Dynamic link prediction plays a crucial role in diverse applications including social network analysis, communication forecasting, and financial modeling. While recent Transformer-based approaches have demonstrated promising results in temporal graph learning, their performance remains limited when capturing complex multi-scale temporal dynamics. In this paper, we propose TFWaveFormer, a novel Transformer architecture that integrates temporal-frequency analysis with multi-resolution wavelet decomposition to enhance dynamic link prediction. Our framework comprises three key components: (i) a temporal-frequency coordination mechanism that jointly models temporal and spectral representations, (ii) a learnable multi-resolution wavelet decomposition module that adaptively extracts multi-scale temporal patterns through parallel convolutions, replacing traditional iterative wavelet transforms, and (iii) a hybrid Transformer module that effectively fuses local wavelet features with global temporal dependencies. Extensive experiments on benchmark datasets demonstrate that TFWaveFormer achieves state-of-the-art performance, outperforming existing Transformer-based and hybrid models by significant margins across multiple metrics. The superior performance of TFWaveFormer validates the effectiveness of combining temporal-frequency analysis with wavelet decomposition in capturing complex temporal dynamics for dynamic link prediction tasks. The code is available at https://github.com/SEUFHTong/TFWaveFormer.

Causal structure learning on event sequences is essential in critical systems such as communications, transportation, and industrial monitoring, where precise modeling of causal dependencies among event types significantly impacts tasks like root-cause alarm localization. Existing approaches often rely on Hawkes processes augmented with static network topology to eliminate the independent and identically distributed (i.i.d.) assumption, yet their dependence on predefined fixed structures and manually chosen kernels limits adaptability to dynamic network systems. The key challenge is to automatically infer accurate causal graphs from event sequences where both temporal evolution and network topology change over time, while accounting for nonlinear dependencies. To address this challenge, we propose Adaptive Neural Hawkes Processes (ANHP), a novel neural point process framework comprising three core modules: (1) Adaptive Event-Graph Learning, which constructs dynamic topology directly from event embeddings; (2) Neural Topological Hawkes Process, which replaces traditional linear excitation kernels with neural parameterization to capture nonlinear, time-varying conditional intensities; and (3) Masked Sparse Causal Structure, which balances likelihood maximization and model complexity via kernel-parameters masking and Bayesian Information Criterion (BIC) penalization to suppress redundant edges. Experimental results on real-world communication network alarm datasets from Huawei Shennong Intelligent Maintenance and Operation Center (IMOC) and synthetic datasets demonstrate that ANHP significantly outperforms state-of-the-art methods in accuracy, robustness, and scalability. The code is available at https://github.com/ChngYJ/ANHP.

To address the security and privacy challenges in Internet of Things (IoT) enabled systems, this paper introduces a differential privacy-based distributed model-free adaptive control framework for secure consensus control of nonlinear IoT-based multi-agent systems (MASs). First, by embedding a differential privacy mechanism into inter-agent communications, the privacy protection accuracy is theoretically guaranteed while ensuring data confidentiality. Second, a distributed model-free adaptive control algorithm is developed, which only uses local input-output (I/O) data, thereby removing the need for explicit system models and global network topology information, offering high scalability and robustness for large-scale IoT networks with unknown dynamics. Furthermore, an integrated control framework is proposed to achieve consensus control for heterogeneous nonlinear MASs under simultaneous FDI attacks and privacy perturbations. It is theoretically established that the method maintains mean-square boundedness for estimation errors, consensus errors, and output trajectories despite the joint impact of adversarial attacks and privacy noise. Simulation results demonstrate that the approach effectively resists stealthy data tampering attacks while maintaining communication privacy and system stability.

This paper proposes ABIGX (Adversarial fault reconstruction-Based Integrated Gradient eXplanation), a unified framework for explainable fault detection and classification (FDC). ABIGX builds on the foundational principles of established fault diagnosis methods, including contribution plots (CP) and reconstruction-based contribution (RBC), while extending their applicability to general FDC models and improving fault explanation results. Central to ABIGX is the Adversarial Fault Reconstruction (AFR) method, which rethinks fault reconstruction from the perspective of adversarial attacks, introducing a novel fault index applicable to both fault detection and classification tasks. In fault detection, we theoretically bridge ABIGX with conventional fault diagnosis methods by proving that CP and RBC are the linear specifications of ABIGX. For fault classification, we address the challenge of fault class smearing, an inherent issue that can obscure accurate explanations. We demonstrate that ABIGX effectively mitigates this issue, outperforming current gradient-based explanation methods. The experiments evaluate the explanations of FDC by quantitative metrics and intuitive illustrations. The results validate the generality and accuracy of AFR, and show that ABIGX provides more comprehensive and precise explanations across various FDC models, offering a significant improvement over existing methods.

The presence of nonlinearities and actuator faults poses significant challenges to achieving optimal control of quadrotors. This article investigates an adaptive dynamic programming algorithm to solve the optimal attitude regulation problem of quadrotors with nonlinear hysteresis. The optimal regulation problem is modeled as a graphical game, and optimality is defined by the Nash equilibrium. A nonlinear hysteresis inverse model is first designed to compensate for the nonlinearity of the hysteresis. To eliminate matched disturbances caused by compensation errors, an integral sliding mode mechanism is proposed, improving fault tolerance. Through problem transformation, the Nash equilibrium is achieved by solving interconnected Hamilton–Jacobi–Bellman equations. A data-based policy iteration algorithm is then developed to numerically solve the approximate optimal solution using a least-squares approach. Finally, a quadrotor team is employed to verify the effectiveness of the proposed algorithm.

This article proposes a distributed Lagrange alternating gradient descent (LAGD) algorithm with a fixed step size for constrained optimization over a multiagent communication network. Interconnected by multiagent networks, agents optimize their own objective function subject to local constraints cooperatively, and the whole network shares globally coupled constraints. All agents reach consensus on the estimations of multipliers via the network communication to handle the globally coupled constraints, and the decision variable vectors converge to the optimal solution along the Lagrange gradient direction. The convergence of the algorithm is proven under the condition of fixed step sizes subject to a theoretical upper bound. An economic dispatch problem in a power system and a numerical example are elaborated to verify and demonstrate the effectiveness of the algorithm.

The study of dynamics in complex systems has increasingly incorporated higher order interactions, which capture the collective influence among three or more units, extending beyond traditional pairwise connections. Although such interactions are observed in biological neural networks, their precise role in shaping network dynamics and the feasibility of controlling these dynamics remain unclear. This article proposes a controlled diffusion hub neural network model that explicitly includes higher order interactions. To regulate the resulting spatiotemporal dynamics, a cross-node associated delayed feedback control (CNADFC) method is further introduced. Our analysis establishes conditions for local stability, Turing instability, and Hopf bifurcation. We show that while Turing instability cannot arise, spatially periodic patterns emerge under specific parametric conditions. Numerical simulations confirm these theoretical findings and highlight the pronounced effects of self-feedback, control, and first-order interaction on stability and dynamic behaviors; in contrast, higher order interactions exert a comparatively modest influence. Furthermore, simulations illustrate how the CNADFC method can effectively optimize spatiotemporal dynamics. This work advances the understanding of diffusion neural network behavior under complex higher order interaction and provides a reference for the effective control of such networks.

This article investigates an aggregative game with local closed convex set constraints over time-varying unbalanced communication graphs, and aims to compute the Nash equilibrium (NE) in a distributed manner. To this end, we propose a distributed discrete-time NE seeking algorithm. It combines the average tracking technique and the push-sum protocol to estimate the global aggregate over time-varying unbalanced graphs, and incorporates the method of feasible direction to handle the set constraints. Based on the small gain theorem, we establish the linear convergence of the proposed algorithm and provide explicit estimates for the step-size upper bounds. Finally, numerical simulations of a Nash-Cournot game are given to confirm the effectiveness of our algorithm.

Distributed formation tracking control with obstacle avoidance of multiagent systems (MASs) under random switching topologies and external disturbances is considered in this article. To achieve the complex objective, an effective control strategy is developed in three steps. First, under the transition probability (TP)-based mode-dependent average dwell-time (MDADT) switching topologies, a distributed objective trajectory achieves almost sure global exponential tracking of the desired formation trajectory. Second, a safe objective trajectory approach is designed by geometrically projecting the unsafe parts of the existing formation trajectory onto the boundary of the obstacle region. Finally, an integral-multiplicative barrier Lyapunov function (IMBLF) is proposed to allow agents to track the safe objective trajectory, where the IMBLF can further guarantee the safety of the MASs. One of the interesting merits of our results is that the impulsive increasing of Lyapunov function at switching instants which is necessary for classical analysis methods has been removed. The feasibility of the proposed formation control method with obstacle avoidance is verified by simulations.

Distributed energy scheduling in residential microgrids faces challenges from renewable uncertainty and privacy constraints. While multiagent reinforcement learning (MARL) enables decentralized coordination, classical MARL methods suffer from exponential growth in the joint state–action space, leading to high computational complexity and low sample efficiency. Moreover, centralized training paradigms often rely on shared representations, raising privacy concerns. In this article, we propose a multiagent distributional reinforcement learning framework with the dynamic hyper policy network (DHPN), which constructs permutation-invariant (PI) representations via entitywise dynamic weight generation and multihead attention, reducing input redundancy and obviating the need for full joint information. To capture stochasticity from renewable variability and demand, we further introduce a distributional value function factorization framework to model return distributions, leveraging quantile regression and mean–shape decomposition. Experiments on a data-driven microgrid demonstrate that the DHPN outperforms strong baselines by achieving substantially lower mean-square error in representational evaluation and higher cumulative rewards, while exhibiting faster convergence, enhanced training stability, and reduced grid fluctuations. These results highlight the effectiveness of combining PI representations with distributional value modeling for scalable privacy-aware multiagent energy management.

Multiobjective optimization problems (MOPs) arise in numerous real-world scenarios, yet finding their solutions with optimal trade-offs can be a formidable challenge. This article studies the continuous optimization problem involving large-scale variables, many objectives, and intricate constraints, which is rarely comprehensively discussed in existing works, due to the coexisting difficulties posed by the curse of dimensionality, selection pressure, and feasibility restrictions. To address these problems, this work pioneers a novel optimization framework, optimization pattern learning, embedded with machine learning (ML) techniques. Within this framework, the concept of measurable order and its corresponding learning mechanism are proposed to extract valuable knowledge from solutions. This measurable order is a general form of those orders used explicitly or implicitly in the existing studies, providing a more flexible means to evaluate solutions for efficient optimization adaptively. By substituting original solutions with their measurable orders, this framework effectively avoids the selection pressure from many objectives and the feasibility restrictions from intricate constraints. Furthermore, two novel ML models based on measurable orders are developed to progressively learn effective optimization patterns from iterative data in high-dimensional search spaces. Leveraging these learned patterns, this framework successfully addresses the curse of dimensionality from large-scale variables and thus achieves efficient optimization. Owing to the strong adaptability and search capabilities of this framework, it also demonstrates excellent scalability as the number of variables, objectives, and constraints increases. Extensive simulations validate the effectiveness of the framework and underscore its competitiveness relative to state-of-the-art algorithms in this field.

In longitudinal platooning, some key sources of uncertainty are the powertrain time constants of the vehicles. Because such time constants appear in the input matrix of the platooning dynamics, their correct estimation is either impractical with methods requiring persistence of excitation or impossible with methods requiring the input matrix to be known. This work proposes a novel adaptive longitudinal platooning method with correct estimation of the powertrain time constants. To achieve correct estimation, the composite adaptive control framework and its stability analysis are suitably modified to handle the time constant uncertainty in the design of the adaptive law. The result is a platooning protocol that guarantees convergence of the estimated time constants to their true values without the need for persistence of excitation: it is sufficient that the derivative of the acceleration is nonzero over a possibly short transient, an extremely relaxed excitation condition. Comparisons with state-of-the-art platooning solutions reveal advantages such as no required measurements of acceleration derivative or collection of past data. The robustness and practicality of the proposed design are also verified with CarSim-based platooning experiments.

Renewable energy is incorporated to the energy supply for heterogeneous networks (HetNets) to mitigate the high energy consumption and meet carbon-neutral targets. This paper investigates resource management in HetNets with hybrid energy supply, where base stations are powered by renewable energy and power grid, and can share the harvested renewable energy with each other. The objective is to maximize the long-term average utility of the network defined as a weighted sum of system data rate and power grid energy cost. In view of the difference of dynamics characteristics between the radio and energy resources, the problem is formulated by describing energy resources over the large timescale relative to the small one for radio resources. To address the problem without prior knowledge, a two-timescale deep reinforcement learning (DRL)-based optimization framework is proposed, which is structured with two layers of decision-making, including the energy scheduling layer over the large timescale for renewable energy sharing among BSs and power grid energy consumption, and the power control layer over the small timescale for transmit power, respectively. To enhance the performance of the cross-layer collaborative optimization, in the energy scheduling layer an improved soft actor-critic with two-timescale update rule (TTUR-SAC) algorithm is designed with a novel strategy of differentiating the training frequencies of actor and critic networks, and in the power control layer the successive convex approximation method is leveraged to solve the non-convex subproblem for the transmit power. Simulation results demonstrate that under various system configurations our proposed solution outperforms the typical baseline methods.

Causal discovery aims to learn causal relationships between variables from targeted data, making it a fundamental task in machine learning. However, causal discovery algorithms often rely on unverifiable causal assumptions, which are usually difficult to satisfy in real-world data, thereby limiting the broad application of causal discovery in practical scenarios. Inspired by these considerations, this work extensively benchmarks the empirical performance of various mainstream causal discovery algorithms, which assume i.i.d. data, under eight model assumption violations. Our experimental results show that differentiable causal discovery methods exhibit robustness under the metrics of Structural Hamming Distance and Structural Intervention Distance of the inferred graphs in commonly used challenging scenarios, except for scale variation. We also provide the theoretical explanations for the performance of differentiable causal discovery methods. Finally, our work aims to comprehensively benchmark the performance of recent differentiable causal discovery methods under model assumption violations, and provide the standard for reasonable evaluation of causal discovery, as well as to further promote its application in real-world scenarios.

Spatio-temporal prediction is a pivotal task with broad applications in traffic management, climate monitoring, energy scheduling, etc. However, existing methodologies often struggle to balance model expressiveness and computational efficiency, especially when scaling to large real-world datasets. To tackle these challenges, we propose STH-SepNet (Spatio-Temporal Hypergraph Separation Networks), a novel framework that decouples temporal and spatial modeling to enhance both efficiency and precision. Therein, the temporal dimension is modeled using lightweight large language models, which effectively capture low-rank temporal dynamics. Concurrently, the spatial dimension is addressed through an adaptive hypergraph neural network, which dynamically constructs hyperedges to model intricate, higher-order interactions. A carefully designed gating mechanism is integrated to seamlessly fuse temporal and spatial representations. By leveraging the fundamental principles of low-rank temporal dynamics and spatial interactions, STH-SepNet offers a pragmatic and scalable solution for spatio-temporal prediction in real-world applications. Extensive experiments on large-scale real-world datasets across multiple benchmarks demonstrate the effectiveness of STH-SepNet in boosting predictive performance while maintaining computational efficiency. This work may provide a promising lightweight framework for spatio-temporal prediction, aiming to reduce computational demands and while enhancing predictive performance. Our code is avaliable at https://github.com/SEU-WENJIA/ST-SepNet-Lightweight-LLMs-Meet-Adaptive-Hypergraphs.

In Healthcare Internet of Things Networks (HIoTNs), safeguarding the sensitivity of patients’ electric healthcare records (EHRs) is imperative, necessitating effective privacy protection while ensuring ample data for training. Decentralized federated learning (DFL), as a peer-to-peer distributed machine learning architecture, serves a pivotal role in preserving the data privacy of EHRs. However, two primary challenges in applying DFL to HIoTNs include safeguarding the privacy of EHRs at individual hospitals and optimizing communication resources among hospitals. This article proposes a three-layer healthcare framework comprising a physical layer, a communication layer and an edge-encrypted layer to segregate hospital local data from interaction models. Moreover, a novel doubly accelerated DFL algorithm (AccDFL) is introduced to integrate DFL training and information interaction into the communication layer of HIoTNs. By employing the heavy-ball and Nesterov methods, AccDFL achieves double acceleration, ensuring both$\epsilon _{i}$-differential privacy (DP) and linear convergence. The theoretical analysis of AccDFL delves into the interaction among distributed gradient tracking (DGT), DP, and accelerated mechanisms, presenting comprehensive convergence and privacy analyses to overcome the exponential increase in parameters brought by the acceleration and DP mechanisms. Experimental results with realistic non-IID grayscale and color medical datasets of different disease types affirm the significant advantages of AccDFL over other algorithms in terms of accuracy and communication efficiency.

Evidences have been provided that the effect of poorly designed vehicle automation systems may propagate from the single car up to the traffic dynamics. A reported example consists of car-following driver assistance systems triggering destabilizing group phenomena like phantom traffic jams and stop-and-go waves. It then becomes fundamental to study ‘group-oriented’ vehicle shared control algorithms that are able to assist the driver while at the same time prevent the propagation of destabilizing effects in the traffic when these systems are widely deployed. A key challenge in vehicle shared control is that the heterogeneity and uncertainty of human driving characteristics require personalized adaptation: it is an open problem to realize stabilizing traffic properties from personalized adaptive vehicle shared control. The distinguishing contribution of this work is a car-following shared control method that, while adapting to the personal characteristics of each driver, contains a ‘group’ model with desirable traffic properties defined in terms of string stability and collision avoidance. It is proven analytically that the proposed shared control is able to assist each driver in approaching the group model adaptively (i.e., handling heterogeneity and uncertainties) and optimally (i.e., with minimum control authority over the driver). Numerical experiments performed in SUMO with Highway Fuel Economy Test Cycle (HWFET) data and stop-and-go wave data validate that the proposed assistance improves traffic smoothing while handling heterogeneity and uncertainties in the driver parameters.

This study addresses resilient human-in-the-loop (HiTL) formation-tracking of multi-UAV systems against$f$-local Byzantine attacks. In the HiTL settings, a human operator plays a key role in detecting any physical hazard, monitoring the whole UAV swarm, and sending secure execution signals to a non-autonomous leader UAV. Moreover, there exists a fraction of Byzantine UAVs in the multi-UAV systems, which propagate incorrect information to their neighbors (called Byzantine edge attacks (BEAs)) and adopt false input signals (called Byzantine node attacks (BNAs)) when swarming. In order to suppress the above aggressive Byzantine attacks, this paper proposes a Byzantine-resilient hierarchical control scheme, including a virtual Digital Twin Layer (DTL) apart from a Cyber-Physical Layer (CPL). First, a distributed resilient estimation scheme is proposed on the DTL, which can realize resilient estimation on the state of the non-autonomous leader UAV against BEAs on the premise that the DTL topology is strongly$(2f+1)$-robust. Second, a series of decentralized and chattering-free controllers is formulated on the CPL, which is resilient to both BNAs and inter-layered faults. The asymptotical control performance of the above controllers is strictly proven based on Cromwell-Bellman Lemma. To demonstrate the practicality of the theoretical results, a resilient HiTL multi-UAV systems experiment has been further conducted. The experimental results verify the effectiveness and practicality of the designed two-layered controllers against$f$-local Byzantine attacks.Note to Practitioners—Owing to the wide application of multi-UAV systems, the resilience of the whole swarm against malicious attacks has grasped the great attention of both academia and industry. This work considers a rather aggressive kind of attacks, named Byzantine attacks, where a fraction of unidentified UAVs act as traitors. Inspired by the digital twin technology, a two-layered control architecture for multi-UAV systems is formatted, including a Digital Twin Layer (DTL) and a Cyber-Physical Layer (CPL). Here are the highlights: 1) Control Architecture: The DTL handles Byzantine edge attacks (BEAs), while the CPL addresses Byzantine node attacks (BNAs), ensuring reliable human-swarm cooperation in adversarial environments. 2) Resilient Estimation against BEAs: A novel resilient estimation scheme on the DTL is designed, using edge-based feedback, which can estimate the states of the leader UAV manipulated by human operators. 3) Adaptive Controller against BNAs and Inter-layered Faults: On the CPL, a decentralized adaptive controller with adjustable and exponential convergence is proposed, enhancing its precision and flexibility. 4) Practical Application: A UAV swarm formation-tracking experiment validates the control architecture’s effectiveness in human-in-the-loop scenarios, demonstrating its practicality in the realm of swarm robotics and human-swarm interaction.

This paper presents a novel control framework that combines reinforcement learning (RL) with filtered position barrier certificate (FPBC) for distributed collision-free multi-agent systems (MASs) control. By introducing a filtered position model on the basis of a velocity-controlled double-integral system, the collision avoidance analysis is greatly simplified. The proposed FPBC is designed based on this filtered position model and enables collision-free interaction among agents using a less conservative first-order control barrier function (CBF), thereby eliminating the need for complex high-order CBFs (HOCBFs). The proposed FPBC is used in a Quadratic Program (QP)-based safety filter that enforces collision avoidance on the actions generated by a RL controller. This RL controller only needs to be trained in a single-agent setting and can learn an effective policy through a stability-optimality reward function to reduce computing resource consumption. Furthermore, a deadlock resolution mechanism is proposed to prevent agent stagnation and task failure in large-scale MASs. Extensive simulations and real-world experiments in UGV and UAV environments validate the proposed framework, which demonstrates superior safety and performance compared to conventional HOCBFs. The experiment video and other supplementaries are available at https://github.com/mahafeeling/FPBC.

Time-series prediction has drawn considerable attention during the past decades fueled by the emerging advances of deep learning methods. However, most neural network based methods fail in extracting the hidden mechanism of the targeted physical system. To overcome these shortcomings, an interpretable sparse system identification method without any prior knowledge is proposed in this study. This method adopts the Fourier transform to reduces the irrelevant items in the dictionary matrix, instead of indiscriminate usage of polynomial functions in most system identification methods. It shows an visible system representation and greatly reduces computing cost. With the adoption of$l_{1}$norm in regularizing the parameter matrix, a sparse description of the system model can be achieved. Moreover, three data sets including the water conservancy data, global temperature data and financial data are used to test the performance of the proposed method. Although no prior knowledge was known about the physical background, experimental results show that our method can achieve long-term prediction regardless of the noise and incompleteness in the original data more accurately than the widely-used baseline data-driven methods. This study may provide some insight into time-series prediction investigations, and suggests that a white-box system identification method may extract the easily overlooked yet inherent periodical features and may beat neural-network based black-box methods on long-term prediction tasks.

Multiobjective shortest path problem (MSPP) is one of the most critical issues in network optimization, aimed at identifying all efficient paths across conflicting objectives. Nowadays, existing methods face substantial bottlenecks in addressing the diverse preferences of decision makers and high spatiotemporal overhead caused by the calculation process, particularly in cases with large-scale networks. To overcome these obstacles, a generalized MSPP in large-scale networks is investigated with the aim of solving it with diverse preferences of decision makers satisfied and low spatiotemporal overhead. Toward this end, with a novel concept, the generalized dominance relation is introduced, and the generalized multiobjective shortest path algorithm via the generalized dynamic programming approach is developed. Moreover, the H-reducible technique is further employed to accelerate the convergence of the proposed algorithm. Additionally, several rigorous proofs are provided for the conclusions that all efficient paths could be found within a tolerable time by the developed algorithm and the algorithm could be implemented in a distributed manner under mild assumptions. Finally, numerous routing experiments are conducted on large-scale communication networks for demonstrating the effectiveness and competitiveness of our approach.

In this article, two types of multiagent systems (MASs) are developed for distributed bilevel constrained optimization. Within the framework of the distributed bilevel optimization modeling, the objective function is in a summation manner of local objective functions. Multiple agents connected via a communication network are harnessed for optimizing the local objective functions cooperatively while adhering to coupled constraints with global information, and each agent is tasked with solving an individual inner problem and it is subject to multiple local constraints. To address challenges posed by the distributed computation requirement of the proposed bilevel optimization models and multiple complex constraints, first and second-order MASs are customized and proven to converge to the optimal solution. Three examples involving two numerical simulations and an economic dispatch problem are elaborated to verify and demonstrate the optimality, enhanced robustness to communication blocking, and fast convergence of the proposed approaches.

In an integrated energy system (IES), fluctuations in coupled district heating networks and renewable energy sources pose risks to the power system’s operation. To effectively mitigate the risk of rare events, it is crucial to identify the key factors that influence their likelihood. Traditional global sensitivity analysis (GSA) assesses the sensitivity of full probability density functions (PDFs) of the system output to uncertain inputs. However, it fails to evaluate the sensitivity of rare event probabilities, which are at the tail of the PDF. It also neglects the uncertainties of the input PDFs, whose hyperparameters can heavily affect the rare event probabilities. To address these issues, we propose a novel framework calledrare-event-based global sensitivity analysis(REGSA) that prioritizes the input PDF parameters that impact the risks of the operating state. We also improve the computational efficiency of this framework by quantifying rare event probabilities through subset simulation and using sparse polynomial chaos expansion (SPCE) in REGSA (hereafter referred to as SPCE-REGSA). The simulations reveal the excellent performance of the proposed method.

In intelligent transportation systems (ITS), machine learning is highly effective in anomaly detection for state estimation (SE) in traffic flow measurement, but it requires resource-intensive collection of anomaly samples and overlooks spatial characteristics. Additionally, the original SE in traffic flow measurement exhibits low-frequency characteristics due to computational complexity. Considering these limitations, this paper proposes a fast and efficient anomaly detection framework for SE in traffic flow measurement. Initially, an attention-based spatiotemporal graph convolutional network (ASTGCN) model is utilized to extract both temporal and spatial features of SE. The ASTGCN model is trained using quantile regression, relying solely on normal samples during training. This approach eliminates the need for collecting anomalous samples and reduces computational demands. The model establishes a safe interval for SE that significantly improves anomaly detection capabilities. Furthermore, a teacher-student network is implemented, where the teacher network, trained offline, distills its ability to convert low-frequency SE data into high-frequency representations into a simpler student network. The student network executes real-time reconstruction of high-frequency SE, thus enhancing the precision of anomaly detection without substantial resource expenditure. Finally, the analysis conducted on the California’s 7th district highway measurement system demonstrates the proposed method’s ability to accurately detect anomalous SE in traffic flow measurement.

Spatiotemporal dynamics in the brain have been recognized as strongly related to the formation of perceived and cognitive diseases, such as delusions and hallucinations in Alzheimer's disease. However, two practical considerations are rarely mentioned in related mechanism research: the connectomics networking and the anomalous diffusion generated by the complex medium between neurons and the complex topology of neural networks, respectively. Furthermore, how to optimize the corresponding dynamics behaviors has excellent implications for treating brain diseases. This article first realizes the networking under connectomics for an anomalous-diffusion single-neuron model and applies a nonlinear state feedback control to generate optimized dynamic behaviors, which provides a paradigm of nonequilibrium self-organization driven by anomalous diffusion. Then, by tracing the root distribution of the characteristic equation, some controlled conditions causing or inhibiting Turing instability and Hopf bifurcation are deduced, and the effects of self-diffusion and cross diffusion on Turing instability range are also revealed. At last, thorough numerical simulations are updated to illustrate the results. It is emphasized that delay, self-diffusion, cross diffusion, and fractional order occupy dominant positions in determining the network's spatiotemporal dynamics, and utilizing the control strategy can efficiently reduce Turing instability and delay Hopf bifurcation.

Detecting spatiotemporal anomalies is imperative for addressing critical societal and engineering challenges, including public safety assurance, environmental hazard identification, epidemic surveillance, and transportation system optimization. Existing methodologies, however, face persistent limitations due to sparse labeled datasets and the inherent complexity of dynamic spatiotemporal systems. In order to bridge this gap, we present unsupervised-semi-supervised stacking (USemiS), a novel framework that synergizes semi-supervised learning with ensemble meta-learning. USemiS introduces three core innovations: 1) unsupervised component learners that extract low-level representations of heterogeneous anomalies, 2) a consensus-based tuning mechanism that dynamically weights robust learners via stability metrics, and 3) spatiotemporal MixUp (ST-MixUp), a tailored augmentation strategy that interpolates anomalies across spatial and temporal dimensions to enhance decision boundaries. By integrating these components, USemiS effectively disentangles latent anomaly patterns while mitigating label scarcity. Evaluated on large-scale traffic anomaly and crowd fall detection datasets, USemiS achieves state-of-the-art performance, outperforming existing methods by 1.3% and 2.1% in AUC under extreme low-label regimes (0.4% and 0.8% labeled data, respectively). These results underscore USemiS's capacity to generalize across diverse spatiotemporal contexts, offering a scalable and robust solution for real-world applications where labeled anomalies are scarce yet critical.

This article focuses on the fixed-time bipartite consensus problems of multiagent systems under time-varying disconnected topologies. Different from the jointly connected topology, an enhanced fixed-time local pinning algorithm is proposed to overcome challenges posed by disconnected signed networks without introducing additional topological assumptions. Especially, the motion tendencies of isolated agents in cooperative-competitive networks are thoroughly discussed. Event-triggered control with the impulsive effect is utilized to achieve the bipartite consensus of MASs with minimal energy consumption, where the total energy function does not need to be monotonic, and the Zeno behavior can be avoided. Finally, the efficacy of the designed protocol is demonstrated through two numerical examples.

In this article, a momentum-based multiagent optimization approach is developed for distributed nonconvex optimal resource allocation. The proposed resource allocation model is formulated without the convex conditions, and a paradigmatic system based on the gradient descent with momentum method is proposed for handling its functional nonconvexity. Based on the paradigmatic system, a momentum-based multiagent system (MAS) is developed, and its convergence and convergence rate to a local minimizer are proven. Then, a distributed average tracking approach is introduced, based on which a hybrid multiagent optimization approach consisting of multiple MASs and a meta-heuristic rule is designed for seeking global minimizers. Finally, a simulation in a chiller system is elaborated to demonstrate the enhanced stability, fast convergence, and optimality of the developed distributed optimization approaches.

With the continuous advancement of neural network methodologies, time series prediction has attracted substantial interest over the past decades. Nonetheless, the interpretability of neural networks is insufficient and the utilization of deep learning techniques for prediction necessitates significant computational expenditures, rendering its application arduous in numerous scenarios. In order to tackle this challenge, an interpretable sparse system identification method which does not require a time-consuming training through back-propagation is proposed in this study. This method integrates advantages from both knowledge-based and data-driven approaches, and constructs dictionary functions by leveraging Fourier basis and taking into account both the long-term trends and the short-term fluctuations behind data. By using the $l_1$ norm for sparse optimization, prediction results can be gained with an explicit sparse expression function and an extremely high accuracy. The performance evaluation of the proposed method is conducted on comprehensive benchmark datasets, including ETT, Exchange, and ILI. Results reveal that our proposed method attains a significant overall improvement of more than 20\% in accordance with the most recent state-of-the-art deep learning methodologies. Additionally, our method demonstrates the efficient training capability on only CPUs. Therefore, this study may shed some light onto the realm of time series reconstruction and prediction.

Reconfigurable intelligent surface (RIS) is a radical and cost-efficient technology to improve energy efficiency and mitigate interference in the heterogeneous network. In this paper, the resource allocation problem of sub-channels, transmit power and RIS coefficients is investigated in the RIS-aided heterogeneous network. To solve the formulated mixed integer nonlinear programming problem, a two-step centralized resource allocation algorithm and a two-step distributed resource allocation algorithm are proposed based on the alternating optimization method. In the centralized algorithm, the sub-channel allocation, transmit power and RIS coefficients are optimized by the macro base station solely, where the non-convex power optimization problem is transformed into a convex one based on the convex approximation method. In the distributed algorithm, which aims to alleviate the computational burden of the macro base station, the sub-channel allocation and transmit power are optimized by using the cooperation of all the small base stations and the macro base station. Finally, numerical results are presented to demonstrate the convergence of the proposed algorithms and the effectiveness of the sub-channel transfer. More importantly, it is shown that the centralized algorithm can achieve the higher total throughput, while the distributed algorithm greatly decreases the resource allocation time.

The convergence rate and applicability to directed graphs with interaction topologies are two important features for practical applications of distributed optimization algorithms. In this article, a new kind of fast distributed discrete-time algorithms is developed for solving convex optimization problems with closed convex set constraints over directed interaction networks. Under the gradient tracking framework, two distributed algorithms are, respectively, designed over balanced and unbalanced graphs, where momentum terms and two time-scales are involved. Furthermore, it is demonstrated that the designed distributed algorithms attain linear speedup convergence rates provided that the momentum coefficients and the step size are appropriately selected. Finally, numerical simulations verify the effectiveness and the global accelerated effect of the designed algorithms.

Presents corrections to the paper, (Correction for "Consensus in High-Power Multiagent Systems With Mixed Unknown Control Directions via Hybrid Nussbaum-Based Control").

In this article, we propose a collaborative neurodynamic optimization (CNO) method for the distributed seeking of generalized Nash equilibriums (GNEs) in multicluster games with nonconvex functions. Based on an augmented Lagrangian function, we develop a projection neural network for the local search of GNEs, and its convergence to a local GNE is proven. We formulate a global optimization problem to which a global optimal solution is a high-quality local GNE, and we adopt a CNO approach consisting of multiple recurrent neural networks for scattering searches and a metaheuristic rule for reinitializing states. We elaborate on an example of a price-bidding problem in an electricity market to demonstrate the viability of the proposed approach.

This article explores the application of the multiagent reinforcement learning (MARL) algorithm in addressing the large-scale traffic signal control (TSC) problem. To address the TSC problem in complex urban traffic networks, most existing algorithms focus on optimizing local traffic flow at each intersection through decentralized training based on either the local observations or messages from its neighboring intersections, which, however, lacks the concept of cooperative learning. To conquer such limitations, a novel distributed critic with decentralized actor (DCDA) framework is proposed, which allows the communication messages and temporal difference (TD) losses to be exchanged among neighboring intersections. Specially, by considering the traffic network as a communication network of agents (more precisely, intersections and lanes are considered as agents and edges, respectively), a distributed global average TD loss estimation algorithm is designed in the distributed critic step to estimate the global average TD loss estimation and enhance collaboration among agents. Moreover, in the decentralized actor step, the policy gradient decomposition method is adopted for each agents to learn its local policy solely based on its local action-value function. By adhering to the DCDA framework, a novel distributed policy gradient decomposition (DPGD) algorithm is further proposed to address the TSC problem. Empirical experiments demonstrate that the efficiency, robustness, and stability of the DPGD algorithm outperform the state-of-the-art MARL algorithms in both the environments of cooperative adaptive cruise control and adaptive traffic signal control.

Vehicle intelligent terminals often require end-user applications (APPs) to continuously send information to external data aggregator for monitoring or control tasks. However, communication channels exposed to the open environment can lead to an undesirable loss of privacy for drivers, despite the benefits provided by these APPs. It is worth mentioning that different APPs of vehicle intelligent terminals may require different key information. Given these personalized application scenarios, the use of traditional privacy protection technology may encounter limitations. To address this problem, we propose a compressive privacy-preserving algorithm that employs a compression matrix to maintain the normal function of applications while ensuring privacy. Specifically, the algorithm utilizes sensors to linearly transform the original vectors of measurements at each time step into a lower-dimensional space. The compressed measurements are then transmitted to a fusion center. Optimization problems are formulated for the current time step as well as two time steps. The performance of the algorithm is evaluated using the Cramer-Rao bound. Simulation results and comparisons further validate the effectiveness of the compressive privacy algorithm.

Due to the use of inter-vehicle wireless communication, vehicular platooning can be prone to attacks with corrupted data, as in false data injection (FDI) attacks. It is crucial to develop platooning protocols promoting resilience to injected false data. In this work we show that resilience can be attained by making use of a system-theoretic property known as disturbance decoupling. We first show how disturbance decoupling is obtained in nominal platooning protocols without attacks: then, in the presence of FDI attacks, we propose compensation strategies that guarantee to recover the nominal performance of the platoon. The proposed compensation strategies can cope with platoons of heterogeneous vehicles and are designed towards string stability. Numerical experiments, also performed in a SUMO-Veins co-simulation environment with different platooning scenarios under FDI attacks, validate the effectiveness of the proposed protocols in handling cyber-attacks and platoon heterogeneity.

A new class of distributed multiagent reinforcement learning (MARL) algorithm suitable for problems with coupling constraints is proposed in this article to address the dynamic economic dispatch problem (DEDP) in smart grids. Specifically, the assumption made commonly in most existing results on the DEDP that the cost functions are known and/or convex is removed in this article. A distributed projection optimization algorithm is designed for the generation units to find the feasible power outputs satisfying the coupling constraints. By using a quadratic function to approximate the state-action value function of each generation unit, the approximate optimal solution of the original DEDP can be obtained by solving a convex optimization problem. Then, each action network utilizes a neural network (NN) to learn the relationship between the total power demand and the optimal power output of each generation unit, such that the algorithm obtains the generalization ability to predict the optimal power output distribution on an unseen total power demand. Furthermore, an improved experience replay mechanism is introduced into the action networks to improve the stability of the training process. Finally, the effectiveness and robustness of the proposed MARL algorithm are verified by simulation.

Multimodal data fusion analysis is essential to model the uncertainty of environment awareness in digital industry. However, due to communication failure and cyberattack, the sampled time-series data often have the issue of data missing. In some extreme cases, part of units are unobservable for a long time, which results in complete data missing (CDM). To impute missing data, many models have been proposed. However, they cannot address the CDM issue, because no observation data of the unobservable units can be obtained in this case. Thus, to address the CDM issue, a novel cross-modal generative adversarial network (CM-GAN) is proposed in this article. It combines the cross-modal data fusion technique and the deep adversarial generation technique to construct a cross-modal data generator. This generator can generate long-term time-series data from widely existing spatio-temporal modal data in modern industrial system, and then impute missing value by replacing them with generated data. To test the performance of CM-GAN, extensive experiments are conducted on photovoltaic (PV) power output dataset. Compared with other baseline models, the performance of CM-GAN is generally better and reaches the state-of-the-art level. Moreover, sufficient ablation studies are conducted to present the contribution of the cross-modal data fusion technique and show the reasonability of parameter settings of CM-GAN. Apart from this, some prediction experiments are also conducted. The results show that the PV data recovered by CM-GAN can provide more predictability information for improving the prediction accuracy of deep learning model.

This paper investigates a simultaneous wireless information and power transfer-enabled hybrid-powered multicell communication network with a nonlinear energy harvesting model. In this multicell environment, information interaction and energy trading are carried out among base stations (BSs), and each BS powered by hybrid sources simultaneously provides information/energy to its user equipments (UEs) over the downlinks. A novel global utility function is proposed by comprehensively considering the incomes from information and energy transmission, energy trading, and the costs from the electricity companies. To maximize this goal, a nonconvex problem that jointly optimizing energy procurement, power allocation, and power splitting ratios is formulated to deal with the imbalance between energy supply and demand at BSs. Considering the nonconvexity of the problem and the strong coupling among the optimization variables, the formulated problem is difficult to solve directly with conventional convex optimization methods. To overcome these obstacles, a two-step solution combining alternating optimization, distributed optimization, and successive convex approximation is designed, in which the BS layer scheme and the UE layer scheme are performed alternately. Different from the existing centralized schemes, the proposed distributed scheme makes local optimal decisions independently at each BS only resorting to the information of neighbor BSs, which brings great advantages in reducing signaling and computational overheads. Moreover, the convergence and advantages of the proposed distributed scheme are verified by rigorous analyses and simulations.

In this article, the fully distributed neural learning algorithms by neural network approximation for networked multiagent reinforcement learning (NMARL) are studied. To tackle the convergence analysis of methods in NMARL with tremendous state-action space, most of the existing distributed algorithms are designed by linear function approximation, which however would fall into a situation of poor expression. To conquer such limitation, the distributed neural learning algorithms are developed by using a novel neural network approximation that bridges the theory and practice of deep NMARL (DMARL). Specifically, inspired by the overparametrization method for minimizing mean-squared projected bellman error (MSPBE), the distributed neural learning algorithms with population semigradients and stochastic semigradients are respectively, proposed to solve the NMARL problem. Furthermore, the convergence of the proposed algorithms are strictly given by employing the overparametrization method to establish the approximate stationary point of MSPBE to characterize the algorithms toward the global optimum. Finally, some numerical simulations demonstrate the effectiveness of the distributed neural learning algorithms.

This work considers a wireless powered communication network (WPCN), in which wireless nodes store the energy from an energy access point in their batteries for subsequent data transmission. An online energy consumption optimization strategy is proposed for adaptively determining the beamforming vector, data routing, network operation mode and transmitted power based only on the current state of WPCN. In most existing results, the energy/data transmission of WPCNs is based on the ideal battery models and the energy storage efficiencies therein are always assumed to be non-zero constants. Since the energy storage efficiency of batteries may be affected by the ambient environment or aging in real-time, this work considers a WPCN with a time-varying energy storage efficiencies sequence and correspondingly develops an improved Lyapunov optimization strategy to offset the impact of the time-varying energy storage efficiencies. More importantly, a distributed strategy is proposed to optimize the cooperation of wireless nodes over unrestricted numbers of hops, and thus the energy access point does not require channel state information of all data links and the data backlog queues of all nodes during the solving process. Accordingly, the computational burden at the energy access point is greatly reduced due to the use of this distributed strategy. Under this strategy, the time-averaged expected energy consumption of WPCN can be within a bounded gap of the minimum energy required to maintain stability of the network. Finally, the theoretical analysis is further corroborated by simulation results.

The interaction between automated and human-driven vehicles in mixed (human/automated) platoons is far from understood. To study this interaction, the notion of head-to-tail string stability was proposed in the literature. Head-to-tail string stability is an extension of the standard string stability concept where, instead of asking every vehicle to achieve string stability, a lack of string stability is allowed due to human drivers, provided it can be suitably compensated by automated vehicles sparsely inserted in the platoon. This work introduces a theoretical framework for the problem of head-to-tail string stability of mixed platoons: it discusses a suitable vehicle-following human driver model to study mixed platoons, and it gives a reduced-order design strategy for head-to-tail string stability only depending on three gains. The work further discusses the safety limitations of the head-to-tail string stability notion, and it shows that safety improvements can be attained by an appropriate reduced-order design strategy only depending on two additional gains. To validate the effectiveness of the design, linear and nonlinear simulations show that the string stability/safety trade-offs of the proposed reduced-order design are comparable with those resulting from full-order designs.

Transportation simulation is non-trivial due to the co-existence of thousands of heterogeneous decision makers (or vehicles). Such large-scale decision making is intrinsically a complex decentralized problem, the resolution of which is at the forefront of transportation simulation. Despite many physical or mathematical models proposed to date, underlying them is usually a set of universal rules plus some random perturbations to characterize vehicular movements. Inspired by the decision-making mechanism of rational human beings (i.e., learning iteratively from experience), this study proposes a novel two-stage ensemble reinforcement learning (TERL) paradigm for large-scale decentralized decision making in transportation simulation, in order to enhance the computational efficiency and thus scalability of RL to practical applications at scale. After establishing a problem-specific Markov decision process, the first stage utilizes clustering to group heterogeneous vehicles into quasi-homogeneous clusters. A representative RL model (or agent) is employed for each cluster where the included vehicles share and jointly optimize the policy parameters. The second stage develops an ensemble control strategy based on representative RL models for vehicles isolated as noise during clustering. While vehicles are simultaneously simulated, RL models are separately trained with cluster-specific experience replay. Application of TERL to the classical multi-user dynamic route choice problem in a real-world network of the Gusu District in Suzhou, China demonstrates the effectiveness of the proposed approach in deriving desirable simulation results, compared with the classical shortest path model and the dynamic user equilibrium model.

Actor-critic (AC) cooperative multiagent reinforcement learning (MARL) over directed graphs is studied in this article. The goal of the agents in MARL is to maximize the globally averaged return in a distributed way, i.e., each agent can only exchange information with its neighboring agents. AC methods proposed in the literature require the communication graphs to be undirected and the weight matrices to be doubly stochastic (more precisely, the weight matrices are row stochastic and their expectation are column stochastic). Differently from these methods, we propose a distributed AC algorithm for MARL over directed graph with fixed topology that only requires the weight matrix to be row stochastic. Then, we also study the MARL over directed graphs (possibly not connected) with changing topologies, proposing a different distributed AC algorithm based on the push-sum protocol that only requires the weight matrices to be column stochastic. Convergence of the proposed algorithms is proven for linear function approximation of the action value function. Simulations are presented to demonstrate the effectiveness of the proposed algorithms.

We study the asymptotical consensus problem for multi-agent systems (MASs) consisting of a high-dimensional leader and multiple followers with unknown nonlinear dynamics under directed switching topology by using a neural network (NN) adaptive control approach. First, we design an observer for each follower to reconstruct the states of the leader. Second, by using the idea of discontinuous control, we design a discontinuous consensus controller together with an NN adaptive law. Finally, by using the average dwell time (ADT) method and the Barbǎlat's lemma, we show that asymptotical neuroadaptive consensus can be achieved in the considered MAS if the ADT is larger than a positive threshold. Moreover, we study the asymptotical neuroadaptive consensus problem for MASs with intermittent topology. Finally, we perform two simulation examples to validate the obtained theoretical results. In contrast to the existing works, the asymptotical neuroadaptive consensus problem for MASs is firstly solved under directed switching topology.

This article investigates the finite-time distributed adaptive consensus for nonlinear uncertain multiagent systems (MASs). The performance of the consensus errors can be prespecified in a funnel sense. Three achievements make this work depart from available results on prespecified performance and funnel control: first, a novel error transformation is constructed to prespecify the performance, which avoids the singularity problem pointed out in the literature in the differentiation of the control law; second, the funnel control method is extended in a MAS setting by suitably modifying the backstepping technique in a power integrator sense; and third, it is shown that finite-time stability notions can be attained without extra complexity being involved in the design. Stability analysis and comparative simulations demonstrate the method.

It is challenging and critical to achieve zero error consensus tracking in multiagent systems (MASs) with nonautonomous leaders (i.e., leaders with nonzero inputs). The traditional approach is to use discontinuous controllers which may cause a chattering phenomenon. How to achieve zero error consensus tracking via a chattering-free controller is still open. We propose a class of adaptive continuous controllers to achieve zero error consensus tracking for Lipschitz nonlinear MASs with a nonautonomous leader and directed communication topology. Unlike existing works that use discontinuous functions to eliminate the impacts of leaders’ inputs, we use a continuous function by introducing an exponential decay function into the denominator. First, we design a continuous controller with fixed coupling strengths and prove that zero error consensus tracking can be achieved if the coupling strengths are greater than some positive constants. Second, we design a continuous controller with dynamic coupling strengths under which fully distributed zero error consensus tracking can be achieved. Moreover, the case with undirected communication topology is studied. Finally, three examples are given to verify the theoretical results. Specifically, convergence results between the continuous controller here and that is developed via the boundary layer technique are compared. Compared with existing works, the designed adaptive continuous controllers here can not only achieve zero error consensus tracking but also is chattering free.

We propose a reinforcement learning method for setting up the game of detecting objects within an image. Unlike some traditional image detection methods, which produce a large number of candidate boxes to detect objects, our approach allows an agent to use a small set of image locations to detect a visual object effectively. We train the agent to identify the useless information in the four edges of the image and discard them by representing predefined candidate areas in a tree-like hierarchy. Such a series of procedures that build the game environment is designed to detect locations of target objects. We also show that the updatable target network can make the agent reach stability faster and improve training results prominently, which utilizes good samples. Extensive comparison experiments on the benchmark dataset of Pascal VOC verify the outperformance of the proposed method.

This work studies the formation control problem for mobile robots. The distinguishing feature of this work is considering the leader and the followers dynamics to be non-ideal, i.e. subject to disturbances/unmodelled terms. Distributed joint disturbance-and-leader estimators are designed to solve the problem, allowing to reconstruct the leader’s signals in a distributed way. The estimates of the leader and the follower disturbances provided by the estimators are embedded in the control law to reject such disturbances and achieve the formation asymptotically. Lyapunov technique is employed to analyze stability of the overall distributed formation control algorithm. Simulations are conducted to illustrate the theoretical results.

Switch-based adaptive dynamic programming (ADP) is an optimal control problem in which a cost must be minimized by switching among a family of dynamical modes. When the system dimension increases, the solution to switch-based ADP is made prohibitive by the exponentially increasing structure of the value function approximator and by the exponentially increasing modes. This technical correspondence proposes a distributed computational method for solving switch-based ADP. The method relies on partitioning the system into agents, each one dealing with a lower dimensional state and a few local modes. Each agent aims to minimize a local version of the global cost while avoiding that its local switching strategy has conflicts with the switching strategies of the neighboring agents. A heuristic algorithm based on the consensus dynamics and Nash equilibrium is proposed to avoid such conflicts. The effectiveness of the proposed method is verified via traffic and building test cases.

In this article, we generalize the results on self-synchronization of Lur'e networks diffusively interconnected through dynamic relative output-feedback from the undirected graph case in Zhang et al. 2016 to the general directed graph case. A linear dynamic self-synchronization protocol of the same structure is adopted as the one proposed in Zhang et al. 2016. That is, the Lur'e-type nonlinearity is not involved in our self-synchronization protocol. It is in fact unknown and only assumed to be incrementally sector bounded within a given sector. In the absence of a leader Lur'e system defining the synchronization trajectory, we construct a novel self-synchronization manifold in order to derive the self-synchronization error dynamics. Meanwhile, the connectivity of the general directed graph having a directed spanning tree is quantified by the global connectivity, instead of the so-called general algebraic connectivity used in the directed graph case under static relative state feedback. The global connectivity plays a crucial role in handling self-synchronization problems of directed nonlinear networks via dynamic relative output feedback, including directed networks with the Lipschitz nonlinear node dynamics, which is also discussed in this article. The protocol parameter matrix design is performed by solving the obtained LMI conditions in sequence. In addition, some discussions are complemented on the important technical details in our self-synchronization protocol design along with extensions. Finally, our theoretical results are illustrated through numerical simulations over a directed nonlinear dynamical network.

Dynamic resource allocation problem (DRAP) with unknown cost functions and unknown resource transition functions is studied in this article. The goal of the agents is to minimize the sum of cost functions over given time periods in a distributed way, that is, by only exchanging information with their neighboring agents. First, we propose a distributed Q -learning algorithm for DRAP with unknown cost functions and unknown resource transition functions under discrete local feasibility constraints (DLFCs). It is theoretically proved that the joint policy of agents produced by the distributed Q -learning algorithm can always provide a feasible allocation (FA), that is, satisfying the constraints at each time period. Then, we also study the DRAP with unknown cost functions and unknown resource transition functions under continuous local feasibility constraints (CLFCs), where a novel distributed Q -learning algorithm is proposed based on function approximation and distributed optimization. It should be noted that the update rule of the local policy of each agent can also ensure that the joint policy of agents is an FA at each time period. Such property is of vital importance to execute the ε -greedy policy during the whole training process. Finally, simulations are presented to demonstrate the effectiveness of the proposed algorithms.

This article investigates the distributed time-varying optimization problem for second-order multiagent systems (MASs) under limited interaction ranges. The goal is to seek the minimum of the sum of local time-varying cost functions (CFs), where each CF is only available to the corresponding agent. Limited communication range refers to the scenario where the agents have limited sensing and communication capabilities, that is, a pair of agents can communicate with each other only if their distance is within a certain range. To handle such a problem, a new continuous connectivity-preserving mechanism is presented to preserve the connectivity of the considered network. Then, two distributed optimization algorithms are presented to solve the optimization problem with time-varying CFs and time-invariant CFs, respectively. Theoretical analysis and two numerical examples are provided to verify the effectiveness of the methods.

In this article, the constrained optimization problem with its global objective function being the sum of convex local cost functions and the constraint being a closed convex set is researched. The aim of this study is to solve the researched problem in a distributed manner, that is, using only local computations and local information exchanges. Toward this end, two gradient-tracking-based distributed optimization algorithms are designed for the considered problem over weight-balanced and weight-unbalanced graphs, respectively. Since the classical projection method is unsuitable to handle the closed convex set constraint under the gradient-tracking framework, a new indirect projection method is employed in this article to deal with the involved closed convex set constraint. Furthermore, two time scales are introduced to complete the convergence analyses. In addition, under the condition that all local cost functions are strongly convex and L -smooth, it is proved that the algorithms with well-selected fixed step sizes have linear convergence rates.

This work investigates the consensus tracking problem for high-power nonlinear multiagent systems with partially unknown control directions. The main challenge of considering such dynamics lies in the fact that their linearized dynamics contain uncontrollable modes, making the standard backstepping technique fail; also, the presence of mixed unknown control directions (some being known and some being unknown) requires a piecewise Nussbaum function that exploits the a priori knowledge of the known control directions. The piecewise Nussbaum function technique leaves some open problems, such as Can the technique handle multiagent dynamics beyond the standard backstepping procedure? and Can the technique handle more than one control direction for each agent? In this work, we propose a hybrid Nussbaum technique that can handle uncertain agents with high-power dynamics where the backstepping procedure fails, with nonsmooth behaviors (switching and quantization), and with multiple unknown control directions for each agent.

This article considers the fully distributed leaderless synchronization in a complex network by only utilizing local neighboring information to design and tune the coupling strength of each node such that the synchronization problem can be solved without involving any global information of the network. For an undirected network, a fully distributed synchronization algorithm is presented to adjust the coupling strength of each node based on a simple adaptive law. When the topology of a network is directed, two different types of adaptive algorithms are developed to achieve synchronization in a fully distributed manner, where the coupling strength of each node is designed to be either the sum or product of two non-negative scalar functions. The fully distributed leaderless synchronization of a directed network is investigated in a leader-follower framework, where the leader subnetwork is analyzed by using the techniques from constrained Rayleigh quotients and the follower subnetwork is addressed by employing the properties of nonsingular M -matrices. Simulations are given to illustrate the theoretical results.

We aim to address the consensus tracking problem for multiple-input-multiple-output (MIMO) linear networked systems under directed switching topologies, where the leader is subject to some nonzero but norm bounded inputs. First, based on the relative outputs, a full-order unknown input observer (UIO) is designed for each agent to track the full states' error among neighboring agents. With the aid of such an observer, a discontinuous feedback protocol is subtly designed. And it is proven that consensus tracking can be achieved in the closed-loop networked system if the average dwell time (ADT) for switching among different interaction graph candidates is larger than a given positive threshold. By using the boundary layer technique, a continuous feedback protocol is skillfully designed and employed. It is shown that the consensus error converges into a bounded set under the designed continuous protocol. Second, as part of the full states' error can be constructed via the agents' outputs, a reduced-order UIO is thus designed based on which discontinuous and continuous feedback protocols are, respectively, proposed. By using the stability theory of the switched systems, it is proven that the consensus error converges asymptotically to 0 under the designed discontinuous protocol, and converges into a bounded set under the designed continuous protocol. Finally, the obtained theoretical results are validated through simulations.

In this article, the asymptotic tracking consensus problem of higher-order multiagent systems (MASs) with general directed communication graphs is addressed via designing event-triggered control strategies. One common assumption utilized in most existing results on such tracking consensus problem that the inherent dynamics of the leader are the same as those of the followers is removed in this article. In particular, two cases that the dynamics of the leader are subjected, respectively, to bounded input and unknown nonlinearity are considered. To do this, distributed event-triggered observers are first constructed to estimate the state information of the leader. Then, local event-triggered tracking control protocols are designed for each follower to complete the goal of tracking consensus. One distinguishing feature of the present distributed observers lies in the fact that they could avoid the continuous monitoring for the states of the neighbors' observer states. It is also worth pointing out that the present tracking consensus control strategies are fully distributed as no global information related to the directed communication graph is involved in designing the strategies. Two simulation examples are finally presented to verify the efficiency of the theoretical results.

The problem of fault-tolerant adaptive fuzzy tracking control against actuator faults is investigated in this article for a type of uncertain nonaffine fractional-order nonlinear full-state-constrained multi-input-single-output (MISO) system. By means of the existence theorem of the implicit function and the intermediate value theorem, the design difficulty arising from nonaffine nonlinear terms is surmounted. Then, the unknown ideal control inputs are approximated by using some suitable fuzzy-logic systems. An adaptive fuzzy fault-tolerant control (FTC) approach is developed by employing the barrier Lyapunov functions and estimating the compounded disturbances. Moreover, under the drive of the reference signals, a sufficient condition ensuring semiglobal uniform ultimate boundedness is obtained for all the signals in the closed-loop system, and it is proved that all the states of nonaffine nonlinear fractional-order systems are guaranteed to remain inside the predetermined compact set. Finally, two numerical examples are provided to exhibit the validity of the designed adaptive fuzzy FTC approach.

Adaptive output-feedback consensus with funnel performance is studied for nonlinear uncertain multiagent systems (MASs). The nonlinear MASs contain unknown dynamics and only an output variable can be measured. The other states are not measured directly and are reconstructed via fuzzy state observers. The presence of output feedback makes the proposed design significantly different from the existing literature on control with funnel performance. In particular, appropriate adaptive laws must be defined to handle the presence of uncertain dynamics and local output information from a few neighboring nodes. Interestingly, with a suitable error transformation, it is shown that the proposed control law has a simpler structure than barrier function methods proposed in the literature to handle funnel-like performance. With respect to this point, simulation studies illustrate that the proposed method can dramatically reduce the control effort while satisfying transient and steady-state performance imposed by the funnel.

This article presents the observer-based event-triggered adaptive hybrid fuzzy dynamic surface control strategy for a category of uncertain nonstrict-feedback fractional-order nonlinear multi-input multi-output systems, including unknown time-varying delays and actuator faults. First, an adaptive hybrid fuzzy state observer and a serial-parallel estimation system are constructed to estimate the unmeasured system states and incorporate them into the control design scheme, respectively, where some appropriate fuzzy logic systems are introduced to approximate the unknown nonlinear functions. According to the dynamic surface control technique, the designed adaptive fuzzy control approach can surmount the deficiency of “complexity explosion.” Then, an observer-based adaptive event-triggered control algorithm is developed by constructing the Lyapunov–Krasovskii functionals and estimating the compounded disturbances. Furthermore, it is proved that under the drive of the reference signals, all the signals in the closed-loop system are semiglobally uniformly ultimately bounded and Zeno behavior can be successfully excluded. Finally, an example with numerical simulations is utilized to exhibit the applicability of the obtained observer-based event-triggered adaptive fuzzy control approach.

This paper investigates the spatiotemporal characteristics and predictability of the emerging modern traffic behavior, ridesourcing. We collect a comprehensive data set of Didi ridesourcing cars on a large geographical scale of a capital city in China, including both the temporal order information and the GPS-recorded spatial trajectories. To extract the features of this kind of traffic behavior, we construct a large-scale network by considering every traffic flow of the orders. Therein, a driver consecutively visiting different regions of the city connects the relationship of these sites. The weighted ridesourcing network shows a consistency of the distribution of trip orders and the Clark model for population distribution. The network also has spatial and temporal features with power laws, sometimes with exponential truncations and log-normal distributions. Furthermore, we propose a general analytical method to quantify the predictability of this kind of behavior by calculating the entropy at a collective level, which can be extended to quantify other traffic behaviors. Finally, by considering the traffic congestion factor, we propose a better neural network based model for predicting dwelling time of the ridesourcing behavior. We suggest that the traffic behavior of ridesourcing cars indicates specific non-Markovian characteristics, which can be systematically analyzed from the viewpoint of network sciences.

The broad learning system (BLS) paradigm has recently emerged as a computationally efficient approach to supervised learning. Its efficiency arises from a learning mechanism based on the method of least-squares. However, the need for storing and inverting large matrices can put the efficiency of such mechanism at risk in big-data scenarios. In this work, we propose a new implementation of BLS in which the need for storing and inverting large matrices is avoided. The distinguishing features of the designed learning mechanism are as follows: 1) the training process can balance between efficient usage of memory and required iterations (hybrid recursive learning) and 2) retraining is avoided when the network is expanded (incremental learning). It is shown that, while the proposed framework is equivalent to the standard BLS in terms of trained network weights,much larger networks than the standard BLS can be smoothly trained by the proposed solution, projecting BLS toward the big-data frontier.

This work investigates a reduced-complexity adaptive methodology to consensus tracking for a team of uncertain high-order nonlinear systems with switched (possibly asynchronous) dynamics. It is well known that high-order nonlinear systems are intrinsically challenging as feedback linearization and backstepping methods successfully developed for low-order systems fail to work. Even the adding-one-power-integrator methodology, well explored for the single-agent high-order case, presents some complexity issues and is unsuited for distributed control. At the core of the proposed distributed methodology is a newly proposed definition for separable functions: this definition allows the formulation of a separation-based lemma to handle the high-order terms with reduced complexity in the control design. Complexity is reduced in a twofold sense: the control gain of each virtual control law does not have to be incorporated in the next virtual control law iteratively, thus leading to a simpler expression of the control laws; the power of the virtual and actual control laws increases only proportionally (rather than exponentially) with the order of the systems, dramatically reducing high-gain issues.

This article investigates the distributed average tracking (DAT) problem for disturbed second-order multiagent systems, where a crowd of agents is required to track the average of the multiple time-varying signals. First, a new kind of distributed average estimator is developed for each agent to estimate the average of the multiple time-varying signals in finite time. The protocol possesses the distinguished feature of robustness to initialization errors, which can recover from network alterations. Then, an observer-based finite-time tracking protocol is proposed to make each agent exactly track the average of the multiple time-varying signals in finite time in the absence of velocity measurement. By carefully analyzing the dynamic properties of the tracking error system, a suitable Lyapunov function is constructed to estimate the settling time for convergence of the tracking error system theoretically. Furthermore, an adaptive DAT protocol is proposed, which is a fully distributed protocol because it can solve the DAT problem without using any global information. Finally, two simulation examples are provided to verify the effectiveness of the methods.

A fast architecture for real-time (i.e., minute-based) training of a traffic predictor is studied, based on the so-called broad learning system (BLS) paradigm. The study uses various traffic datasets by the California Department of Transportation, and employs a variety of standard algorithms (LASSO regression, shallow and deep neural networks, stacked autoencoders, convolutional, and recurrent neural networks) for comparison purposes: all algorithms are implemented in MATLAB on the same computing platform. The study demonstrates a BLS training process two-three orders of magnitude faster (tens of seconds against tens-hundreds of thousands of seconds), allowing unprecedented real-time capabilities. Additional comparisons with the extreme learning machine architecture, a learning algorithm sharing some features with BLS, confirm the fast training of least-square training as compared to gradient training.

The distributed stabilization problem is studied in this article for a group of heterogeneous second-order agents in the strong-weak competition network containing three kinds of relationships among agents: 1) cooperation; 2) strong competition; and 3) weak competition. The entire network satisfies the structural balance condition which can be partitioned into two subnetworks, while the strong and weak competitions are alternate actions on the agents from different subnetworks. To stabilize such heterogeneous networked systems in a distributed way, the switched system approach is developed and utilized in this article, where it is revealed that distributed stabilization can be achieved provided that the ratio on the activating periods of strong and weak competition is chosen appropriately. As an extension, a periodical switching law is taken into account to simplify the design process, where the periodical competition function is introduced correspondingly and several effective sufficient conditions are attained. Finally, the derived analytical results are demonstrated by performing numerical simulations.

This article investigates adaptive control problems for unknown second-order nonlinear multiagent systems (MASs) via an event-triggered approach. An adaptive event-triggered consensus controller is given to second-order MAS with unknown nonlinear dynamics. We prove that the proposed consensus controller is free from Zeno behavior. Next, an adaptive event-triggered tracking controller is developed for leader-follower MAS with the leader having bounded nonzero control input. Both consensus and tracking controllers are fully distributed, which means that event-triggered controllers only use local cooperative information. Finally, an unknown second-order nonlinear MAS is used to verify the given event-triggered controllers.

In this paper, we study a distributed convex optimization problem with inequality constraints. Each agent is associated with its cost function, and can only exchange information with its neighbors. It is assumed that each cost function is convex and the optimization variable is subject to an inequality constraint. The objective is to make all the agents reach consensus, and meanwhile converge to the minimum point of the sum of local cost functions. A distributed protocol is proposed to guarantee that all agents can reach consensus in finite time and converge to the optimal point within the inequality constraints. Based on the ideas of parameter projection, the protocol includes two decent directions. One makes the cost function decrease, and the other makes agents step forward to the constraint set. It is shown that the proposed protocol solves the problem under connected undirected graphs without using a Lagrange multiplier technique. Especially, all of the agents could reach the constraint sets in finite time and stay in there after. The method could also be used in the centralized optimization problems.

In this paper, the finite-time output consensus problem is considered for a class of second-order multiagent systems (MASs), where the mismatched disturbance exists in the dynamics of each agent, and the communication topology is directed. First of all, a basic backstepping control protocol is proposed to solve the finite-time consensus problem without mismatched disturbance. Then, a finite-time disturbance observer is designed to estimate the mismatched disturbance, based on which, two adaptive finite-time consensus protocols are proposed to solve the finite-time output consensus and tracking consensus problems without using any global information with respect to the communication topology. Finally, two simulation examples are illustrated to verify the theoretical results.

In this article, a class of uncertain nonstrict-feedback fractional-order nonlinear single-input-single-output (SISO) systems is investigated. Fuzzy-logic systems (FLSs) are employed to approximate the unknown nonlinear functions and model the uncertain fractional-order nonlinear systems. For the states measurable case, an adaptive fuzzy state-feedback control scheme is developed under the framework of the backstepping technique. For the states unmeasurable case, an observer-based output-feedback control design is proposed by introducing a serial-parallel estimation model and using the dynamic surface control (DSC) technique. Under the drive of the reference signals, the semiglobally uniformly ultimate boundedness for all signals and the tracking errors converging to a small neighborhood of the origin are proved based on the Lyapunov function theory by choosing appropriate design parameters. Two examples with numerical simulations are presented to illustrate the availability of the proposed control approaches.

In adaptive platooning strategies proposed in literature to handle uncertain and nonidentical uncertain vehicle dynamics (uncertain heterogeneous platoons) two aspects requiring proper design are neglected: bidirectional interaction among vehicles which might lead to loss of string stability, and engine saturation constraints which might lead to loss of cohesiveness. This work proposes a novel adaptive platooning strategy handling these two crucial aspects. Specifically, bidirectional interaction is handled by designing bidirectional reference dynamics with proven string stability properties, to which the uncertain heterogeneous platoon should homogenize; engine constraints are handled via a proposed a mechanism that makes such reference dynamics `not too demanding', by properly saturating their action. The saturation action will allow all vehicles in the platoon to not hit their engine limits, preserving cohesiveness. Simulations are conducted to validate the theoretical analysis and show the effectiveness of the method in retaining cohesiveness of the platoon.

By using the event-triggered technique, we study the distributed control of a class of nonlinear multiagent systems (MASs) with aperiodic sample information. Taking advantage of the combinational sample measurements, we first present an event-triggered consensus algorithm for the leaderless MAS. Thereafter, we design the event-triggered tracking algorithm for the leader–follower MAS with a leader having bounded input. Furthermore, we prove that both consensus and tracking controllers do not exist Zeno behavior. Finally, a numerical example is given to verify the designed event-triggered consensus algorithm.

This article addresses and solves the adaptive asymptotic tracking for a class of uncertain switched positive linear dynamics (also known in the literature as compartmental models) subject to dwell-time constraints. Compared to the state-of-the-art, the innovative feature of this method is to attain for the first time asymptotic set-point tracking, while guaranteeing non-negativity of the systems states. To achieve asymptotic tracking, an interpolated Lyapunov function is adopted, which is nonincreasing at the switching instants and decreasing in two consecutive switching instants. Such Lyapunov function results in a novel adaptive law with time-varying adaptive gains, as opposed to state-of-the-art laws with fixed positive adaptive gains. The developed design is applicable to classes of compartmental systems compatible with those proposed in the literature: an example involving the infusion of anesthesia is conducted to show that the proposed method can achieve better performance than existing methods.

This paper proposes a novel set-invariance adaptive dynamic surface control (DSC) design for a larger class of uncertain large-scale nonlinear input-saturated systems. The peculiarity of this class is that noa prioribound on the continuous control gain functions is assumed (i.e., their boundedness cannot be assumed before obtaining system stability). This requires a new design. Differently from the available methods, the proposed design involves the construction of appropriate invariant sets for the closed-loop trajectories, which allows to remove the restrictive assumption ofa prioribounds of the control gain functions. Furthermore, we show that such set-invariance design can handle input constraints in the form of input saturation. In line with the DSC methodology, semi-globally uniformly ultimate boundedness is proven: however, differently from the standard methodology, stability analysis requires the combination of Lyapunov and invariant set theories.

One fundamental yet challenging issue in security control for resilient complex networks is to construct distributed control laws for the networks to perform various cooperative tasks in the presence of failures and attacks, where resilient indicates that the complex networks are exposed to the environment with cyber uncertainties and malicious adversaries. This is particularly important in today's critical infrastructure networks since most of them are vulnerable to attacks in the era of the Internet. Inspired by this observation, this paper focuses on synchronization control for resilient complex networks subject to cyber and physical attacks, where the states of nodes being attacked may change abruptly (i.e., the synchronization error may suffer impulsive disturbances), and some nodes as well as their corresponding connections may not work in some instances. Suppose that a smart control center is equipped in the considered network to detect the attacks in real time. Furthermore, the nodes and communication channels are assumed to be recovered through some repair work after detecting the attacks. On the theoretical side, by using the M-matrix theory, we get a few sufficient criteria to guarantee the achievement of secure synchronization against attacks on both nodes and communication links. On the algorithmic side, security control algorithm and architecture are proposed to select the coupling strength and the feedback gain matrix to realize synchronization. Finally, we perform two simulation examples to validate our theoretical results.

A great deal of attention from various scientific communities has been recently drawn to complex network systems (CNSs), with many profound results established in this active research field. This article provides a state-of-the-art survey on coordination and control of CNSs with switching network topologies, with emphasis on relationships between the switchings among different topology candidates and the network controllability, and between the switchings among different topology candidates and the emergence of coordination behaviors (including synchronization, consensus, and containment) of such CNSs. First, some fundamental properties of CNSs and the essentials of analytical methodologies for the stability of the fixed point of switched dynamical systems are briefly reviewed. Then, network controllability and the emergence of coordination behaviors of CNSs with switching topologies and the corresponding analytical approaches are discussed in detail, where some of the existing results along these topics are presented in a tutorial-like fashion. This article ends by presenting some interesting future research topics on the coordination and control of CNSs with switching topologies.

This paper investigates the resource allocation problem for a group of agents communicating over a strongly connected directed graph, where the total objective function of the problem is composted of the sum of the local objective functions incurred by the agents. With local convex sets, we first design a continuous-time projection algorithm over a strongly connected and weight-balanced directed graph. Our convergence analysis indicates that when the local objective functions are strongly convex, the output state of the projection algorithm could asymptotically converge to the optimal solution of the resource allocation problem. In particular, when the projection operation is not involved, we show the exponential convergence at the equilibrium point of the algorithm. Second, we propose an adaptive continuous-time gradient algorithm over a strongly connected and weight-unbalanced directed graph for the reduced case without local convex sets. In this case, we prove that the adaptive algorithm converges exponentially to the optimal solution of the considered problem, where the local objective functions and their gradients satisfy strong convexity and Lipachitz conditions, respectively. Numerical simulations illustrate the performance of our algorithms.

A distributed nonsmooth convex optimization problem subject to a general type of constraint, including equality and inequality as well as bounded constraints, is studied in this paper for a multiagent network with a fixed and connected communication topology. To collectively solve such a complex optimization problem, primal-dual dynamics with projection operation are investigated under optimal conditions. For the nonsmooth convex optimization problem, a framework under the LaSalle's invariance principle from nonsmooth analysis is established, where the asymptotic stability of the primal-dual dynamics at an optimal solution is guaranteed. For the case where inequality and bounded constraints are not involved and the objective function is twice differentiable and strongly convex, the globally exponential convergence of the primal-dual dynamics is established. Finally, two simulations are provided to verify and visualize the theoretical results.

This paper proposes a novel adaptive fuzzy dynamic surface control (DSC) method for an extended class of periodically disturbed strict-feedback nonlinear systems. The peculiarity of this extended class is that the control gain functions are not bounded a priori but simply taken to be continuous and with a known sign. In contrast with existing strategies, controllability must be guaranteed by constructing appropriate compact sets ensuring that all trajectories in the closed-loop system never leave these sets. We manage to do this by means of invariant set theory in combination with the Lyapunov theory. In other words, boundedness is achieved a posteriori as a result of stability analysis. The approximator composed of fuzzy logic systems and Fourier series expansion is constructed to deal with the unknown periodic disturbance terms.

In this article, the dynamic economic dispatch (DED) problem for smart grid is solved under the assumption that no knowledge of the mathematical formulation of the actual generation cost functions is available. The objective of the DED problem is to find the optimal power output of each unit at each time so as to minimize the total generation cost. To address the lack of a priori knowledge, a new distributed reinforcement learning optimization algorithm is proposed. The algorithm combines the state-action-value function approximation with a distributed optimization based on multiplier splitting. Theoretical analysis of the proposed algorithm is provided to prove the feasibility of the algorithm, and several case studies are presented to demonstrate its effectiveness.

The work presented in this paper concerns a switching-based control formulation for multi-intersection and multiphase traffic light systems. A macroscopic traffic flow modeling approach is first presented, which is instrumental to the development of a model-based and switching-based optimization method for traffic signal operation, in the framework of adaptive dynamic programming (ADP). The main advantage of the switching-based formulation is its capability to determine both “when”' to switch and “which” mode to switch on without the need to use the cycle-based average flow approximation typical of state-of-the-art formulations. In addition, the framework can handle different cycle times across intersections without the need for synchronization constraints and, moreover, minimum dwell-time constraints can be directly enforced to comply with minimum green/red times in each phase. The simulation experiments on a multi-intersection and multiphase traffic light systems are presented to show the effectiveness of the method.

In this paper, the global pinning synchronization problem is studied for a complex dynamical network to follow a dynamic target system. A distinguished feature of the present network model is that the target system may have some predesigned control inputs. This implies that, when pinning synchronization is guaranteed, the states of the nodes within such a pinning-controlled dynamical network may approach a specified trajectory which does not satisfy the system equation of the uncoupling individual node system within the network. The practical constraint that the external control inputs acting on the target system are unknown to any node in the considered network poses a big challenge in solving such a pinning synchronization problem. The designed scheme for achieving pinning synchronization is executed in two steps. Specifically, the first step is to select some nodes to pin such that the augmented interaction topology has at least one directed spanning tree rooted at the node describing the target system, while the second step is to construct a coupling law to synchronize all the states of nodes within the network. Moreover, two kinds of discontinuous coupling laws with static and adaptive coupling gains are, respectively, proposed to achieve pinning synchronization. Meanwhile, by utilizing nonsingular ${M}$ -matrix theory and Lyapunov stability analysis for nonsmooth system, some efficient criteria are established for guaranteeing synchronization in the pinning-controlled networks. Numerical simulations on pinning synchronization of networking Chua's circuit systems are finally given to verify the analytic results.

In this paper, the finite-time coordination behavior of multiple Euler-Lagrange systems in cooperation-competition networks is investigated, where the coupling weights can be either positive or negative. Then, two auxiliary variables about the information exchange among agents are designed, and the finite-time distributed protocol is proposed based on the auxiliary variables and the property of the Euler-Lagrange system. By combining the approach of adding a power integrator with the homogeneous domination method, it is shown that finite-time bipartite consensus can be achieved if the cooperation-competition network is structurally balanced and the parameters of the distributed protocol are chosen appropriately; otherwise, finite-time distributed stabilization can be achieved. Furthermore, from the perspective of network decomposition, the finite-time coordination behavior is further considered, and some sufficient conditions about the cooperation subnetwork and the competition subnetwork are obtained. As an extension, finite-time coordination behavior only with partial state information of the neighbors is discussed, and some similar results are obtained. Finally, four numerical examples are shown for illustration.

One typical reflection of our understanding on multiagent systems (MASs) is our ability to design the emergence mechanism responsible for their various cooperative behaviors. This paper is concerned with the cooperative robust containment control problem of multileader MASs subject to unknown nonlinear dynamics and external disturbances. Specifically, quasi-containment and asymptotic containment problems are, respectively, considered by using tools from neural network (NN) approximation theory and Lyapunov stability theory of nonsmooth systems. A new kind of containment controllers consisting of a linear local information-based feedback term, a neuro-adaptive approximation term and a nonsmooth feedback term are designed to complete the goal of quasi-containment. Under the assumption that the subgraph depicting the coupling configuration among followers is detail-balanced and each follower can be influenced by at least one leader, it is proven that the containment error vector of the closed-loop MASs will be uniformly ultimately bounded if the control parameters of the proposed containment controllers are suitably designed. By introducing a pseudo ideal weighting matrix for NN approximator embedded at each follower, a novel class of containment controllers are further designed to precisely achieve asymptotic containment in the considered MASs where the Euclidean norm of containment error vector asymptotically converges to zero. At last, numerical simulations are given to verify the validity of these derived theoretical results.

In this note, the consensus tracking problem is studied for MASs with undirected switching communication topologies under impulsive disturbances. Unlike the impulsive disturbances considered in most existing literature which are caused by sudden noise, frequency change and so forth, the disturbances under consideration are owing to malicious attacks on the agents. By constructing a topology independent multiple Lyapunov function, we shall prove that consensus tracking could be achieved by selecting appropriate coupling strength and feedback gain matrix provided that the average dwell time is greater than a positive threshold. The obtained theoretical result is finally validated by simulation.

The popular DQN algorithm is known to have some instability and variability which make its performance poor sometimes. In prior work, there is only one target network, the network that is updated by the latest learned Q-value estimate. In this paper, we present multiple target networks which are the extension to the Deep Q-Networks (DQN). Based on the previously learned Q-value estimate networks, we choose several networks that perform best in all previous networks as our auxiliary networks. We show that in order to solve the problem of determining which network is better, we use the score of each episode as a measure of the quality of the network. The key behind our method is that each auxiliary network has some states that it is good at handling and guides the agent to make the right choices. We apply our method to the Atari 2600 games from the OpenAI Gym. We find that DQN with auxiliary networks significantly improves the performance and the stability of games.

In this note, the asymptotic consensus tracking problem is addressed for uncertain multi-agent systems (MASs) with undirected communication topologies and a high-dimensional leader, where the uncertainties may contain unmodeled dynamics and external disturbance which are prior unknown. To remove the effect of high-dimensional leader, an observer based compensation controller is firstly designed. A neural-adaptive based feedback controller is then designed. Note that the feedback term contains a discontinuous controller which is used to eliminate the effect of imprecise approximation of neural network. Furthermore, if the leader is assumed to be globally reachable, it is shown that asymptotic consensus tracking is achieved in MAS by choosing appropriate control parameters. The obtained theoretical result is finally validated by simulation.

In this paper, finite-time consensus problem is considered for a class of second-order multi-agent systems with a directed communication topology. A fully-distributed control protocol is proposed for solving the finite-time consensus problem, without using any global information. A simulation example is presented to verify the theoretical result and to show the effectiveness of the protocol.

Cooperative consensus tracking and its -gain performance is investigated in this paper for a class of multiple agent systems (MASs) in the presence of a single high-dimensional leader. Compared with the traditional models for MASs, the inherent dynamics of the leader are allowed to be different with those of the followers in the present framework, which is thus much more favorable in various practical applications. A new kind of distributed controllers associated with a reduced-order state observer are designed for each follower to track the high-dimensional leader under directed switching topology. With the help of -matrix theory and stability analysis methods of switched systems, some efficient criteria are derived for cooperative consensus tracking of MASs without any external disturbance under directed switching topology. Theoretical analysis is further extended to the case of consensus tracking for MASs subject to unknown external disturbances by showing that, a finite -gain performance for tracking errors against external disturbances can be ensured if some suitable conditions are satisfied. At last, the synthesis issue of designing an observer-based controller to achieve a prescribed -gain performance for consensus tracking is studied by using tools from control theory, where the underlying topology is assumed to be undirected and fixed. The effectiveness of theoretical results is verified by performing numerical simulations.

The economic dispatch problem is investigated in this paper for a class of smart grids subject to unknown communication uncertainties. Compared with existing works related to economic dispatch where the dispatch algorithms are carried out by a centralized controller, a new kind of distributed dispatch algorithms are developed to achieve optimal dispatch of electric power by appropriately sharing the load among different generating units while guaranteeing consensus among incremental costs. An adaptive weight-adjustment technique is suggested that enables the dispatch algorithms to choose the communication weights among neighboring generating units which yield consensus of incremental costs under both cases with or without capacity limitations. The achievement of such a consensus leads to optimal dispatch of electronic power and secures the system performance against unknown communication uncertainties. Meanwhile, it is proved that the power demand and supply of the considered smart grids will be kept in a balanced state during the dispatch process. The interesting issue of how to assign the power outputs among generating units to balance the power demand and supply of the considered smart grids is also addressed. Finally, the numerical results of several case studies have been provided to verify the effectiveness of the proposed algorithms.

In this paper, the swarming behavior of multiple Euler-Lagrange systems with cooperation-competition interactions is investigated, where the agents can cooperate or compete with each other and the parameters of the systems are uncertain. The distributed stabilization problem is first studied, by introducing an auxiliary system to each agent, where the common assumption that the cooperation-competition network satisfies the digon sign-symmetry condition is removed. Based on the input-output property of the auxiliary system, it is found that distributed stabilization can be achieved provided that the cooperation subnetwork is strongly connected and the parameters of the auxiliary system are chosen appropriately. Furthermore, as an extension, a distributed consensus tracking problem of the considered multiagent systems is discussed, where the concept of equi-competition is introduced and a new pinning control strategy is proposed based on the designed auxiliary system. Finally, illustrative examples are provided to show the effectiveness of the theoretical analysis.

This paper investigates the stability of equilibrium point and periodic solution for impulsive fuzzy high-order bidirectional associative memory neural networks with continuously distributed delays. By applying the inequality analysis technique, -matrix, and Banach contraction mapping principle and constructing some suitable Lyapunov functionals, some sufficient conditions for the uniqueness and global exponential stability of equilibrium point and global exponential stability of periodic solutions are established. In addition, three examples with numerical simulations are presented to demonstrate the feasibility and effectiveness of the theoretical results.

Under the mild assumption that only the sampled-data output information about the master system is available, synchronization of networked master-salve system consisting of a high-order master system and a low-order slave system is investigated in this paper. Specifically, the dynamics of the master system and those of the slave system are allowed to be characterized by heterogeneous nonlinear systems. The communication between these two systems are transmitted by multiple sensors over a communication network, while at each sampling instant, only one sensor is allowed to transmit its current information to the controller's side according to some carefully designed scheduling protocols. To achieve master-salve synchronization, the stochastic scheduling and the Round-Robin scheduling protocols are, respectively, proposed and utilized. By appropriately designing observer and controller for the slave system, some sufficient synchronization criteria regarding to the gain matrices, sampling intervals and communication delays are derived for the closed-loop master-salve system under respectively the stochastic scheduling and the Round-Robin scheduling protocols. Last, two numerical examples are simulated to validate the effectiveness of the theoretical results.

Distributed practical node-to-node state consensus problem is studied in this paper for a class of two-layer multi-agent systems. It is supposed that there are two layers, i.e., the leaders' layer and followers' layer, in the considered multi-agent systems. Unlike most existing results on distributed consensus of multi-agent systems, the control objective in this paper is to make the states of each follower located on followers' layer track those of its corresponding leader located on leaders' layer. Furthermore, the network topologies of the leaders and the followers may be heterogeneous. Based on the assumption that the states of leaders are uniformly bounded, some sufficient criteria for node-to-node practical consensus are obtained by using differential equation theory.

This paper is concerned with the distributed consensus tracking problem of uncertain multiagent systems with directed communication topology and a single high-dimensional leader. Compared with existing related works, the dynamics of each follower in the present framework are subject to unmodeled dynamics and unknown external disturbances, which is more practical in various applications. Furthermore, the dimensions of leader's dynamics may be different with those of the followers' dynamics. Under the mild assumption that each follower can directly or indirectly sense the output information of the leader, a distributed robust adaptive neural network controller together with a local observer are designed to each follower to ensure that the states of each follower ultimately synchronize to the leader's output with bounded residual errors under a fixed topology. By appropriately constructing some multiple Lyapunov functions, the derived results are further extended to consensus tracking with switching directed communication topologies. The effectiveness of the analytical results is demonstrated via numerical simulations.

In this paper, the new decoupled distributed sliding-mode control (DSMC) is first proposed for second-order consensus in multiagent systems, which finally solves the fundamental unknown problem for sliding-mode control (SMC) design of coupled networked systems. A distributed full-order sliding-mode surface is designed based on the homogeneity with dilation for reaching second-order consensus in multiagent systems, under which the sliding-mode states are decoupled. Then, the SMC is applied to the decoupled sliding-mode states to reach their origin in finite time, which is the sliding-mode surface. The states of agents can first reach the designed sliding-mode surface in finite time and then move to the second-order consensus state along the surface in finite time as well. The DSMC designed in this paper can eliminate the influence of singularity problems and weaken the influence of chattering, which is still very difficult in the SMC systems. In addition, DSMC proposes a general decoupling framework for designing SMC in networked multiagent systems. Simulations are presented to verify the theoretical results in this paper.

In this paper, the robust fixed-time consensus problem for multiagent systems with nonlinear dynamics and uncertain disturbances under a weighted undirected topology is investigated. Some nonlinear control protocols are proposed under which fixed-time consensus in the considered multiagent systems can be ensured. Compared with the initial-condition based finite-time consensus, it is theoretically shown that any prescribed convergence time for the achievement of consensus can be guaranteed within fixed time regardless of the initial conditions. Furthermore, the achievement of consensus is shown to be robust against bounded uncertain disturbances affecting the agents. Finally, some numerical examples are provided to illustrate the performance and effectiveness of the theoretical results.

This paper deals with a consensus tracking problem for multiagent systems (MASs) with Lipschitz-type nonlinear dynamics and directed switching topology. Unlike most existing works where the relative full state measurements of neighboring agents are utilized, it is assumed that only the relative output measurements of neighboring agents are available for coordination. To achieve consensus tracking in the considered MASs, a new class of observer-based protocols is proposed. By appropriately constructing some topology-dependent multiple Lyapunov functions, it is theoretically shown that distributed consensus tracking in the closed-loop MASs equipped with the designed protocols can be ensured if each possible topology contains a directed spanning tree rooted at the leader and the dwell time for the switchings among different topology is less than a derived positive quantity. Interestingly, it is found that the communication topology for observers' states may be independent with that of the feedback signals. The derived results are further extended to the case of directed switching topology with only average dwell time constraints. Finally, the effectiveness of the analytical results is demonstrated via numerical simulations.

In the above paper[1], there are errors regarding the description of(4), and misquotes in Algorithm 1 and 2. In Algorithm 1, the first equation referenced should be (5) and not (40). In Algorithm 2, the first equation referenced should be (40) and not (5). The correction for(4)is as follows:\begin{equation*} \mathcal {L}^{(\sigma (t))}=\left [{\begin{array}{cc} \widetilde {\mathcal {L}}^{(\sigma (t))}& \mathrm {a}^{(\sigma (t))}\\ \mathrm {0}_{N}^{T}& 0 \end{array}}\right ] \tag{4}\end{equation*}where$\widetilde {\mathcal {L}}^{(\sigma (t))}\in \mathbb {R}^{N\times N}$,$\mathrm {a}^{(\sigma (t))}=-[a_{1(N+1)}^{(\sigma (t))},a_{2(N+1)}^{(\sigma (t))},\cdots ,~a_{N(N+1)}^{(\sigma (t))}]^{T}\in \mathbb {R}^{N}$, and$\mathcal {A}^{(\sigma (t))} = [a_{ij}^{(\sigma (t))}]_{(N+1) \times (N+1)}$is the adjacency matrix of$\mathcal {G}^{(\sigma (t))}$.

This paper deals with node-to-node consensus tracking problem for multi-agent systems (MASs) with linear dynamics and directed switching topologies. The coordination goal in the present framework is to employ some distributed control laws such that each follower can track its corresponding leader. Unlike most existing works where the relative full state information of neighboring agents are utilized, it is assumed that only the relative output measurements of neighboring agents are available for coordination. To achieve node-to-node consensus in the considered MASs, a new class of observer-based protocols is proposed. By appropriately constructing a topology-dependent multiple Lyapunov function, it is theoretically shown that such a node-to-node consensus in the closed loop MASs equipped with the designed protocols can be guaranteed if each follower can directly or indirectly sense at least one leader over some uniformly bounded time intervals. Finally, a numerical simulation is performed to verify the effectiveness of the theoretical result.

This paper is concerned with the finite-time synchronization (FTS) issue of switched coupled neural networks with discontinuous or continuous activations. Based on the framework of nonsmooth analysis, some discontinuous or continuous controllers are designed to force the coupled networks to synchronize to an isolated neural network. Some sufficient conditions are derived to ensure the FTS by utilizing the well-known finite-time stability theorem for nonlinear systems. Compared with the previous literatures, such synchronization objective will be realized when the activations and the controllers are both discontinuous. The obtained results in this paper include and extend the earlier works on the synchronization issue of coupled networks with Lipschitz continuous conditions. Moreover, an upper bound of the settling time for synchronization is estimated. Finally, numerical simulations are given to demonstrate the effectiveness of the theoretical results.

This paper studies the synchronization problem for a network of coupled harmonic oscillators by proposing a distributed control algorithm based only on delayed position states, i.e., outdated position states stored in memory. The coupling strength of the network is conveniently designed according to the absolute values and the principal arguments of the nonzero eigenvalues of the network Laplacian matrix. By analyzing a finite number of stability switches of the network with respect to the variation in the time delay, some necessary and sufficient conditions are derived for reaching synchronization in networked harmonic oscillators with positive and negative coupling strengths, respectively, and it is shown that the time delay should be taken from a set of intervals bounded by some critical values. Simulation examples are given to illustrate the effectiveness of the theoretical analysis.

To reduce information exchange requirements in smart grids, an event-triggered communication-based distributed optimization is proposed for economic dispatch. In this work, the θ-logarithmic barrier-based method is employed to reformulate the economic dispatch problem, and the consensus-based approach is considered for developing fully distributed technology-enabled algorithms. Specifically, a novel distributed algorithm utilizes the minimum connected dominating set (CDS), which efficiently allocates the task of balancing supply and demand for the entire power network at the beginning of economic dispatch. Further, an event-triggered communication-based method for the incremental cost of each generator is able to reach a consensus, coinciding with the global optimality of the objective function. In addition, a fast gradient-based distributed optimization method is also designed to accelerate the convergence rate of the event-triggered distributed optimization. Simulations based on the IEEE 57-bus test system demonstrate the effectiveness and good performance of proposed algorithms.

In this paper, we study the problem of finite-time consensus of multiagent systems on a fixed directed interaction graph with a new protocol. Existing finite-time consensus protocols can be divided into two types: 1) continuous and 2) discontinuous, which were studied separately in the past. In this paper, we deal with both continuous and discontinuous protocols simultaneously, and design a centralized switching consensus protocol such that the finite-time consensus can be realized in a fast speed. The switching protocol depends on the range of the initial disagreement of the agents, for which we derive an exact bound to indicate at what time a continuous or a discontinuous protocol should be selected to use. Finally, we provide two numerical examples to illustrate the superiority of the proposed protocol and design method.

In this paper, demand side management problem is reformulated by the jointly constrained noncooperative game. The corresponding networked optimization method that concentrates on seeking generalized Nash Equilibrium for noncooperative game is developed for the problem. Due to the large scale of users in demand side management, the noncooperative game based demand side management is divided into groups of sub games, which can be efficiently solved by Nikaido-Isoda function based Newton method. Simulation results verify that the effectiveness of the designed algorithm.

This paper studies the global pinning synchronization problem for a class of complex networks with switching directed topologies. The common assumption in the existing related literature that each possible network topology contains a directed spanning tree is removed in this paper. Using tools from M -matrix theory and stability analysis of the switched nonlinear systems, a new kind of network topology-dependent multiple Lyapunov functions is proposed for analyzing the synchronization behavior of the whole network. It is theoretically shown that the global pinning synchronization in switched complex networks can be ensured if some nodes are appropriately pinned and the coupling is carefully selected. Interesting issues of how many and which nodes should be pinned for possibly realizing global synchronization are further addressed. Finally, some numerical simulations on coupled neural networks are provided to verify the theoretical results.

Concerning on optimal economic dispatch, interior point method via 6-logarithmic barrier is employed to reformulate the cost function of power generation. Fully distributed technology-enabled algorithm is developed to solve the economic dispatch. More specifically, the minimum connected dominating set based distributed algorithm aims at efficiently allocating the task of supply-demand balance for the whole power grid. A fast gradient based distributed optimization method is designed to fast converge to optimal solution. The simulations illustrate the effectiveness and good performance of our algorithms.

This paper investigates the distributed consensus problem of fractional-order multi-agent systems under a time-invariant communication topology, where the dynamics of each agent is described by a general fractional-order differential equation. To achieve consensus, a fractional-order observer-type consensus protocol based on relative output measurements is introduced. By using tools from Lyapunov stability theory for fractional-order systems, two theorems about the consensus of fractional-order multi-agent system with a fixed communication topology having a spanning tree are then proposed. Finally, the effectiveness of the theoretical results is demonstrated through numerical simulations.

In this paper, pinning synchronization on complex networks of networks is investigated, where there are many subnetworks with the interactions among them. The subnetworks and their connections can be regarded as the nodes and interactions of the networks, respectively, which form the networks of networks. In this new setting, the aim is to design pinning controllers on the chosen nodes of each subnetwork so as to reach synchronization behavior. Some synchronization criteria are established for reaching pinning control on networks of networks. Furthermore, the pinning scheme is designed, which shows that the nodes with very low degrees and large degrees are good candidates for applying pinning controllers. Then, the attack and robustness of the pinning scheme are discussed. Finally, a simulation example is presented to verify the theoretical analysis in this paper.

Synchronization in complex networks has been widely investigated recently. Almost all the existing conditions for reaching certain dynamics in complex networks require the global spectrum information of the network. A challenging problem for how the network structure affects the network dynamics in a distributed way especially with directed topologies is still unreleased in the recent decade. In particular, what kind of network structure or coupling weights in the general directed complex networks are very critical and how to change these weights in a local setting to achieve the desired behavior? This paper aims to solve this challenging problem.

This paper considers the leader-following consensus problem for multiagent systems with inherent nonlinear dynamics. Some M-matrix strategies are developed to address several challenging issues in the pinning control of multiagent systems by using algebraic graph theory and the properties of nonnegative matrices. It is shown that second-order leader-following consensus in a nonlinear multiagent system can be reached if the virtual leader has a directed path to every follower and a derived quantity is greater than a positive threshold. In particular, this paper analytically proves that leader-following consensus may be easier to be achieved by pinning more agents or increasing the pinning feedback gains. A selective pinning scheme is then proposed for nonlinear multiagent systems with directed network topologies. Numerical results are given to verify the theoretical analysis.

This paper reviews some main results and progress in distributed multi-agent coordination, focusing on papers published in major control systems and robotics journals since 2006. Distributed coordination of multiple vehicles, including unmanned aerial vehicles, unmanned ground vehicles, and unmanned underwater vehicles, has been a very active research subject studied extensively by the systems and control community. The recent results in this area are categorized into several directions, such as consensus, formation control, optimization, and estimation. After the review, a short discussion section is included to summarize the existing research and to propose several promising research directions along with some open problems that are deemed important for further investigations.

This paper studies second-order consensus in multi-agent systems with sampled position and velocity data. A distributed linear consensus protocol with second-order dynamics is first designed, where both sampled position and velocity data are utilized. A necessary and sufficient condition based on the sampling period, the coupling gains, and the spectra of the Laplacian matrix, is established for reaching consensus of the system in this setting. It is found that second-order consensus in such a multi-agent system can be achieved by appropriately choosing the sampling period determined by a polynomial with order three. In particular, second-order consensus cannot be reached for a sufficiently large sampling period while it can be reached for a sufficiently small one under some conditions. Then, the coupling gains are carefully designed under the given network structure and the sampling period. Furthermore, the consensus regions are characterized for the spectra of the Laplacian matrix. On the other hand, second-order consensus in delayed undirected networks with sampled position and velocity data is then discussed. A necessary and sufficient condition is also given, by which appropriate sampling period can be chosen to achieve consensus in multi-agent systems. Finally, simulation examples are given to verify and illustrate the theoretical analysis.

This paper investigates quasi-synchronization of switched linearly coupled complex networks with discontinuous nonlinear functions. The existence and boundedness of solutions for discontinuous complex networks are derived by the matrix measure approach and Filippov solutions. A sufficient condition is derived to ensure quasi-synchronization of switched coupled complex networks with discontinuous isolated nodes, which could be controlled by some designed linear controllers. The main results extend the previous work on the synchronization issue of coupled switched networks with Lipschitz continuous conditions. Numerical simulations are given to demonstrate the effectiveness of the theoretical results.

This paper considers a second-order consensus problem for multiagent systems with nonlinear dynamics and directed topologies where each agent is governed by both position and velocity consensus terms with a time-varying asymptotic velocity. To describe the system's ability for reaching consensus, a new concept about the generalized algebraic connectivity is defined for strongly connected networks and then extended to the strongly connected components of the directed network containing a spanning tree. Some sufficient conditions are derived for reaching second-order consensus in multiagent systems with nonlinear dynamics based on algebraic graph theory, matrix theory, and Lyapunov control approach. Finally, simulation examples are given to verify the theoretical analysis.

Topology identification of a network has received great interest for the reason that the study on many key properties of a network assumes a special known topology. Different from recent similar works in which the evolution of all the nodes in a complex network need to be received, this brief presents a novel criterion to identify the topology of a coupled FitzHugh-Nagumo (FHN) neurobiological network by receiving the membrane potentials of only a fraction of the neurons. Meanwhile, although incomplete information is received, the evolution of all the neurons including membrane potentials and recovery variables are traced. Based on Schur complement and Lyapunov stability theory, the exact weight configuration matrix can be estimated by a simple adaptive feedback control. The effectiveness of the proposed approach is successfully verified by neural networks with fixed and switching topologies.

This paper introduces a novel complex network model to evaluate the reputation of virtual organizations. By using the Lyapunov function and linear matrix inequality approaches, the local synchronization of the proposed model is further investigated. Here, the local synchronization is defined by the inner synchronization within a group which does not mean the synchronization between different groups. Moreover, several sufficient conditions are derived to ensure the local synchronization of the proposed network model. Finally, several representative examples are given to show the effectiveness of the proposed methods and theories.

In this paper, a new filtering problem for sensor networks is investigated. A new type of distributed consensus filters is designed, where each sensor can communicate with the neighboring sensors, and filtering can be performed in a distributed way. In the pinning control approach, only a small fraction of sensors need to measure the target information, with which the whole network can be controlled. Furthermore, pinning observers are designed in the case that the sensor can only observe partial target information. Simulation results are given to verify the designed distributed consensus filters.

In this paper, stability and bifurcation of a general recurrent neural network with multiple time delays is considered, where all the variables of the network can be regarded as bifurcation parameters. It is found that Hopf bifurcation occurs when these parameters pass through some critical values where the conditions for local asymptotical stability of the equilibrium are not satisfied. By analyzing the characteristic equation and using the frequency domain method, the existence of Hopf bifurcation is proved. The stability of bifurcating periodic solutions is determined by the harmonic balance approach, Nyquist criterion, and graphic Hopf bifurcation theorem. Moreover, a critical condition is derived under which the stability is not guaranteed, thus a necessary and sufficient condition for ensuring the local asymptotical stability is well understood, and from which the essential dynamics of the delayed neural network are revealed. Finally, numerical results are given to verify the theoretical analysis, and some interesting phenomena are observed and reported.