This work discusses the consensus tracking for stochastic multi-agent systems with a leader-follower structure. An observer-based distributed control approach is put forward, leveraging control Lyapunov functions and quadratic programming framework. This control method ensures that each follower can track with the leader's state in the sense of expectation, even under stochastic disturbances. Two observers are given for each follower to observe its own state and the leader's state information, respectively, enabling fully distributed control requirement. Theoretical analysis guarantees the convergence of this control approach, and simulation results validate its effectiveness in achieving consensus tracking.

Control barrier functions (CBFs) provide a rigorous framework for enforcing safety in control-affine systems by ensuring system states remain within predefined safe sets. However, practical deployment faces fundamental challenges that limit real-world applicability. This review analyzes recent progress in CBF methodologies across three interconnected domains: uncertainty handling, structural optimization, and feasibility assurance. For uncertainty, we distinguish strategies tailored to unknown dynamics, modeling discrepancies, and dynamic environments, spanning robust theoretical methods and learning-based approaches. For structural design, we examine class- $\mathcal {K}$ function selection, parameter tuning, and advanced modifications that jointly address conservatism and feasibility. For feasibility, we identify the root causes of CBF-QP infeasibility and survey solution strategies, including constraint relaxation, structural redesign, and mathematical guarantees. By synthesizing these directions into a unified framework, this review highlights key interdependencies and outlines future research opportunities for advancing CBF-based safety-critical control in robotics, autonomous systems, and beyond.

Model-based reinforcement learning (MBRL) aims to promote sample efficiency and reduce the number of interactions with the true environment, via learning an environment dynamic model, compared with model-free reinforcement learning (MFRL). However, the success of MBRL heavily relies on two key aspects: model learning and planning. The former refers to learning an accurate model, and the latter aims to improve the behavior policy. In this article, we investigate these two aspects further with model ensemble learning. We design a deep residual attention U-Net (RauNet) with fewer neurons (or weights) than the widely used shallow neural network as our base models and further apply the Hilbert–Schmidt independence criterion (HSIC) as a regularization term to pursue model diversity explicitly for the model ensemble. Furthermore, we propose an adaptive trust region policy optimization (TRPO), in which the parametric Rényi alpha divergence substitutes for the Kullback–Leibler (KL) divergence for measuring the difference between two successive policies, and the alpha value can be adaptively adjusted during TRPO training iterations. This method is called diversity-driven model ensemble adaptive TRPO, or simply diversity-driven model ensemble adaptive trust region policy optimization. Our detailed experiments on six benchmark environments show that our proposed approach is optimal, compared with five state-of-the-art RL techniques.

Recommender systems continuously strive to recommend items that the users potentially like accurately. Most recommender systems assume that latent user preferences and item features are linearly combined. However, the existing linear interaction patterns do not realistically reflect users’ decision-making processes. The formation of users’ opinions on items and the evolutionary preference interaction process among users needs to be explored. In our work, we bridge social psychology and recommender systems to develop a social recommendation model, nonlinearly utilizing latent user preferences and item features to simulate the intrinsic formation of users’ decision-making. We extend the cognitive opinion formation mechanism by improving the two-stage process and seamlessly combine it and matrix factorization, simulating the nonlinear interactions between users and items. We incorporate the implicit user influence and explicit social dynamics with bounded confidence effect into the nonlinear cognitive recommendation framework to characterize the evolutionary preference interactions among users. We conduct comprehensive experiments on real-world datasets to compare the proposed method with the state-of-the-art models. The results indicate that our method makes notable improvements in rating prediction for all users and cold-start users. In addition, the nonlinear cognitive opinion formation has a significant effect on improving performance, conferring higher interpretability to the recommendation.

Social media has a significant influence, which greatly facilitates people to stay up-to-date with information. Unfortunately, a great deal of fake news on social media misleads people and causes a lot of losses. Therefore, fake news detection is necessary to address this issue. Recently, social content category-based methods have become a crucial component of fake news detection. Different from news context-based category, which focuses on word embedding, it tends to explore the potential relationships and structures between users and news. In this article, a third-order tensor, which obtains massive information and connections, is constructed by the social links and engagements of social networks. Then, a sparse and graph-regularized CANDECOMP/PARAFAC (SGCP) tensor decomposition learning method is proposed for fake news detection on social network. In SGCP, a news factor matrix is constructed by CP decomposition of the tensor, which reflects the complex connections among users and news. Furthermore, SGCP retains sparsity of the news factor matrix and preserves the manifold structures from the original space. In addition, an efficient optimization algorithm, which is proven to be monotonically nonincreasing, is proposed to solve SGCP. Finally, abundant experiments are conducted on real-world datasets and demonstrate the effectiveness of the proposed SGCP.

The Gaussian process (GP) algorithm is considered as a powerful nonparametric-learning approach, which can provide uncertainty measurements on the predictions. The standard GP requires clearly observed data, unexpected perturbations in the input may lead to learned regression model mismatching. Besides, GP also suffers from the lack of good generalization performance guarantees. To deal with data uncertainty and provide a numerical generalization performance guarantee on the unknown data distribution, this article proposes a novel robust noisy input GP (NIGP) algorithm based on the probably approximately correct (PAC) Bayes theory. Furthermore, to reduce the computational complexity, we develop a sparse NIGP algorithm, and then develop a sparse PAC-Bayes NIGP approach. Compared with NIGP algorithms, instead of maximizing the marginal log likelihood, one can optimize the PAC-Bayes bound to pursue a tighter generalization error upper bound. Experiments verify that the NIGP algorithms can attain greater accuracy. Besides, the PAC-NIGP algorithms proposed herein can achieve both robust performance and improved generalization error upper bound in the face of both uncertain input and output data.

Unsupervised video prediction aims to predict future outcomes based on the observed video frames, thus removing the need for supervisory annotations. This research task has been argued as a key component of intelligent decision-making systems, as it presents the potential capacities of modeling the underlying patterns of videos. Essentially, the challenge of video prediction is to effectively model the complex spatiotemporal and often uncertain dynamics of high-dimensional video data. In this context, an appealing way of modeling spatiotemporal dynamics is to explore prior physical knowledge, such as partial differential equations (PDEs). In this article, considering real-world video data as a partly observed stochastic environment, we introduce a new stochastic PDE predictor (SPDE-predictor), which models the spatiotemporal dynamics by approximating a generalized form of PDEs while dealing with the stochasticity. A second contribution is that we disentangle the high-dimensional video prediction into low-level dimensional factors of variations: time-varying stochastic PDE dynamics and time-invariant content factors. Extensive experiments on four various video datasets show that SPDE video prediction model (SPDE-VP) outperforms both deterministic and stochastic state-of-the-art methods. Ablation studies highlight our superiority driven by both PDE dynamics modeling and disentangled representation learning and their relevance in long-term video prediction.

This article presents a new convolution algorithm: convolution kernel first operated (CKFO), which can solve the problem that the actual calculation is not reduced after pruning the weight of the convolution neural network. According to the convolution algorithm, this article proposes a simulated memristor implementation of a convolutional neural network (CNN). After that, we use the method of ex-situ training to train CNN in Tensorflow and then download the trained parameters to the Simulink system by compiling the conductance value of memristor to test the proposed simulation model. Finally, the effectiveness of the proposed model is verified. In addition, we prune the weights of CNN and retrain it, then adjust the simulation model according to the parameters after being pruned. We are surprised to find that the convolution layer designed according to the new convolution algorithm can apply the results of the pruned weight without any modification to the circuit, which is very cumbersome in other memristor-based CNN because the distribution of the pruned weight is irregular. The parameters are reduced by 75.24% and the number of multiplication operations in the convolution layer was reduced by 30.1%, while the accuracy is just reduced by 0.06%.

This article investigates the synchronization problem of multiple memristive neural networks (MMNNs) in the case of switching communication topologies and parameter mismatch. First, the distributed event-triggered control under continuous sampling conditions is studied. Then, a periodic event-triggered control (PETC) model is proposed to substantially reduce control consumption. Using the Lyapunov method, the properties of M -matrix, and some inequalities, the sufficient criteria of synchronous control are derived. The results can be used in the analysis of other multiagent nonlinear systems. A norm-based threshold function is given to determine the update time of the controller, and it is proved that the trigger condition excludes the Zeno behavior. Subject to parameter mismatch, a quasisynchronous control strategy is proposed, which can be extended to complete synchronization provided that the system mismatch or disturbance disappears. It is worth mentioning that this article introduces the signal function into the controller, so that the theoretical error can be limited to an arbitrarily small range. Furthermore, this new controller is used in the PETC strategy which automatically avoids the Zeno behavior. Finally, one example is given to illustrate our results.

As an emerging social dynamic system, geo-social network can be used to facilitate viral marketing through the wide spread of targeted advertising. However, unlike traditional influence spread problem, the heterogeneous spatial distribution has to incorporated into geo-social network environment. Moreover, from the perspective of business managers, it is indispensable to balance the tradeoff between the objective of influence spread maximization and objective of promotion cost minimization. Therefore, these two goals need to be seamlessly combined and optimized jointly. In this paper, considering the requirements of real-world applications, we develop a multiobjective optimization-based influence spread framework for geo-social networks, revealing the full view of Pareto-optimal solutions for decision makers. Based on the reverse influence sampling (RIS) model, we propose a similarity matching-based RIS sampling method to accommodate diverse users, and then transform our original problem into a weighted coverage problem. Subsequently, to solve this problem, we propose a greedy-based incrementally approximation approach and heuristic-based particle swarm optimization approach. Extensive experiments on two real-world geo-social networks clearly validate the effectiveness and efficiency of our proposed approaches.

In this article, we investigate a class of memristive neural networks (MNNs) with time-varying delays and leakage delays via sliding mode control (SMC) with and without control disturbance. SMC is used to ensure MNNs' stability. According to the characteristics of the MNNs, we consider the following three models: the first is the MNNs with time-varying delays, the second is the MNNs with time-varying delays and the control disturbance, and the third is the MNNs with time-varying delays, leakage delays, and the control disturbance. We quote some assumptions and lemmas to ensure that our main results are true. The sliding surface, the corresponding sliding mode controller, and the Lyapunov functions are constructed in different models to ensure MNNs' stability. Finally, some examples and simulations verify the validity of our main results by solving linear matrix inequality (LMI), and the conclusions and analysis of the results are given.

This article presents a simple and intuitive solution for multilabel image classification, which achieves the competitive performance on the popular COCO and PASCAL VOC benchmarks. The main idea is to capture how humans perform this task: we recognize both labels (i.e., objects and attributes) and the correlation of labels at the same time. Here, label recognition is performed by a standard ConvNet pipeline, whereas label correlation modeling is done by projecting both labels and image features extracted by the ConvNet to a common latent vector space. Specifically, we carefully design the loss function to ensure that: 1) labels and features that co-appear frequently are close to each other in the latent space and 2) conversely, labels/features that do not appear together are far apart. This information is then combined with the original ConvNet outputs to form the final prediction. The whole model is trained end-to-end, with no additional supervised information other than the image-level supervised information. Experiments show that the proposed method consistently outperforms previous approaches on COCO and PASCAL VOC in terms of mAP, macro/micro precision, recall, and$F$-measure. Further, our model is highly efficient at test time, with only a small number of additional weights compared to the base model for direct label recognition.

Social recommender systems have attracted a lot of attention from academia and industry. On social media, users' ratings and reviews can be observed by all users, and have implicit influence on their future ratings. When these users make subsequent decisions about an item, they may be affected by existing ratings on the item. Thus, implicit influence propagates among the users who rated the same items, and it has significant impact on users' ratings. However, implicit influence propagation and its effect on recommendation rarely have been studied. In this article, we propose an information propagation-based social recommendation method (SoInp) and model the implicit user influence from the perspective of information propagation. The implicit influence is inferred from ratings on the same items. We investigate the concrete effect of implicit user influence in the propagation process and introduce it into recommender systems. Furthermore, we incorporate the implicit user influence and explicit trust information in the matrix factorization framework. To demonstrate the performance, we conduct comprehensive experiments on real-world datasets to compare the proposed method with the state-of-the-art models. The results indicate that SoInp makes notable improvements in rating prediction.

Weather forecasting is usually solved through numerical weather prediction (NWP), which can sometimes lead to unsatisfactory performance due to inappropriate setting of the initial states. In this paper, we design a data-driven method augmented by an effective information fusion mechanism to learn from historical data that incorporates prior knowledge from NWP. We cast the weather forecasting problem as an end-to-end deep learning problem and solve it by proposing a novel negative log-likelihood error (NLE) loss function. A notable advantage of our proposed method is that it simultaneously implements single-value forecasting and uncertainty quantification, which we refer to as deep uncertainty quantification (DUQ). Efficient deep ensemble strategies are also explored to further improve performance. This new approach was evaluated on a public dataset collected from weather stations in Beijing, China. Experimental results demonstrate that the proposed NLE loss significantly improves generalization compared to mean squared error (MSE) loss and mean absolute error (MAE) loss. Compared with NWP, this approach significantly improves accuracy by 47.76%, which is a state-of-the-art result on this benchmark dataset.

Back propagation (BP) based on stochastic gradient descent is the prevailing method to train multilayer neural networks (MNNs) with hidden layers. However, the existence of the physical separation between memory arrays and arithmetic module makes it inefficient and ineffective to implement BP in conventional digital hardware. Although CMOS may alleviate some problems of the hardware implementation of MNNs, synapses based on CMOS cost too much power and areas in very large scale integrated circuits. As a novel device, memristor shows promises to overcome this shortcoming due to its ability to closely integrate processing and memory. This paper proposes a novel circuit for implementing a synapse based on a memristor and two MOSFET tansistors (p-type and n-type). Compared with a CMOS-only circuit, the proposed one reduced the area consumption by 92%-98%. In addition, we develop a fuzzy method for the adjustment of the learning rates of MNNs, which increases the learning accuracy by 2%-3% compared with a constant learning rate. Meanwhile, the fuzzy adjustment method is robust and insensitive to parameter changes due to the approximate reasoning. Furthermore, the proposed methods can be extended to memristor-based multilayer convolutional neural network for complex tasks. The novel architecture behaves in a human-liking thinking process.

The residual network has witnessed a great success in computer vision particularly on classification tasks, however, it has not been well studied in regression. In this work, we show its competence in a regression task - crowds flow prediction, which has strong implication to city safety and management. The problem of crowds flow prediction is challenging due to its fast dynamics. To address this issue, we explore residual learning with Gaussian regularization and propose a novel convolutional neural network called Gaussian noise residual networks (Noise-ResNet). Compared with the benchmark ST-ResNet on crowds flow prediction, the proposed architecture has three advantages: 1) Superior performance. Especially, it attains the state-of-the-art results on benchmark dataset BikeNYC. 2) Light architecture. Noise-ResNet only utilises one residual unit rather than STResNet with multiple ones, which greatly reduces the training time. 3) Interpretable input sequences. Noise-ResNet takes an input sequence that only considers the most important periodic data and closeness data, which makes the learning process more interpretable. Furthermore, experimental results substantiate that the Noise-ResNet can outperform ResNet with dropout on the same regression task.

Global optimization is a long-lasting research topic in the field of optimization, posting many challenging theoretic and computational issues. This paper presents a novel collective neurodynamic method for solving constrained global optimization problems. At first, a one-layer recurrent neural network (RNN) is presented for searching the Karush-Kuhn-Tucker points of the optimization problem under study. Next, a collective neuroydnamic optimization approach is developed by emulating the paradigm of brainstorming. Multiple RNNs are exploited cooperatively to search for the global optimal solutions in a framework of particle swarm optimization. Each RNN carries out a precise local search and converges to a candidate solution according to its own neurodynamics. The neuronal state of each neural network is repetitively reset by exchanging historical information of each individual network and the entire group. Wavelet mutation is performed to avoid prematurity, add diversity, and promote global convergence. It is proved in the framework of stochastic optimization that the proposed collective neurodynamic approach is capable of computing the global optimal solutions with probability one provided that a sufficiently large number of neural networks are utilized. The essence of the collective neurodynamic optimization approach lies in its potential to solve constrained global optimization problems in real time. The effectiveness and characteristics of the proposed approach are illustrated by using benchmark optimization problems.

In general, nonlinear model predictive control (NMPC) entails solving a sequential global optimization problem with a nonconvex cost function or constraints. This paper presents a novel collective neurodynamic optimization approach to NMPC without linearization. Utilizing a group of recurrent neural networks (RNNs), the proposed collective neurodynamic optimization approach searches for optimal solutions to global optimization problems by emulating brainstorming. Each RNN is guaranteed to converge to a candidate solution by performing constrained local search. By exchanging information and iteratively improving the starting and restarting points of each RNN using the information of local and global best known solutions in a framework of particle swarm optimization, the group of RNNs is able to reach global optimal solutions to global optimization problems. The essence of the proposed collective neurodynamic optimization approach lies in the integration of capabilities of global search and precise local search. The simulation results of many cases are discussed to substantiate the effectiveness and the characteristics of the proposed approach.

This paper is concerned with the global exponential synchronization of two memristor-based recurrent neural networks (MRNNs) with time delays via static or dynamic coupling. First, four coupling rules (i.e., static state coupling, static output coupling, dynamic state coupling, and dynamic output coupling) are designed for the exponential synchronization of drive-response pair of MRNNs. Then, several global exponential synchronization criteria are derived by constructing suitable Lyapunov-Krasovskii functionals based on the Lyapunov stability theory. Compared with existing results on synchronization of MRNNs, the conditions herein are easy to be verified. Moreover, the designed dynamic state coupling and output coupling rules have good anti-interference capacity. Finally, two illustrative examples are presented to substantiate the effectiveness and characteristics of the presented theoretical results.

In this paper, a neurodynamic optimization approach is proposed for robust eigenstructure assignment problem of second-order descriptor systems via state feedback control. With a novel robustness measure serving as the objective function, the robust eigenstructure assignment problem is formulated as a pseudoconvex optimization problem. Two coupled recurrent neural networks are applied for solving the optimization problem with guaranteed optimality and exact pole assignment. Simulation results are included to substantiate the effectiveness of the proposed approach.

This paper is concerned with formation control problems of multi-robot systems in framework of model predictive control. The formation control of robots herein is based on the leader-follower scheme. The followers are controlled by torques to track the desired trajectories to form and keep a formation. A model predictive control approach is proposed for solving the formation control problem, where the control problem is formulated as a dynamic quadratic optimization problem. A one-layer recurrent neural network called the simplified dual network is applied for computing the optimal control input in real time. Simulation results substantiate that the formation of robots can be well controlled by the proposed approach.

A neurodynamic optimization approach is proposed for robust pole assignment problem of second-order control systems via output feedback. With a suitable robustness measure serving as the objective function, the robust pole assignment problem is formulated as a quasi-convex optimization problem with linear constraints. Next, the problem further is reformulated as a convex feasibility problem. Two coupled recurrent neural networks are applied for solving the optimization problem with guaranteed optimality and exact pole assignment. Simulation results are included to substantiate the effectiveness of the proposed approach.

This paper presents new theoretical results on the invariance and attractivity of memristor-based cellular neural networks (MCNNs) with time-varying delays. First, sufficient conditions to assure the boundedness and global attractivity of the networks are derived. Using state-space decomposition and some analytic techniques, it is shown that the number of equilibria located in the saturation regions of the piecewise-linear activation functions of an n-neuron MCNN with time-varying delays increases significantly from 2(n) to 2(2n2)+n) (2(2n2) times) compared with that without a memristor. In addition, sufficient conditions for the invariance and local or global attractivity of equilibria or attractive sets in any designated region are derived. Finally, two illustrative examples are given to elaborate the characteristics of the results in detail.

This paper presents new theoretical results on the passivity and passification of a class of memristor-based recurrent neural networks (MRNNs) with time-varying delays. The casual assumptions on the boundedness and Lipschitz continuity of neuronal activation functions are relaxed. By constructing appropriate Lyapunov-Krasovskii functionals and using the characteristic function technique, passivity conditions are cast in the form of linear matrix inequalities (LMIs), which can be checked numerically using an LMI toolbox. Based on these conditions, two procedures for designing passification controllers are proposed, which guarantee that MRNNs with time-varying delays are passive. Finally, two illustrative examples are presented to show the characteristics of the main results in detail.

This paper presents a neural network approach to robust model predictive control (MPC) for constrained discrete-time nonlinear systems with unmodeled dynamics affected by bounded uncertainties. The exact nonlinear model of underlying process is not precisely known, but a partially known nominal model is available. This partially known nonlinear model is first decomposed to an affine term plus an unknown high-order term via Jacobian linearization. The linearization residue combined with unmodeled dynamics is then modeled using an extreme learning machine via supervised learning. The minimax methodology is exploited to deal with bounded uncertainties. The minimax optimization problem is reformulated as a convex minimization problem and is iteratively solved by a two-layer recurrent neural network. The proposed neurodynamic approach to nonlinear MPC improves the computational efficiency and sheds a light for real-time implementability of MPC technology. Simulation results are provided to substantiate the effectiveness and characteristics of the proposed approach.

This paper presents a neurodynamic approach to bicriteria model predictive control (MPC) of nonlinear affine systems based on a goal programming formulation. Bicriteria MPC refers to finding optimal control inputs that minimizes two performance indexes corresponding to tracking errors and control efforts. The bicriteria MPC is formulated as the solution to a nonlinear optimization problem via goal programming technique and is solved by using a two-layer recurrent neural network. Simulation results are included to illustrate the effectiveness of the proposed approach.

Based on a recurrent neural network, a model predictive control (MPC) method for control of a class of autonomous underwater vehicles (AUVs) is presented. A coupled nonlinear kinematic model with constrains is considered. The model predictive control problem of AUVs is formulated as a time-varying quadratic programming problem, and a one-layer recurrent neural network called the simplified dual network is applied for real-time optimization. It is able to converge to the global optimal solution of the constrained optimization problem. Simulation results are discussed to demonstrate the effectiveness and characteristics of the proposed model predictive control method.

This paper presents new results on a neural network approach to nonlinear model predictive control. At first, a nonlinear system with unmodeled dynamics is decomposed by means of Jacobian linearization to an affine part and a higher-order unknown term. The unknown higher-order term resulted from the decomposition, together with the unmodeled dynamics of the original plant, are modeled by using a feedforward neural network via supervised learning. The optimization problem for nonlinear model predictive control is then formulated as a quadratic programming problem based on successive Jacobian linearization about varying operating points and iteratively solved by using a recurrent neural network called the simplified dual network. Simulation results are included to substantiate the effectiveness and illustrate the performance of the proposed approach.

A robust model predictive control (MPC) method is proposed for nonlinear affine systems with bounded disturbances. The robust MPC technique requires on-line solution of a minimax optimal control problem. The minimax strategy means that worst-case performance with respect to uncertainties is optimized. The minimax optimization problem involved in robust MPC is reformulated to a minimization problem and then is solved by using a two-layer recurrent neural network. Simulation examples are included to illustrate the effectiveness of the proposed method.