm ( $p_{n}\in \{1,2,+\infty \}$ ), the convex objective guarantees the global optimal solution of the cluster centroids. This survey conducts a comprehensive review of convex clustering. It starts with the convex clustering as well as its nonconvex variants and then concentrates on the optimization algorithms and the hyperparameters setting. In particular, the statistical properties, the applications, and the connections of convex clustering with other methods are reviewed and discussed thoroughly for a better understanding the convex clustering. Finally, we briefly summarize the development of convex clustering and present some potential directions for future research.

This article studies the problem of an adaptive fuzzy predefined-time tracking control approach for a type of uncertain nonstrict-feedback high-order nonlinear systems with input quantization. The considered plants contain unknown nonlinear functions, input quantization, and external disturbances. Based on the backstepping recursive technique and predefined-time stability criterion, a fuzzy adaptive predefined-time control strategy is presented. To address the difficulties posed by the uncertain nonlinearities within the original systems, the fuzzy logic systems are incorporated into estimate the unknown nonlinear functions, while power integrator technology is used to overcome the hurdle presented by high-order terms. Using the predefined-time Lyapunov stability theory, the system stability analysis is provided, and it is proved that all signals in the closed-loop system are bounded within the preset time interval. Ultimately, the effectiveness of the presented control approach is corroborated through numerical simulation.

Humans are able to compliantly interact with the environment by adapting its motion trajectory and contact force. Robots with the human versatility can perform contact tasks more efficiently with high motion precision. Motivated by multiple capabilities, we develop an approximation-based admittance control strategy that adapts and tracks the trajectory with guaranteed performance for the robots interacting with unknown environments. In this strategy, the robot can adapt and compensate its feedforward force and stiffness to interact with the unknown environment. In particular, a reference trajectory is generated through the admittance control to achieve a desired interaction level. To improve the interaction performance, a tracking error bound for both the transient and steady states is prespecified, and a controller is designed to ensure the tracking control performance. In the presence of unknown robot dynamics, neural networks are integrated into tracking controller to compensate uncertainties. The stability and convergence conditions of the closed-loop system are analysed by the Lyapunov theory. The effectiveness of the proposed control method is demonstrated on the Baxter robot.

Feature mining is a challenging work in the field of multivariate time series (MTS) data mining. Traditional methods suffer from three major issues. 1) Learned shapelets may seriously diverge from original subsequences since learning methods do not restrain the learned ones similar to raw sequences, which reduces interpretability. 2) Existing rule mining methods just generate association rules based on feature combination of different variables without considering temporal relations among features, which could not adequately express the essential characteristics of MTS data. 3) Most deep learning methods only mine global and high-level features of MTS data, which affects interpretability. To address these issues, we propose a temporal association rule mining method based on Generative Adversarial Network (GAN) called TAR-GAN. First, a shapelet mining method based on GAN (SGAN) is advanced to discover dataset-level and sample-level shapelets of all variables in MTS data. Second, a Temporal Graph based Rule Mining method (TGRM) is introduced to discover temporal association rules based on the temporal relationships among shapelets of different variables. Meanwhile, a Fast Convolution-based Similarity Measure methods (FCSM) is introduced to measure the similarity between MTS samples and temporal association rules. Furthermore, an adversarial training strategy is introduced to ensure the effectiveness and stability of generated temporal association rules, which could reflect the essential characteristics of MTS data. Extensive experiments on 12 datasets show the effectiveness and efficiency of our method.

Imbalanced data biases the classifier towards the majority class. Accompanied with high-dimensional characteristics, classification performance is further degraded. Existing researches for skewed data mainly involve resampling, cost-sensitive learning, and classifier ensemble. However, these approaches have some limitations: 1) resampling suffers from noisy and redundant features in high-dimensional skewed data; 2) cost-sensitive learning is hard to construct an optimal cost matrix for sample misclassification; 3) ensemble with random feature subspace easily leads to information loss; 4) ensemble with sample subspace on small-size data easily leads to insufficient description of sample space and suffers from negative impacts of high-dimensional data. This paper proposes an improved contraction-expansion subspace ensemble (ICESE) for high-dimensional imbalanced data classification. First, a contraction-expansion subspace optimization (CESO) is designed to perform subspace selection and transformation, which is beneficial for enhancing the discrimination and diversity of subspace. Then, to strengthen classification capabilities, a CESO-based multilayer optimization structure is developed to construct the improved subspace. Finally, to mitigate the effects of skewed data, ICESE performs a resampling scheme on the improved subspace for constructing a rebalanced subset to base classifier. Experimental results on 24 high-dimensional imbalanced data sets demonstrate that our ICESE outperforms different mainstream ensemble systems in terms of F-score and G-mean.

A novel neural network, namely, broad learning system (BLS), has shown impressive performance on various regression and classification tasks. Nevertheless, most BLS models may suffer serious performance degradation for contaminated data, since they are derived under the least-squares criterion which is sensitive to noise and outliers. To enhance the model robustness, in this article we proposed a modal-regression-based BLS (MRBLS) to tackle the regression and classification tasks of data corrupted by noise and outliers. Specifically, modal regression is adopted to train the output weights instead of the minimum mean square error (MMSE) criterion. Moreover, the $\ell _{2,1}$ -norm-induced constraint is used to encourage row sparsity of the connection weight matrix and achieve feature selection. To effectively and efficiently train the network, the half-quadratic theory is used to optimize MRBLS. The validity and robustness of the proposed method are verified on various regression and classification datasets. The experimental results demonstrate that the proposed MRBLS achieves better performance than the existing state-of-the-art BLS methods in terms of both accuracy and robustness.

Graph representation learning focuses on abstracting critical information from raw graphs. Unfortunately, there always exist various kinds of uncertainties, such as attribute noise and network topology corruption, in raw graphs. Under the message passing mechanism, certainties are likely to spread throughout the whole graph. Matters like these would induce deep graph models into producing uncertain representations and restrict representation expressiveness. Considering this, we propose a pioneering framework to defend graph uncertainties by improving the robustness and capability of graph neural networks (GNNs). In our framework, we consider that weights and biases are all fuzzy numbers, thus generating representations to assimilate graph uncertainties, which are finally released by defuzzification. To describe the process of the framework, in this article, a graph convolutional network (GCN) is employed to construct a robust graph model, called FuzzyGCN. To verify the effectiveness of FuzzyGCN, it is trained in both supervised and unsupervised ways. In the supervised setting, we find that FuzzyGCN has stronger power and is more immune to data uncertainties when compared with various classical and robust GNNs. In the unsupervised setting, FuzzyGCN surpasses many state-of-the-art models in node classification and community detection over several real-world datasets.

Image outpainting is a challenge for image processing since it needs to produce a big scenery image from a few patches. In general, two-stage frameworks are utilized to unpack complex tasks and complete them step-by-step. However, the time consumption caused by training two networks will hinder the method from adequately optimizing the parameters of networks with limited iterations. In this article, a broad generative network (BG-Net) for two-stage image outpainting is proposed. As a reconstruction network in the first stage, it can be quickly trained by utilizing ridge regression optimization. In the second stage, a seam line discriminator (SLD) is designed for transition smoothing, which greatly improves the quality of images. Compared with state-of-the-art image outpainting methods, the experimental results on the Wiki-Art and Place365 datasets show that the proposed method achieves the best results under evaluation metrics: the Fréchet inception distance (FID) and the kernel inception distance (KID). The proposed BG-Net has good reconstructive ability with faster training speed than those of deep learning-based networks. It reduces the overall training duration of the two-stage framework to the same level as the one-stage framework. Furthermore, the proposed method is adapted to image recurrent outpainting, demonstrating the powerful associative drawing capability of the model.

A graph neural network (GNN) is a powerful architecture for semi-supervised learning (SSL). However, the data-driven mode of GNNs raises some challenging problems. In particular, these models suffer from the limitations of incomplete attribute learning, insufficient structure capture, and the inability to distinguish between node attribute and graph structure, especially on label-scarce or attribute-missing data. In this article, we propose a novel framework, called graph coneighbor neural network (GCoNN), for node classification. It is composed of two modules: GCoNN $_{\Gamma }$ and GCoNN $_{\mathop {\Gamma }\limits ^{\circ }}$ . GCoNN $_{\Gamma }$ is trained to establish the fundamental prototype for attribute learning on labeled data, while GCoNN $_{ {\mathop {\Gamma }\limits ^{\circ }}}$ learns neighbor dependence on transductive data through pseudolabels generated by GCoNN $_{\Gamma }$ . Next, GCoNN $_{\Gamma }$ is retrained to improve integration of node attribute and neighbor structure through feedback from GCoNN $_{ {\mathop {\Gamma }\limits ^{\circ }}}$ . GCoNN tends to convergence iteratively using such an approach. From a theoretical perspective, we analyze this iteration process from a generalized expectation–maximization (GEM) framework perspective which optimizes an evidence lower bound (ELBO) by amortized variational inference. Empirical evidence demonstrates that the state-of-the-art performance of the proposed approach outperforms other methods. We also apply GCoNN to brain functional networks, the results of which reveal response features across the brain which are physiologically plausible with respect to known language and visual functions.

This article focuses on the singularity-free predefined time control design problem of the quantized nonstrict feedback (NSF) nonlinear systems. Radial basis function neural networks (NNs) are introduced to model the unknown nonlinear dynamics. With the property of the NN basis function, the algebraic loop problem posed by the NSF control structures is addressed. The input quantization is addressed by using the nonlinear decomposition technique. A nonlinear filter with predefined time stability is constructed to decrease the computational complexity. Further, by introducing the designed predefined time filter into the backstepping recursive framework, a predefined time dynamic surface control algorithm is developed, in which the improved adding power integration technique is introduced to prevent control singularities. The Lyapunov theory demonstrates the predefined time stability of the closed-loop quantized nonlinear systems. By the developed control algorithm, the controlled system can effectively track the specified command signal. Both the tracking and filtering errors can reach a small neighborhood around zero within the preset time. The validity and superiority of the proposed control algorithm are illustrated by an actual system simulation.

This article investigates the adaptive optimal output-feedback consensus tracking problem for nonlinear multiagent systems (MASs). Although adaptive optimal output-feedback control schemes for nonlinear systems have been developed recently, most results do not consider the two-way interaction between the state observer and its associated subsystem. To address this issue, we formulate the state-observer and the subsystem as a two-player Stackelberg game framework, where the state-observer acts as the follower-player and the subsystem acts as the leader-player. Such a framework helps us to reveal the two-way interaction between the subobserver and the subsystem. Based on this, we design the optimal auxiliary input of the state-observer and the optimal subsystem controller. We implement the optimal policy pair using integral reinforcement learning (IRL) and adaptive critic learning, which provides a critic-only structure. We prove that the Stackelberg-Nash equilibrium is reached and that the closed-loop signals are ultimately uniformly bounded (UUB). We demonstrate the effectiveness of the proposed scheme using a numerical simulation example.

Optimizing a performance objective during control operation while also ensuring constraint satisfactions at all times is important in practical applications. Existing works on solving this problem usually require a complicated and time-consuming learning procedure by employing neural networks, and the results are only applicable for simple or time-invariant constraints. In this work, these restrictions are removed by a newly proposed adaptive neural inverse approach. In our approach, a new universal barrier function, which is able to handle various dynamic constraints in a unified manner, is proposed to transform the constrained system into an equivalent one with no constraint. Based on this transformation, a switched-type auxiliary controller and a modified criterion for inverse optimal stabilization are proposed to design an adaptive neural inverse optimal controller. It is proven that optimal performance is achieved with a computationally attractive learning mechanism, and all the constraints are never violated. Besides, improved transient performance is obtained in the sense that the bound of the tracking error could be explicitly designed by users. An illustrative example verifies the proposed methods.

Machine learning aims to generate a predictive model from a training dataset of a fixed number of known classes. However, many real-world applications (such as health monitoring and elderly care) are data streams in which new data arrive continually in a short time. Such new data may even belong to previously unknown classes. Hence, class-incremental learning (CIL) is necessary, which incrementally and rapidly updates an existing model with the data of new classes while retaining the existing knowledge of old classes. However, most current CIL methods are designed based on deep models that require a computationally expensive training and update process. In addition, deep learning based CIL (DCIL) methods typically employ stochastic gradient descent (SGD) as an optimizer that forgets the old knowledge to a certain extent. In this article, a broad learning system-based CIL (BLS-CIL) method with fast update and high retainability of old class knowledge is proposed. Traditional BLS is a fast and effective shallow neural network, but it does not work well on CIL tasks. However, our proposed BLS-CIL can overcome these issues and provide the following: 1) high accuracy due to our novel class-correlation loss function that considers the correlations between old and new classes; 2) significantly short training/update time due to the newly derived closed-form solution for our class-correlation loss without iterative optimization; and 3) high retainability of old class knowledge due to our newly derived recursive update rule for CIL (RULL) that does not replay the exemplars of all old classes, as contrasted to the exemplars-replaying methods with the SGD optimizer. The proposed BLS-CIL has been evaluated over 12 real-world datasets, including seven tabular/numerical datasets and six image datasets, and the compared methods include one shallow network and seven classical or state-of-the-art DCIL methods. Experimental results show that our BIL-CIL can significantly improve the classification performance over a shallow network by a large margin (8.80%–48.42%). It also achieves comparable or even higher accuracy than DCIL methods, but greatly reduces the training time from hours to minutes and the update time from minutes to seconds.

Target tracking is difficult to achieve high accurate and efficient results due to the cases of occlusion, scale variation, and fast motion in the tracking process. In recent years, feature fusion and bounding box refinement are used as an extent to improve the accuracy of tracking. However, these new methods generally require multilevel linkage and offline training, which need long training time, and affects the portability of the algorithm. In this article, a novel method is proposed to improve the tracking accuracy using broad learning system (BLS). The proposed method trains Intersection over Union (IoU) network based on BLS, which is called BLIoU for scale and drift correction in target tracking. BLIoU learns target features and IoU discrimination ability of bounding box through network training, which can be combined with any baseline tracking methods. BLIoU performs scale correction in the case of accurate positioning of the baseline tracker and drift correction in the case of inaccurate positioning. In Experiments, several benchmark datasets are used, BLIoU improves the tracking performance of the baseline tracker through scale and drift correction, with short training time and strong portability.

Despite the recent development of distributed constrained optimization algorithms in the literature, it is still a challenging issue to construct distributed algorithms to efficiently solve the constrained optimization problem with convergence rate guarantees, especially for the case with general constraints and unbalanced time-varying digraphs. This article aims to investigate the distributed discrete-time optimization problem over time-varying unbalanced digraphs with general constraints including the nonidentical closed convex set constraints, the multiple equality, and inequality constraints. Toward this end, a new kind of distributed discrete-time algorithm synthesizing some graph topology-dependent row stochastic and column stochastic weight matrix sequences is proposed and employed. In virtue of a randomized constraint solving method, it is theoretically shown that the proposed algorithm can efficiently deal with the considered distributed optimization problem with a large number of inequality constraints and the inequality constraints that cannot be known in advance. Furthermore, the almost sure convergence of the proposed distributed constrained optimization algorithm is theoretically demonstrated under some mild assumptions. The explicit convergence rate for the designed distributed algorithm is provided, like the centralized counterpart. Finally, numerical simulations are given to verify the effectiveness of the present algorithm.

For a class of nontriangular structural multiagent systems, this article presents a neuro-adaptive prescribed performance consensus control scheme. By using mean value theorem to isolate the virtual variables and neural networks to approximate the ideal controller, the system model is reconstructed, based on which the virtual controllers are able to be derived. The algebraic-loop problem is circumvented utilizing the properties of basis function. With the proposed performance functions, an error transformation is presented, based on which the controller scheme is developed. It is ensured that the follower agents synchronize at a predefined speed, and synchronization error converges to a specified range within a given time. Two Simulations demonstrate the effectiveness of the presented control method.

At present, the dynamic encoding–decoding scheme is utilized in the impulsive consensus control of multiagent systems (MASs) to solve the limited bandwidth problem. However, the unknown nonlinear dynamics and deception attacks will generate some uncertainties inevitably in the encoding–decoding, which may cause the quantizer saturation and then influence the consensus performance. Therefore, the impulsive consensus control problem of uncertain nonlinear MASs based on encoding–decoding under deception attacks is investigated in this article. To address the system uncertainty, an adaptive algorithm with neural networks is designed. Under the proposed estimator for each follower, the designed adaptive law for every follower only needs the information from its own sensor and estimator instead of the quantized information from its neighbors. Then a more general scenario of uncertain deception attack is considered, in which the uncertain deception attacks can occur in the both parts of hybrid impulsive control protocol. An attack observer is introduced to handle this more complex attack by compensating impacts of deception attacks. Next the sufficient conditions for secure consensus of MASs with limited bandwidth are derived. Moreover, although some uncertainties exist in the encoding–decoding, the quantizer saturation can be eliminated by adjusting the parameters of controller. Finally, the validity of given theorems is demonstrated by the simulation experiments.

In this article, a fuzzy adaptive fixed-time asymptotic consistent control scheme is developed for a class of nonlinear multiagent systems (NMASs) with a nonstrict-feedback (NSF) structure. In the control process, a fixed-time consistency control method without control singularity is proposed by combining fuzzy logic systems (FLSs) with good approximation capability, fixed-time stability theory, and plus power integration techniques. Then, by using Barbalat’s Lemma, the asymptotic stability of tracking errors and the boundedness of the controlled systems are successfully achieved, which means that the tracking errors can converge to zero in a fixed time. Finally, the effectiveness of the designed control scheme is demonstrated by a simulation example.

In this article, an adaptive reinforcement learning (RL) control problem is explored for a class of nonstrict-feedback discrete-time systems. First, different from the existing results, considering the noncausal problem which may exist in the backstepping design procedure, a universal system transformation method is first proposed for a class of nonstrict-feedback discrete-time systems. Second, by defining a compensation term to compensate the controller and utilizing the property of radial-basis-function neural network (RBFNN), an RL-based direct adaptive control strategy is developed via a backstepping method to achieve optimal control, and the multigradient recursive (MGR) algorithm is employed to estimate the weight vector. Finally, the stability of the control system is guaranteed and all signals in the closed-loop system are semiglobal uniformly ultimately bounded (SGUUB) on the basis of the Lyapunov theory. In addition, a universal system transformation is first proposed which breaks through the limitations on the controller design for the discrete-time nonstrict-feedback nonlinear system by using the traditional method. The validity of this strategy is verified by two simulation examples that include a course keeping system of the marine vessel.

This paper is dedicated to the trajectory tracking control of under-actuated unmanned surface vessel (USV) with state and input quantization. In terms of kinematics, a distributed guidance law is introduced to track the time-varying trajectory of USV. In terms of kinetics, a fuzzy adaptive quantization control method rooted in an event-triggered mechanism is proposed. Uncertainties within the ship model are estimated through a fuzzy logic system, and a linear analytical model is employed to elucidate the input quantization process. This approach reduces the actuator's execution frequency, alleviates the communication burden and conserves valuable communication resources. The boundedness of the internal signals and quantization errors in the closed-loop system are substantiated by presenting some theoretical lemmas. Furthermore, the stability of the proposed control strategy is proved through Lyapunov stability theory. Finally, the effectiveness and feasibility of the proposed fuzzy adaptive quantization control strategy based on event-triggered mechanism are verified by simulation experiments.

In this article, we investigate the problem of optimizing the joint offloading policy in a distributed manner for multiple intelligent vehicles (IVs). During the journey in vehicular edge computing (VEC) networks, IVs continually optimize their joint offloading policy to minimize the long-term accumulated costs generated by executing computational tasks. The stochastic and repetitive interactions among IVs is modeled as a Markov game process. In this way, the optimization of the joint offloading policy is transformed to approximate a Markov perfect equilibrium in a general-sum Markov game. Moreover, we argue that training in the practical VEC networks using the classical centralized training and decentralized executing (CTDE) framework involves challenges of privacy and computational complexity. Motivated by these, we propose a reward-shared distributed policy optimization (RSDPO) method for the considered VEC networks to optimize the joint offloading policy. The experimental results demonstrate that the set of joint offloading policies using RSDPO approximates a Markov perfect equilibrium, and our RSDPO presents significant advantages in terms of converged latency and energy consumption compared with other methods.

Currently, most Discriminative Correlation Filters (DCF) algorithms used for Unmanned Aerial Vehicle (UAV) target tracking primarily focus on improving the tracking model. However, in UAV tracking, the tracked targets are typically small in size and frequently undergo scale variations, making singular improvements to tracking models less effective. As a response to this challenge, we propose a novel feature preprocessing approach. Specifically, for the extracted Histogram of Oriented Gradients (HOG) and Color Names (CN) features, we simulate their transformations at different scales and electively enhance the target region features based on global features to obtain multi-scale enhanced features. By implementing these procedures, the tracker improves its ability to recognize targets and exhibits increased adaptability in challenging tracking scenarios. Furthermore, in contrast to the conventional approach used by most UAV algorithms, which unidirectionally incorporate historical filters into model updates to prevent filter divergence, we introduce dual second-order difference terms that correspond to features and filters. This integration enables a more effective fusion of historical information with current frame data, thereby enhancing the robustness of the filtering process. Extensive experiments are conducted to evaluate the proposed tracker against other state-of-the-art trackers using the DTB70, UAV123@10fps, and UAVDT datasets. The experimental results affirm the effectiveness of our approach.

Promoting cooperation in the network has always been a focus of evolutionary game dynamics research. In this paper, a three-strategy local decision model is designed to promote cooperative behavior between agents. The hide right is introduced to accurately describe the agents which tend to choose conservative strategy to achieve stable payoffs. Agents only consider their own and non-defective neighbors’ payoffs information to make their decisions for next move. According to the adaptive dynamics, the equilibrium states under different conditions have been studied. It is found that the introduction of hide strategy helps to reduce the occurrence of defection. The conclusion of this paper will provide a reference for the cooperation promotion mechanism of selfish agents that are closer to the actual situation.

This article considers the finite-time consensus control issue of high-order multi-input and multi-output nonlinear multiagent systems. In the process of establishment, this article uses fuzzy logic systems to identify unknown nonlinear dynamics. Then, according to the backstepping recursive technique and finite-time stability criterion, a fuzzy adaptive finite-time consensus control scheme is designed. At the same time, a communication-restricted control scheme is established according to the dynamic event-triggered strategy with a relative threshold to reduce the execution time of the controller and save communication resources. In addition, a novel integral Lyapunov function is established by introducing the adding power integrator technology, which proves the stability and convergence of consensus tracking errors of closed-loop systems. Finally, taking a marine surface vehicle as an example, the availability of the established event-triggered consensus control scheme is described.

This article studies the optimized backstepping consensus control problem for uncertain nonstrict-feedback nonlinear multiagent systems with intermittent actuator faults and input quantization. A fuzzy approximation-based optimal consensus control scheme is proposed via the reinforcement learning algorithm. Meanwhile, a time-varying constraint function is embedded into the optimized backstepping consensus design to guarantee the consensus errors converge to a preassigned residual set within the prescribed time. To overcome the difficulty of the virtual optimized controller design caused by unknown virtual control coefficients, a class of intermediate variables is designed. A modified variable separation technique is proposed to circumvent the problem of algebraic loop caused by the construction of virtual optimized controllers. Then, based on the reconstruction of unknown bounds, a fault-tolerant controller under the quantization action is developed to compensate for the impact of unknown actuator faults automatically, and achieve semiglobally ultimately uniformly bounded results. In the end, a practical example of a group of single-link manipulators is given to illustrate the validity of the presented method.

This article investigates the problem of attitude stabilization for a quadrotor unmanned aerial vehicle (UAV) in the presence of parametric uncertainties, control input saturation, and external disturbances. Two robust adaptive control strategies, i.e., bounded adaptive control (BAC) and asymptotical adaptive control (AAC) are developed, respectively, where the construction of saturation auxiliary system and the design of adaptive laws for parameters and disturbance's bound are considered. As a result, the compensation of input saturation, the estimation of physical parameters, and the suppression of external disturbance are achieved. In BAC, the real attitude tracking error is guaranteed to converge to a neighborhood of zero, and its transient performance is constrained to an explicit bounded range. In AAC, the real attitude tracking error is proved to be asymptotically stable, and its transient bound in terms of $L_{2}$ norm is derived by constructing an auxiliary equation, which is a computable bound. The simulation is carried out to verify the robustness and effectiveness of the proposed two control techniques.

The training of the standard broad learning system (BLS) concerns the optimization of its output weights via the minimization of both training mean square error (MSE) and a penalty term. However, it degrades the generalization capability and robustness of BLS when facing complex and noisy environments, especially when small perturbations or noise appear in input data. Therefore, this work proposes a broad network based on localized stochastic sensitivity (BASS) algorithm to tackle the issue of noise or input perturbations from a local perturbation perspective. The localized stochastic sensitivity (LSS) prompts an increase in the network’s noise robustness by considering unseen samples located within a $Q$ -neighborhood of training samples, which enhances the generalization capability of BASS with respect to noisy and perturbed data. Then, three incremental learning algorithms are derived to update BASS quickly when new samples arrive or the network is deemed to be expanded, without retraining the entire model. Due to the inherent superiorities of the LSS, extensive experimental results on 13 benchmark datasets show that BASS yields better accuracies on various regression and classification problems. For instance, BASS uses fewer parameters (12.6 million) to yield 1% higher Top-1 accuracy in comparison to AlexNet (60 million) on the large-scale ImageNet (ILSVRC2012) dataset.

In this article, we propose a multiscale cross-connected dehazing network with scene depth fusion. We focus on the correlation between a hazy image and the corresponding depth image. The model encodes and decodes the hazy image and the depth image separately and includes cross connections at the decoding end to directly generate a clean image in an end-to-end manner. Specifically, we first construct an input pyramid to obtain the receptive fields of the depth image and the hazy image at multiple levels. Then, we add the features of the corresponding dimensions in the input pyramid to the encoder. Finally, the two paths of the decoder are cross-connected. In addition, the proposed model uses wavelet pooling and residual channel attention modules (RCAMs) as components. A series of ablation experiments shows that the wavelet pooling and RCAMs effectively improve the performance of the model. We conducted extensive experiments on multiple dehazing datasets, and the results show that the model is superior to other advanced methods in terms of peak signal-to-noise ratio (PSNR), structural similarity (SSIM), and subjective visual effects. The source code and supplementary are available at https://github.com/CCECfgd/MSCDN-master.

In recent years, the detection of infrared small targets using deep learning methods has garnered substantial attention due to notable advancements. To improve the detection capability of small targets, these methods commonly maintain a pathway that preserves high-resolution (HR) features of sparse and tiny targets. However, it can result in redundant and expensive computations. To tackle this challenge, we propose a sparse infrared-target detector (SpirDet) for the efficient detection of infrared small targets. Specifically, to cope with the computational redundancy issue, we employ a new dual-branch sparse decoder (DBSD) to restore the feature map. First, the fast branch directly predicts a sparse map indicating potential small-target locations. Second, the slow branch conducts fine-grained adjustments at the positions indicated by the sparse map. In addition, we design a lightweight DO-RepEncoder based on reparameterization with the downsampling orthogonality (DO), which can effectively reduce memory consumption and inference latency. Extensive experiments show that the proposed SpirDet significantly outperforms state-of-the-art (SOTA) models while achieving faster inference speed and fewer parameters. For example, on the NUDT-SIRST dataset, SpirDet improves mean intersection over union (MIoU) by 2.09 and has a $3.1\times $ frames/s acceleration compared to the previous SOTA model. The code is available at https://github.com/laCorse/SpirDet-Pytorch.

This paper presents an adaptive fixed-time command-filtered fuzzy controller design method of nonlinear stochastic systems subject to saturating input. Fuzzy logic systems (FLSs) can be utilized to fit the uncertainties. Inverse function theory is first introduced to tackle the design obstacle that exists in the input terminal, that is, saturating input. In particular, an improved fixed-time filter can be obtained to avert the difficulty of complexity explosion when the classic backstepping control strategy is adopted. Due to the adaptive control method, an adaptive fixed-time command-filtered fuzzy controller is proposed. The designed controller can assure that the states contained in nonlinear stochastic systems are bounded and the tracking error can tend to a small interval near the original point within the time interval. Finally, two examples are provided to further demonstrate the effectiveness of the controller design strategy.

Multi-label classification is a challenging problem that has attracted significant attention from researchers, particularly in the domain of image and text attribute annotation. However, multi-label datasets are prone to serious intra-class and inter-class imbalance problems, which can significantly degrade the classification performance. To address the above issues, we propose the multi-label weighted broad learning system (MLW-BLS) from the perspective of label imbalance weighting and label correlation mining. Further, we propose the multi-label adaptive weighted broad learning system (MLAW-BLS) to adaptively adjust the specific weights and values of labels of MLW-BLS and construct an efficient imbalanced classifier set. Extensive experiments are conducted on various datasets to evaluate the effectiveness of the proposed model, and the results demonstrate its superiority over other advanced approaches.

Robust optimization (RO) has been recognized as an effective means to deal with unanticipated events in highly uncertain and risky environments. This paper systematically reviews two types of emerging RO machine scheduling approaches—robust machine scheduling (R-MS) and distributionally R-MS (DR-MS) methods—which usually offer tractable formulations and analytical results for machine scheduling problems under uncertainty. First, after highlighting the advantages of RO methods over the stochastic approach in terms of tractability and robustness, we use the bibliometric method to analyze the literature related to R-MS/DR-MS problems and classify them from the following aspects: (1) uncertain factors, (2) uncertainty descriptions, (3) robustness criteria, (4) machine environments and (5) solution methods. Second, we discuss the uncertainty descriptions, and the robust feasibility and robust optimality criteria. We further provide a state-of-the-art review of R-MS/DR-MS models in different machine environments and discuss the performance of the R-MS/DR-MS models. Third, we review and discuss the existing exact, approximation, online, and heuristic solution methods for solving R-MS/DR-MS models. Finally, we present future research opportunities in two promising areas: green machine scheduling problems and machine learning-enabled algorithms. Note to Practitioners—Machine scheduling plays an essential role in industrial and service systems, such as manufacturing, power generation, transportation and medical systems. However, in practice, scheduling systems usually operate in highly uncertain environments due to noisy measurements, prediction errors, and implementation deviations. To ensure robust feasibility and robust optimality, robust machine scheduling (R-MS) and distributionally R-MS (DR-MS) approaches have been recently proposed to hedge against the uncertainties related to processing time, release time, due date, machine breakdown, etc. This paper provides a comprehensive review of the R-MS/DR-MS models and algorithms in different machine environments from the aspects of uncertainty descriptions, robustness criteria and solution methods. This paper further highlights the challenges of R-MS problems and provides promising and valuable research opportunities in terms of problem formulations and algorithm designs.

This paper proposes an adaptive fuzzy output feedback control approach for quadrotor unmanned aerial vehicles (QUAV) with stochastic disturbances, besides which we consider the unmeasurable states and unknown nonlinear functions. The QUAV system contains stochastic terms which are not bounded and not differentiable. By combining the It $\hat {\rm \textbf {o}}$ differential equation with finite-time theory, a novel stochastic finite-time stability controller for QUAV is raised for the first time. The fuzzy logic system (FLS) is utilized to approximate the unknown nonlinear functions in the model. Dynamic surface control technology is introduced to reduce the complexity of differential. Furthermore, an observer with FLS is designed through the adaptive backstepping technique to estimate the immeasurable states. It is proved that this control approach can ensure that all states of the closed-loop QUAV system are semi-global and finite-time stable in probability. Meanwhile, the errors of system outputs and observer converge to a small neighborhood of origin. The simulation results show the effectiveness of the proposed method.Note to Practitioners—In practical applications, many systems are often affected by internal and external disturbances, and not all of them can be described by mathematical models, so they are called stochastic disturbances. Taking the QUAV as an example, when the system is disturbed by internal parameters, external environment, system input, sensor error, and other stochastic factors, the deterministic system can no longer accurately describe the controlled object. In this paper, the QUAV is regarded as a stochastic system for the first time, and a novel controller is designed to solve the above problems. In addition, the QUAV needs fast action in some applications, such as emergency collision avoidance, which has high requirements for the convergence performance of the controller. Therefore, studying the finite-time control for QUAV systems with stochastic disturbances is necessary. At the same time, this paper also considers the problem that the state is not measurable and the system contains unknown nonlinear equations.

Low-light remote sensing (RS) images generally feature high resolution and high spatial complexity, with continuously distributed surface features in space. This continuity in scenes leads to extensive long-range correlations in spatial domains within RS images. convolutional neural networks (CNNs), which rely on local correlations for long-distance modeling, struggle to establish long-range correlations in such images. On the other hand, transformer-based methods that focus on global information face high computational complexities when processing high-resolution RS images. From another perspective, the Fourier transform can compute global information without introducing a large number of parameters, enabling the network to more efficiently capture the overall image structure and establish long-range correlations. Therefore, we propose a dual-domain feature fusion network (DFFN) for low-light RS image enhancement. Specifically, this challenging task of low-light enhancement is divided into two more manageable subtasks: the first phase learns amplitude information to restore image brightness, and the second phase learns phase information to refine details. To facilitate information exchange between the two phases, we designed an information fusion affine block that combines data from different phases and scales. In addition, we have constructed two dark light RS datasets to address the current lack of datasets in dark light RS image enhancement. Extensive evaluations show that our method outperforms existing state-of-the-art methods. The code is available at https://github.com/iijjlk/DFFN.

In this article, we propose bionic swarm control based on second-order communication topology (SOCT) inspired by the migration of birds, which solves the difficulty in constructing communication topologies and high-computational complexity in controlling large-scale swarm systems. To realize bionic swarm control, there are three problems supposed to be solved. First, the adjacency matrix and the Laplacian matrix in traditional methods cannot be applied to SOCT directly, which should be redesigned. Second, sub-swarm systems formed based on 2-order communication topology (2-OCT) and independently distributed with each other also need to be put forward to reduce computational complexity. At last, the followers in 1-order communication topology (1-OCT) are set as the leaders of sub-swarm systems in 2-OCT. As a result, coupling in large-scale swarm systems would be reduced. The bionic swarm controller is designed through the backstepping method. In this case, the stability of bionic swarm controller is proven by the designed Lyapunov function. The simulations show the efficiency of the designed bionic swarm controller. And the tracking-containment control based on SOCT with 42 swarm members is realized.

A prescribed time fuzzy adaptive consensus control method is constructed for multiagent systems with sensor faults and dead-zone input. Sensor faults inevitably occur in actual engineering systems and may distort the state information. Besides, the control effect would be further dramatically affected when systems exist dead-zone input. Thus, a fuzzy adaptive compensation strategy is established by the bounded adaptive optimized method to eliminate the impact of the above constraints. Furthermore, a given performance consensus control method is investigated with the aid of nonlinear transformation. Meanwhile, combined with the prescribed time technology, it further achieves that the systems settling time can be preselected while the performance of the systems is given. Finally, some simulation experiments are adopted to demonstrate the feasibility and effectiveness of the investigated control method. Note to Practitioners—This work studies the consensus problem for multiagent systems, which is important in engineering collaborative applications. Due to measurement noise and electronic damage, sensor faults inevitably happen in industrial applications. Besides, dead-zone input often occurs in actual systems as physical properties of electronic components. Based on the bounded adaptive optimized method, a fuzzy adaptive compensation strategy is constructed to deal with those issues. To further improve the control performance in the collaborative process, prescribed time technology and given performance strategy are applied to construct the control method. The investigated approach can be useful in multiagent systems to achieve more steady consensus operation, which is more in line with the application requirements.