While semi-asynchronous federated learning (SAFL) combines the efficiency of synchronous training with the flexibility of asynchronous updates, it inherently suffers from participation bias, which is further exacerbated by non-IID data distributions. More importantly, hierarchical architecture shifts participation from individual clients to client groups, thereby further intensifying this issue. Despite notable advancements in SAFL research, most existing works still focus on conventional cloud-end architectures while largely overlooking the critical impact of non-IID data on scheduling across the cloud–edge–client hierarchy. To tackle these challenges, we propose FedCure, an innovative semiasynchronous Federated learning framework that leverages Coalition construction and participation-aware scheduling to mitigate participation bias with non-IID data. Specifically, FedCure operates through three key rules: (1) a preference rule that optimizes coalition formation by maximizing collective benefits and establishing theoretically stable partitions to reduce non-IID-induced performance degradation; (2) a scheduling rule that integrates the virtual queue technique with Bayesian-estimated coalition dynamics, mitigating efficiency loss while ensuring mean rate stability; and (3) a resource allocation rule that enhances computational efficiency by optimizing client CPU frequencies based on estimated coalition dynamics while satisfying delay requirements. Comprehensive experiments on four real-world datasets demonstrate that FedCure improves accuracy by up to 5.1x compared with four state-of-the-art baselines, while significantly enhancing efficiency with the lowest coefficient of variation 0.0223 for per-round latency and maintaining long-term balance across diverse scenarios.

Asynchronous Federated Learning (AFL) is acclaimed for accelerating collaborative training on heterogeneous systems by eliminating the wait for stragglers. While current solutions focus on improving convergence amidst update delays, they neglect how delayed aggregation fosters free-riding attacks, allowing malicious clients to easily extract the global model without contribution. This behavior results in significant fairness issues and performance degradation. To address this challenge, we propose OPTION, the first online pricing strategy tailored to mitigate free-riding in AFL. OPTION establishes an economic model in which access to model updates is purchased using credits earned from verified contributions. Specifically, OPTION values each model update according to its marginal performance gain and training cost, and subsequently necessitates a download fee from each client based on the Hotelling model to prevent zero-cost acquisition. Moreover, OPTION rewards clients for successful updates under non-arbitrage constraints, effectively balancing individual utility and task budget. To maximize the average model performance while satisfying these conditions, OPTION leverages the Lyapunov drift framework and a probabilistic sampling-based algorithm to optimize the pricing parameters. Extensive experimental results on three real-world datasets demonstrate that OPTION effectively mitigates freeriding attacks in AFL, increases the number of valid updates by at least 23.97%, and achieves a model accuracy improvement of at least 3.01% compared to state-of-the-art baselines.

With the increasing application of high-stakes decisionmaking application in Federated Learning (FL), ensuring fairness across different populations to prevent biases against certain groups has become crucial. However, achieving group fairness (GF) in FL presents a formidable challenge due to its decentralization, which complicates the global GF estimation by the server. Moreover, distrust and fragility hinder the server from gathering GF values from unreliable clients. This challenge motivates our proposal of OursFed, a provable GF-aware FL framework that integrates a privacy pairbased contract and robust GF estimation method to address issues of distrust and fragility. Methodologically, we categorize client unreliability into two categories: active unreliability stemming from distrust and passive unreliability arising from fragility. To mitigate active unreliability, we design a privacy pair-based contract to guarantee truthful GF reporting, and enhance multivariate analysis by identifying relationships among multiple private data. To counteract passive unreliability, we develop a robust GF estimation using non-parametric techniques to smooth data and estimate probability densities and regression functions, improving per-client GF accuracy under multi-dimensional data perturbation. Theoretically, we demonstrate the efficacy of OursFed by analyzing its convergence, GF stability, and accuracy deviation. Experimentally, evaluations on two real datasets show that OursFed improves GF by 28.61% with at most 2.7% trade-off versus state-ofthe-art baselines, and synthetic experiments further confirm its effectiveness in handling fragility and distrust.

The primary objective of this paper is to address the visual servo tracking control problem for robot manipulator. Based on the visual servo control system structure, the system is artificially divided into two parts: the outer-loop (visual feedback control loop) and the inner-loop (robot tracking control loop). First, for the outer loop system, a visual servo pixel kinematics model is established based on the perspective projection equation, and a virtual linear velocity controller for the camera is designed. Second, based on the robot’s Jacobian matrix, the virtual linear velocity of the outer-loop is transformed into the robot joint angular velocity signal (the desired signal for the inner-loop). Then, combining the robot’s dynamic characteristics, a finite-time trajectory tracking controller is designed to ensure that the robot can track the desired joint angular velocity signal in a finite time. Additionally, considering the presence of external disturbances in the robot system, a koopman operator-based disturbance observer is designed to enhance the robustness of the inner loop control system. Finally, numerical simulations and experimental results validate the feasibility of the proposed theoretical algorithms.

Sensor scheduling plays a vital role in remote state estimation of networked systems with constrained communication bandwidth. Various event-triggered scheduling strategies have been proposed for different state estimation tasks. However, for nonlinear systems or systems with unknown noise, it is challenging to derive an exact estimator due to the intractability of noise evolution under the event-triggered mechanism. To address this limitation, we propose a learning-based stochastic event-triggered Kalman net scheme that models the estimation process with neural networks. The network is trained to learn the Kalman gain, which is then embedded into the Kalman filter for state estimation. To address the selective transmission in event-triggered mechanisms, a masking strategy is designed that uses the event-triggering sequence matrices to eliminate the impact of untransmitted data. Furthermore, the trade-off between communication rate and estimation accuracy can be flexibly tuned by adjusting the event-triggering decision matrix. The proposed method is applicable to both linear and nonlinear systems and does not rely on the noise statistics, as the noise characteristics are implicitly encoded in the hidden states of the recurrent neural network. Simulation results and real-world battery examples demonstrate the superiority of the proposed method and highlight its potential for advancing remote state estimation tasks.

Fixed-wing unmanned aerial vehicles (UAVs) performing turn maneuvers in turbulent environments face significant control challenges due to stochastic aerodynamic disturbances. This paper proposes a hybrid turbulence-aware control framework that integrates mathematical modeling, global optimization, and machine learning for adaptive autopilot gain tuning. A semi-invariant-based deterministic reduction of the stochastic lateral-directional model is developed, reducing the dimensionality from 44 to 7 equations while preserving control-relevant statistical characteristics. To determine optimal feedback gains, a Modified Survival of the Fittest Algorithm (MSoFA) is introduced, demonstrating improved global convergence reliability and achieving 5–15% better solution quality compared to conventional evolutionary methods. An offline-generated dataset of optimal gains across varying turbulence intensities and flight altitudes is then used to construct a clustered Long Short-Term Memory (C-LSTM) architecture that combines DBSCAN-based regime identification with recurrent neural approximation. The proposed neural controller achieves 98.3% gain prediction accuracy and reduces computation time by more than three orders of magnitude relative to direct optimization. Extensive numerical simulations confirm stable turn performance over altitudes ranging from 800 to 1500 m and turbulence scales from 150 to 470 m, with terminal yaw-rate deviations below 0.01%. The novelty of the proposed framework lies in the structured integration of (i) semi-invariant-based stochastic model reduction, (ii) globally reliable evolutionary optimization for constrained gain tuning, and (iii) regime-dependent recurrent neural approximation for real-time implementation. To the best of the authors’ knowledge, such an integrated turbulence-aware tuning framework for fixed-wing UAV autopilots has not been previously reported.

The cooperative pursuit games of multiple unmanned surface vessels (USVs) that coordinate the actions of USVs to capture specific targets are of great significance for ensuring maritime security. The existing pursuit algorithms primarily encounter challenges including unclear target capture criteria, limited real-time performance and efficiency, and inadequate environmental adaptability. Combining multi-agent deep reinforcement learning (RL) with threat potential fields (TPFs), a game-based cooperative hunting algorithm is developed for underactuated USVs. The new features of the proposed hunting strategy are threefold: 1) The criteria for successful target capture, including the explicit mathematical expression, are established using a shunting environment and a boundary constraint-free kinematic model. 2) By integrating a multi-head attention (MHA) mechanism into the RL strategy, a new multi-agent proximal policy optimization (MAPPO) framework is developed, which alleviates the sparse reward problem and significantly improves convergence efficiency in maritime scenarios with multiple evaders. 3) To be more suitable for complex marine environments, a new TPFs-based reward mechanism is constructed, which not only helps USVs avoid environmental obstacles but also facilitates efficient cooperative hunting. At last, numerical simulations and experimental results are presented to demonstrate the effectiveness of the developed hunting algorithm.

This study proposes a novel synchronization framework for memristive chaotic systems (MCSs) through an enhanced deep reinforcement learning (DRL) approach, featuring an improved proximal policy optimization (PPO) algorithm. Distinguished from traditional linear/nonlinear control paradigms that necessitate precise mathematical modeling, our DRL-based methodology operates without prior knowledge of system dynamics or analytical model requirements. The developed data-driven control strategy demonstrates significant advantages by reducing the required control forces from four to three dimensions, thereby substantially decreasing control complexity and operational costs compared to conventional item-by-item control methods. Through systematic optimization of the reward function architecture in classical PPO algorithms, we achieve accelerated synchronization convergence rates for MCSs, in which an optimal exponential parameter is obtained accordingly. Finally, the practical efficacy of our DRL-driven synchronization framework is successfully validated in image encryption applications. Comprehensive numerical simulations and comparative analyses demonstrate that the proposed methodology not only maintains robust performance under Gaussian noise perturbations but also achieves synchronization efficiency improvements.

In this article, the social power evolution problem is investigated for a social network with a centralized media and multiple DeGroot individuals, where the centralized media impacts the evolution of individuals’ opinions through the centralization parameter at the broadcast moment, while the network topology among the individuals is influenced by the relative interaction matrix. Then, the convergence of the corresponding opinion dynamics on the time scale is derived by discussing three distinct initial social powers. By integrating the reflected appraisal mechanism, a social power evolution model with the centralized media is established, which is essentially a nonlinear mapping. Based on the Jacobian matrix of this nonlinear mapping, it is proved that both the social powers of the centralized media and DeGroot individuals can converge provided that the centralization parameter exceeds a certain threshold; furthermore, a lower bound for the centralized media’s final social power is estimated, which helps to demonstrate that the centralized media possesses the greatest social power within the whole network. Additionally, concerning individuals’ final social powers, all individuals are first divided into three categories, and a sufficient condition is presented to ensure that the balanced individual has the greatest social power except for the centralized media. Finally, the obtained results are illustrated by a numerical example.

In this article, the evolution of social power is studied within a unified framework comprising two classes of individuals: oblivious individuals and stubborn individuals, whose opinion dynamics are described by the DeGroot averaging model and the Friedkin-Johnsen model, respectively. A proper subset of the simplex is identified to ensure the well-posedness of social power, and it is demonstrated that the corresponding opinion dynamics is convergent for each issue by restricting the initial social power to this proper subset. Through the reflected appraisal mechanism, a nonlinear mapping governing the social power evolution together with its invariant set is derived, and some sufficient conditions with linear time complexity for the convergence of social power are established by proving that this nonlinear mapping is contractive on the invariant set. Furthermore, for the final social power, it is found that both autocratic and democratic social power cannot be achieved during the evolution, and the average social power of oblivious individuals is larger than that of stubborn individuals, indicating that the network topology has a greater impact on social power than individual stubbornness. In addition, it is observed that the final social power ranking of oblivious individuals is consistent with their centrality ranking, and a rigorous lower bound on the final social power is derived for each stubborn individual. Finally, a numerical example is provided to demonstrate the correctness of the theoretical analysis.

This article investigates how Denial-of-Service (DoS) attacks impact the time and energy costs (ECs) associated with the emergence of flocking dynamics in the Cucker-Smale system. We propose resilient finite-time and fixed-time control protocols against DoS attacks and establish conditions under which the Cucker-Smale (C-S) system can achieve flocking within a bounded time. The attack patterns are modeled stochastically and are constrained by the effective duration of the attack. Explicit upper bounds for both time and ECs are derived, demonstrating their dependence not only on the group size and control parameters, but also on the duration of DoS attacks. Theoretical analysis and numerical simulations consistently demonstrate that shorter attack durations facilitate faster convergence and lower energy consumption. Additionally, our analysis uncovers a tradeoff between time cost and EC under DoS attacks, suggesting that optimal communication intensity should be carefully adjusted to meet specific performance requirements of practical applications.

This article studies the event-triggered prescribed-time distributed observer network design problem of linear time-invariant systems subject to unknown input (UI), where each observer node has access only to partial output information of the target system. The issue of the prescribed-time distributed event-triggered state estimation has not been adequately addressed. To this end, a novel prescribed-time distributed unknown input observer (PTDUIO), featuring the periodic delayed terms and prescribed-time coupling gain, is proposed under the scenario of continuous-time communication. It is analytically proved that the constructed PTDUIO enables each observer node to reconstruct the target system's states in the prescribed settling time regardless of initial conditions, with completely eliminating the influence of UI. To reduce the communication frequency among neighboring nodes, an improved event-triggered mechanism with the triggering condition related to the prescribed-time function is designed. Such a design facilitates the simultaneous realization of prescribed-time convergence and event-triggered communication. In addition, the sufficient criterion is derived to achieve the practical prescribed-time distributed state estimation in the event-triggered communication fashion, and the Zeno behavior is excluded. Finally, numerical examples are provided to demonstrate the effectiveness and superiority of the designed PTDUIO.

This work investigates the oriented-covert attacks and corresponding defense strategies on an unmanned aerial vehicle (UAV) equipped with a GPS sensor and an Ultra-WideBand sensor in single and double base-station scenarios. The attacker drives the UAV away from its nominal path and causes a high-velocity collision while remaining stealthy to base station detection. The attack is formulated as a constrained optimal control problem that trades off terminal deviation and impact velocity, subject to oriented-covert constraints that decompose the control input into detectable and undetectable components. To defend against the above attacks, the defender should enable the UAV to avoid collisions while reaching its nominal destination with minimal energy consumption. Essentially, the attacker–defender interaction is modeled as a Stackelberg game with the defender as the leader and the attacker as the follower. The existence and sensitivity of the game equilibrium are analyzed. Moreover, when the defender adopts the optimal strategy in the sense of a Nash equilibrium, the above game reduces to a unilateral defense optimization problem that aims to compute the optimal control inputs that minimize terminal deviation, impact velocity, and energy consumption simultaneously. Pontryagin’s Maximum Principle is used to derive the optimality conditions and theoretically validate the proposed attack and defense strategies. Finally, the effectiveness and practicality of the proposed attack and defense strategies are demonstrated through two simulation examples and one experiment.

This article investigates the formation tracking problem of constrained multiple autonomous surface vehicle (multi-ASV) systems subject to communication link uncertainties and limited availability of the leader's state information. To address this, distributed adaptive observers are constructed for ASVs to estimate the reference states, where the undetectable term is reconstructed through information exchanges among neighbors, and the influence of communication link uncertainties is counteracted by introducing adaptive weights. Then, by incorporating a modified cost function and an experience replay mechanism into the framework, critic-only integral reinforcement learning-based control policies are developed to achieve optimal formation tracking under asymmetric input constraints. It is shown that under finite excitation conditions, which are much weaker than persistent excitation conditions, the tracking errors and critic neural network weight estimation errors are uniformly ultimately bounded, effectively solving the formation tracking problem. Finally, the efficacy of the developed control protocol is demonstrated through numerical simulations.

Multivehicle cooperative lane-change (MVCLC) is a challenging problem in multivehicle trajectory planning, as it involves complex coordination and collision avoidance among vehicles in dynamic environments. While optimal control-based methods have demonstrated promising performance, their high computational complexity often limits practical deployment. To address this, we propose a novel imitation learning (IL) framework for MVCLC trajectory planning, which integrates optimal control-based trajectory generation with neural network (NN) training for efficient real-time inference. Specifically, we first formulate an optimal control framework for MVCLC and employ numerical optimization to generate high-quality reference trajectories. These trajectories are then used to construct a diverse dataset for training two NNs, enabling fast trajectory generation via IL. To ensure the safety and feasibility of the generated trajectories, we introduce a safety monitoring module that guarantees collision-free execution. Extensive simulation results demonstrate that the proposed method achieves near-optimal performance with significantly improved computational efficiency—achieving a reduction in planning time by 97.1% compared to traditional methods.

This article introduces a learning-based model predictive control (MPC) framework that leverages Gaussian mixture models (GMMs) to address dynamic system uncertainties effectively. To address the limitations of traditional MPC methods in handling system disturbances and uncertainties, we integrate GMM into the MPC framework to model and account for these disturbances probabilistically. By reformulating the chance constraints within this framework, the proposed approach provides high-probability safety guarantees. Specifically, GMM can capture complex disturbance distributions in dynamic systems compared with traditional Gaussian processes, thereby enabling more precise prediction and optimization within the MPC loop. This ensures that the resulting control strategies not only satisfy safety constraints but also enhance system performance. Experimental evaluations demonstrate that the proposed method achieves superior performance in satisfying high-probability safety requirements while enhancing the overall robustness of the system. Compared to conventional MPC approaches, the proposed method can effectively tackle the challenges posed by uncertainties, ensuring stability and safety under diverse conditions. This approach has broad applications in domains that require robust control under uncertainties, including autonomous driving, robotic manipulation, and other complex engineering systems.

This article investigates the distributed platoon control problem of connected automated vehicles (CAVs) under hybrid cyber attacks, which include false data injection (FDI) and eavesdropping attacks simultaneously. To mitigate the impact of hybrid cyber attacks on vehicle information exchange, an event-triggered dual-layer control strategy with a hidden layer and competitive interconnection structure is proposed. Specifically, to address malicious data injection from FDI attacks, the proposed framework achieves the objective of vehicle platooning through dynamic interaction between the physical and hidden layers only at triggered time instants. Meanwhile, FDI attacks detection and privacy preservation can also be realized through this strategy. Furthermore, a Zeno-free event-triggered mechanism (ETM) is employed to improve the communication efficiency and reduce resource consumption by avoiding unnecessary state transmissions. Sufficient conditions for control parameters are derived to guarantee resilient platoon control objectives under hybrid cyber attacks. Finally, numerical simulations validate the effectiveness of the proposed approach.

Online Federated Learning (OFL) is a real-time learning paradigm that sequentially executes parameter aggregation immediately for each random arriving client. To motivate clients to participate in OFL, it is crucial to offer appropriate incentives to offset the training resource consumption. However, the design of incentive mechanisms in OFL is constrained by the dynamic variability of Two-sided Incomplete Information (TII) concerning resources, where the server is unaware of the clients’ dynamically changing computational resources, while clients lack knowledge of the real-time communication resources allocated by the server. To incentivize clients to participate in training by offering dynamic rewards to each arriving client, we design a novel Dynamic Bayesian persuasion pricing for online Federated learning (DaringFed) under TII. Specifically, we begin by formulating the interaction between the server and clients as a dynamic signaling and pricing allocation problem within a Bayesian persuasion game, and then demonstrate the existence of a unique Bayesian persuasion Nash equilibrium. By deriving the optimal design of DaringFed under one-sided incomplete information, we further analyze the approximate optimal design of DaringFed with a specific bound under TII. Finally, extensive evaluation conducted on real datasets demonstrate that DaringFed optimizes accuracy and converges speed by 16.99%, while experiments with synthetic datasets validate the convergence of estimate unknown values and the effectiveness of DaringFed in improving the server’s utility by up to 12.6%.

Power delivery issues are increasingly evident in cyber-physical smart grid systems as energy transactions frequently overlook the physical constraints of distribution, leading to transmission congestion and compromising network security and reliability. This article presents a novel and cost-effective solution to power delivery challenges by utilizing electric vehicles (EVs) with dynamic transportation capabilities as free carriers. Unlike traditional approaches, a deep reinforcement learning (DRL)-based optimization framework is designed to effectively manage incomplete information in real-time. Our method first introduces an investment-free model that leverages existing EV routes to transport energy during congestion, operating in a “free-riding” transmission mode. This not only enhances network reliability but also curtails costs. Then, we develop a Markov decision process (MDP) for sequential decision-making of 24-h optimal control, aimed at minimizing operational losses including load shedding and battery degradation. To deal with the stochastic nature of energy requests and EV routes in the control problem, we employ a model-free DRL algorithm to tackle the challenge of incomplete information. An Actor-Critic network, combining value-based and policy-based approaches, helps discover approximately optimal strategies in a continuous action space. Finally, the simulation results numerically demonstrate the performance of the proposed method.

In the control problems of multi-agent systems, collision avoidance is a fundamental safety requirement. One effective approach to ensure safety involves combining control barrier functions (CBFs) with quadratic programming (QP), where nominal control inputs are incorporated into QPs to achieve desired control objectives. Additionally, it is crucial to study the control performance of multi-agent systems to balance these objectives with control efforts. This work demonstrates that the performance index is closely related to the hyperparameters in the CBF-based QP controller, and the Bayesian optimization algorithm is used to optimize and improve performance. Firstly, a safe control approach is developed and a unified performance enhancement framework is established to optimize the performance index. Hyperparameters are then explored and categorized, introducing the concept of feasible hyperparameters to describe the attainability of control objectives. Subsequently, the constrained Bayesian optimization algorithm is employed to identify a set of feasible and optimal hyperparameters in a data-driven manner, even when the functional expressions of performance and constraints are unknown. Finally, experiments are conducted to demonstrate the feasibility of the proposed methods in multi-agent systems. Note to Practitioners—Both safety and optimality are of great importance in the control systems. The design and development of controllers for multi-agent systems are currently undergoing significant evolution. Academic researchers and industrial practitioners are actively refining controller designs to perform better in a variety of collaborative tasks. With practical applications in mind, there is a growing demand for control techniques capable of ensuring a safe operating environment while maintaining efficiency in energy consumption. Therefore, this paper aims to furnish practitioners and researchers with a safe control framework, facilitating the refinement of optimal control solutions for efficient collaboration among multiple agents.

The lag consensus problem of multi-unmanned aerial vehicle (UAV) systems under hybrid attacks is investigated in this paper. First, a dynamic memory event-triggered control protocol is proposed for the multi-UAV system whose normal network communication would be hindered by denial-of-service (DoS) attacks. Different from traditional event-triggered mechanisms, we consider both historically transmitted data and dynamic threshold in the dynamic memory event-triggered protocol, and it will make less data transmissions and better control performance. Second, due to the communication structure is not fixed, we establish a switching-topology-based distributed control architecture. In view of the fact that communication delays among agents cannot be ignored, a distributed controller is proposed to achieves lag consensus of the multi-UAV system. And then, an estimator is designed to address the situation which the system state cannot be measured during the control process. Additionally, the practicality of the distributed control scheme is analyzed by ruling out Zeno behavior. Ultimately, the effectiveness and validity of the proposed control scheme are confirmed through a simulation example.

This study investigates the problem of designing countermeasures for resilient output time-varying formation-tracking of multi-agent systems (MASs) in a composite hazardous scenario consisting of various kinds of attacks, such as actuation attacks and denial-of-service (DoS) attacks. Combined with the digital twins concept, the above problem is decoupled into a DoS attack defense scheme on the Digital Twins Layer (DTL) and an actuation attack defense scheme on the Cyber-Physical Layer (CPL) by introducing a DTL with higher security and privacy. On the DTL, a novel Zeno-free event-triggered protocol with sampling state information, equipped with the backup topology countermeasure, is used to suppress the threat of DoS attacks. Note that the resilient protocol against DoS attacks is fully-distributed, which does not need prior knowledge of network algebraic connectivity and thus possesses sufficient scalability to large-scale networks. Moreover, the event-triggered mechanism can completely avoid Zeno phenomena by introducing a strict lower bound for the time interval between cascading triggered events. On the CPL, this study introduces a decentralized, adaptive, and resilient control strategy to address actuation attacks exhibiting exponentially unbounded destructiveness. It is proven that all followers can reach uniformly ultimately bounded convergence by the proposed two-layered control protocols. The effectiveness and resilience of the proposed algorithm are validated through a numerical simulation example.

This paper addresses the problem of distributed online generalized Nash equilibrium (GNE) learning for multi-cluster games with delayed function feedback. Specifically, each agent in the game is assumed to be informed of a sequence of local cost functions and constraint functions, which are known to the agent with time-varying delays subsequent to decision-making at each round. The objective of each agent within a cluster is to collaboratively optimize the cluster’s cost function, subject to time-varying coupled inequality constraints and local constraint sets over time. Additionally, it is assumed that each agent is required to estimate the decisions of all other agents through interactions with its neighbors, rather than directly accessing the decisions of all agents, i.e., each agent needs to make decisions under partial-decision information. To solve such a challenging problem, a novel distributed online delay-tolerant GNE learning algorithm is developed based upon the primal-dual algorithm with an aggregation gradient mechanism. The system-wise regret and the constraint violation are formulated to measure the performance of the algorithm, demonstrating sublinear growth with respect to the time horizon$\boldsymbol {T}$under certain conditions. Finally, numerical results are presented to verify the effectiveness of the proposed algorithm.

This article presents an approach to ensure the robust forward invariance of safe sets for sampled-data input nonlinear dynamical systems with model uncertainties. We first design a continuous-time composite controller structure for the uncertain system by integrating an uncertainty compensation term and a state feedback term. The uncertainty compensation term is generated by a nonlinear observer, while the feedback term is subject to linear constraints on a high order control barrier function (HOCBF) which effectively mitigates the adverse effects of the uncertainty observation error on the safety constraints. Then, inspired by the continuous-time controller, a sampled-data controller is proposed where the feedback control term is obtained by solving a new quadratic program (QP) problem with modified HOCBF constraints to address the challenges posed by sampled-data input. Sufficient conditions are derived to guarantee the robust forward invariance of the safe sets for the sampled-data nonlinear dynamical system. From the simulation experiments, it is demonstrated that the proposed method successfully ensures the safety of the sampled-data input dynamical systems with model uncertainties.

Autonomous object-searching is crucial for various applications of unmanned aerial vehicles (UAVs). Considering the fact that existing autonomous exploration methods either focus only on maximizing the exploration of unknown areas or suffer from insufficient searches due to repeated and unnecessary exploration, this article introduces an effective object-searching strategy for UAVs in large-scale and complex environments. A novel method is proposed to empower UAVs with the capability to conduct fast, secure, and efficient searches for interested objects in large-scale and complex environments. A Kalman filter-based YOLO algorithm is first proposed to achieve robust object position estimation in cluttered and occlusion-prone scenarios, and a mode-based method is then introduced to conduct a computationally efficient viewpoint generation. A hierarchical searching method is proposed, which not only can increase computational and search efficiency but also can leverage frontier data for search-planning, including coarse global searching paths and optimizing local refined searching trajectories. Experimental results in six different environments indicate that our proposed method outperforms existing techniques in terms of both reduced searching times and computing time. Moreover, the effectiveness of the proposed method is substantiated in various real-world scenarios.

In this article, the security formation control problem is investigated for underactuated quadrotors involving nonlinear coupled dynamics, subject to denial-of-service (DoS) attacks and uncertain communication faults. A security formation control method is proposed, including a distributed resilient observer and a hierarchical data-driven controller. The observer with an adaptive event-triggered mechanism is developed to restrain the influence of DoS and communication faults on interaction information among quadrotors, and Zeno behavior of all observers can be avoided. The optimal control laws are learned iteratively based on observation data and system data by utilizing reinforcement learning without knowledge of system dynamics. The stability of the constructed closed-loop control system is proven, and sufficient conditions are established for the unreliable network. Simulation results demonstrate the advantages of the proposed security control method.

This article investigates the global predefined-time consensus (PTC) of multiagent system (MAS) via constructing a duplex communication network. Unlike the traditional finite-/fixed-time convergence, our method allows the upper-bound of settling-time to be an explicit constant, which is tunable and can be set beforehand without relating with the network information, controlling parameters, and initial conditions. In particular, our approach uses a smooth, nonchattering consensus scheme that avoids conventional discontinuous functions like signum and absolute value functions. By the Lyapunov stability analysis, the sufficient criterion is deduced for ensuring the PTC of MAS. Finally, simulations confirm the effectiveness of our proposed nonchattering scheme.

Fault-tolerant control (FTC) is an effective control method designed to maintain a faulty system within an acceptable risk level while ensuring its safety. However, handling both uncertainties and faults in a system remains challenging. In this article, we propose two probabilistic model-based adaptive FTC methods for faulty nonlinear systems with unknown dynamics. We study Gaussian process (GP) regression in two cases: 1) an offline learning-based control method and 2) an event-triggered online data-driven modeling method, to learn unknown system dynamics. Considering the computational complexity of GP regression in practical applications, we discuss the case of computational delays in real-time predictions. Moreover, we develop four theoretical criteria to ensure the probabilistic stability of closed-loop systems. Finally, numerical simulations validate the effectiveness of proposed control methods and demonstrate their competitiveness compared to existing approaches.

Although numerous distributed control strategies have been developed for formation control of networked multi-UAV systems, they typically rely on the assumption of undirected and connected communication networks. This assumption limits the applicability of control strategies to scenarios with asymmetric information interactions among UAVs. To overcome this limitation, this article addresses the distributed formation control problem of nonlinear multi-UAV systems with unknown uncertainties under general directed communication networks. The approximation capabilities of fuzzy logic systems are leveraged to handle nonlinearities and uncertainties. To conserve limited resources, an event-driven approach is introduced for the design of a distributed formation control strategy. Specifically, the controller of each UAV is updated only when specific events are triggered by a distributed triggering condition, instead of being updated continuously over time. Under intermittent event-driven control updates, all UAVs can achieve a desired time-varying formation configuration, while excluding the Zeno behavior. Adaptive gains, rather than fixed gains, are introduced into the control strategy to enable more flexible control implementation without relying on global information. In addition to formation control, an event-driven attitude control strategy is proposed to ensure that the yaw angles of all UAVs converge to a prescribed value. Finally, simulations are conducted to validate the effectiveness and advantages of the proposed control schemes.

Recently, learning-based hyperspectral anomaly detection (HAD) methods have demonstrated outstanding performance, dominating mainstream research. However, the existing learning-based approaches still have two issues: 1) they rarely consider both the spatial sparsity and the interspectral similarity of hyperspectral imagery (HSI) simultaneously and 2) they treat all regions equally, often overlooking the importance of high-frequency information in HSI, which is key to distinguish background and anomalies. To address these challenges, we propose a novel HAD method based on spatial-spectral adaptive dual-domain learning, termed SSHAD. Specifically, we first introduce the spatial-wise selected state space module (SSSM) with linear complexity and the spectral-wise frequency division self-attention module (FDSM), which are combined in parallel to form a spatial-spectral block (SS-block). The SSSM captures the global receptive field by scanning the HSI spatial dimension through a multidirectional scanning mechanism. The FDSM extracts high-frequency and low-frequency information from the HSI via the discrete wavelet transform (DWT) and applies multiscale convolution and self-similarity attention respectively, ensuring the suppression of anomalies during the reconstruction process. This parallel structure enables the network to model cross-window connections, expanding its receptive field while maintaining linear complexity. We use the SS-block as the main component of our adaptive dual-domain learning network, forming SSHAD. Furthermore, we introduce a frequency-wise loss function to inhibit the reconstruction of high-frequency anomalies during background reconstruction. Comprehensive experiments conducted on four public datasets and two unmanned aerial vehicle (UAV)-borne datasets validate the superiority and effectiveness of SSHAD. The code will be publicly available athttps://github.com/CZhu0066/SSHAD.

Force control strategies are crucial for robot manipulators to effectively adapt to diverse tasks. However, employing force sensors to measure force/torque information significantly increases the cost of robotic systems. Hence, it is crucial to delve into sensorless force/torque estimation techniques. Given the low precision of traditional force estimation algorithms, this article presents a novel algorithm to improve the torque estimation precision of robot manipulators' joints. First, based on the dynamic model, a finite-time sliding-mode torque observer is designed for the robot manipulators via a step-by-step method. A new Lyapunov function is constructed to prove the finite-time convergence of the closed-loop system. Second, in the presence of sampling noise, the robustness of the proposed finite-time torque observer is analyzed. Finally, simulation and experimental results validate the effectiveness of the proposed algorithm.

This article is concerned with distributed adaptive resource allocation over general digraphs with resource-demand constraints. The central aim is to tackle two essential challenges in distributed resource allocation, namely, scalable implementation and anytime feasibility, ensuring continuous satisfaction of constraints. For this purpose, two novel fully distributed optimization algorithms, featuring sum-based and product-based schemes for adaptive gains, are first developed. It is shown that these algorithms offer several advantageous features in terms of fully distributed implementation without global knowledge and algorithm simplicity as well as anytime feasibility guarantees over existing methods. Notably, the incorporation of a double-layer adaptive control law with a damping term into each algorithm prevents the continuous growth of adaptive gains, thus avoiding excessively large system gain values and enhancing practical applicability in real-world scenarios. Furthermore, by constructing appropriate Lyapunov functions, rigorous convergence analysis confirms that both algorithms achieve the optimal resource allocation and global asymptotic convergence. Finally, several simulation case studies are conducted to validate the efficiency of the proposed algorithms.

The distributed energy management (DEM) is of significance for smart grids due to the growing concern over potential cyber threats. This study delves into a multiobjective DEM problem that encompasses economic and environmental costs, as well as transmission losses, while also considering the impact of persistent Denial-of-Service (DoS) attacks. To tackle this challenge, a novel distributed optimization algorithm over a digraph is proposed, leveraging a zeroth-order scheme to handle unavailable gradients and incorporating momentum terms to provide accurate descent directions. The theoretical analysis demonstrates the algorithm's ability to achieve a linear convergence rate while ensuring real-time maintenance of decision variables within the feasible domain. Building on this, a novel reputation-based resilient DEM framework is introduced to address scenarios involving persistent DoS attacks. This framework calculates a reputation index for each communication link to monitor its reliability. Considering the impact of attacked links on network connectivity and their reputation indexes, corresponding strategies are devised. Specifically, if an attacked link disrupts network connectivity and its reputation index falls below the threshold, a connectivity restoration optimization algorithm is activated to reconstruct links, minimizing communication costs and alleviating information congestion. Finally, the effectiveness of the proposed algorithm and framework is validated through numerical simulations.

This article aims to address the distributed robust platooning control of connected automated vehicles (CAVs) with general unknown uncertain dynamics. Despite recent progress in this area, achieving the objective of distributed robust platooning control for CAVs with limited communication resources and uncertain dynamics is an outstanding problem. To solve such a problem, a new Zeno-free event-triggered scheme is successfully established to determine whether the vehicle's state should be sampled and transmitted among the interacting vehicles. An adaptive law for updating the weighting matrix for the neural network approximator is designed, where the relative state variables are utilized only at triggered instants. Moreover, such a neuro-adaptive approach incorporates a low-pass filter structure to effectively mitigate undesirable high-frequency oscillations that may arise with the application of high-gain learning rates. Following this, a new class of distributed event-based neuro-adaptive control protocols is meticulously designed to guarantee the uniform ultimate boundedness of spacing error, relative velocity, and relative acceleration of the whole platoon. Finally, simulation examples with different scenarios are conducted, and it is interesting to find that the proposed protocol has a lower average communication rate than traditional ones without the low-pass filter structure.

Deep learning has become increasingly important in fault diagnosis, but it relies on a large amount of high-quality labeled data. Collecting data from distributed machines can expand the dataset, but it usually leads to privacy concerns. Moreover, since the operating conditions are complex in real-world applications, the collected training data and the test data often have different distributions. Therefore, a well-trained model on the training data may not be suitable for test data due to the domain shift. To preserve privacy and to mitigate the domain shift, in existing federated transfer learning fault diagnosis methods, distributed machines exchange model parameters and features rather than raw data with the central server. However, such methods suffer from a single point of failure and high communication burden. To address these issues, we propose a fully decentralized federated transfer learning fault diagnosis method. More specifically, the proposed method obtains a pretrained model among source nodes with labeled training data where each source node exchanges model parameters with its neighboring source nodes. Moreover, a novel transfer learning strategy is proposed, which aligns features of test data at the target node with features of training data at its connected source nodes to mitigate misclassifications resulting from the domain shift. The effectiveness of the proposed method is verified by various experiments on two public bearing datasets.

This article investigates state estimation in islanded microgrids (ImGs) over peer-to-peer sensor networks, focusing on scenarios involving unknown noise characteristics and measurement data corrupted by random outliers. To address this issue, a novel distributed robust state estimation algorithm is introduced. First, the inverse Wishart distribution serves as the prior distribution for estimating the unknown noise covariance matrix. The prediction probability density function (PDF) adopts a Gaussian framework, while the measurement PDF is characterized by a Gaussian–Student’s t mixture model. Furthermore, a variational Bayesian methodology is implemented to concurrently compute posterior estimations for both the state vector and associated model parameters. Besides, the alternating direction method of multipliers is utilized to achieve consensus among sensor nodes based on estimation results, while reducing communication bandwidth requirements. Finally, simulation experiments on an ImG with two distributed generation units demonstrate the effectiveness of the proposed algorithm through comparative simulations with existing methods.

Learning distributed cooperative policies for large-scale multirobot systems remains a challenging task in the multiagent reinforcement learning (MARL) context. In this work, we model the interactions among the robots as a graph and propose a novel off-policy actor-critic MARL algorithm to train distributed coordination policies on the graph by leveraging the ability of information extraction of graph neural networks (GNNs). First, a new type of Gaussian policy parameterized by the GNNs is designed for distributed decision-making in continuous action spaces. Second, a scalable centralized value function network is designed based on a novel GNN-based value function decomposition technique. Then, based on the designed actor and the critic networks, a GNN-based MARL algorithm named graph soft actor-critic (G-SAC) is proposed and utilized to train the distributed policies in an effective and centralized fashion. Finally, two custom multirobot coordination environments are built, under which the simulation results are performed to empirically demonstrate both the sample efficiency and the scalability of G-SAC as well as the strong zero-shot generalization ability of the trained policy in large-scale multirobot coordination problems.

Hyperspectral image (HSI) restoration is a challenging research area, covering a variety of inverse problems. Previous works have shown the great success of deep learning in HSI restoration. However, facing the problem of distribution gaps between training HSIs and target HSI, those data-driven methods falter in delivering satisfactory outcomes for the target HSIs. In addition, the degradation process of HSIs is usually disturbed by noise, which is not well taken into account in existing restoration methods. The existence of noise further exacerbates the dissimilarities within the data, rendering it challenging to attain desirable results without an appropriate learning approach. To track these issues, in this article, we propose a supervise-assisted self-supervised deep-learning method to restore noisy degraded HSIs. Initially, we facilitate the restoration network to acquire a generalized prior through supervised learning from extensive training datasets. Then, the self-supervised learning stage is employed and utilizes the specific prior of the target HSI. Particularly, to restore clean HSIs during the self-supervised learning stage from noisy degraded HSIs, we introduce a noise-adaptive loss function that leverages inner statistics of noisy degraded HSIs for restoration. The proposed noise-adaptive loss consists of Stein's unbiased risk estimator (SURE) and total variation (TV) regularizer and fine-tunes the network with the presence of noise. We demonstrate through experiments on different HSI tasks, including denoising, compressive sensing, super-resolution, and inpainting, that our method outperforms state-of-the-art methods on benchmarks under quantitative metrics and visual quality. The code is available at https://github.com/ying-fu/SSDL-HSI.

This article develops a novel event-triggered finite-time control strategy to investigate the finite-time synchronization (F-tS) of fractional-order memristive neural networks with state-based switching fuzzy terms. A key distinction of this approach, compared with existing event-based finite-time control schemes, is the linearity of the measurement error function in the event-triggering mechanism (ETM). The advantage of linear measurement error not only simplifies computational tasks but also aids in demonstrating the exclusion of Zeno behavior for fractional-order systems (FSs). Furthermore, to derive F-tS criteria in the form of linear matrix inequalities (LMIs), a novel finite-time analytical framework for FSs is proposed. This framework includes two original inequalities and a weighted-norm-based Lyapunov function. The effectiveness and superiority of the theoretical results are demonstrated through two examples. Both theoretical and experimental results suggest that the criteria obtained using the new analytical framework are less conservative than existing results.

This article proposes two novel projection neural networks (PNNs) with fixed-time ( ) convergence to deal with variational inequality problems (VIPs). The remarkable features of the proposed PNNs are convergence and more accurate upper bounds for arbitrary initial conditions. The robustness of the proposed PNNs under bounded noises is further studied. In addition, the proposed PNNs are applied to deal with absolute value equations (AVEs), noncooperative games, and sparse signal reconstruction problems (SSRPs). The upper bounds of the settling time for the proposed PNNs are tighter than the bounds in the existing neural networks. The effectiveness and advantages of the proposed PNNs are confirmed by numerical examples.

The time cost (TC) of fixed-time consensus (FXTC) is investigated in this article for nonlinear multiagent systems (MASs), with or without noise. By integrating the interaction between agents with the advantages of fixed-time control techniques, economical adaptive switching protocols are devised, facilitating the achievement of FXTC while mitigating energy costs (ECs). Theoretical analyses of the TC and EC to achieve FXTC are provided. Sufficient conditions for stochastic FXTC are derived by employing the stability theory and algebraic graph theory. Finally, in numerical simulations, the tradeoff between TC and EC is explored and the effectiveness of the designed protocols is substantiated.

This article investigates a distributed fixed-time secondary control (FTSC) scheme to eliminate dc voltage deviations caused by voltage-droop control (VDC) in a multiterminal dc transmission system (MTDCTS) with switching topology and achieve precise power sharing within a fixed time frame. The distributed FTSC combines a dc voltage controller and a power sharing controller. The main objective is to restore the average dc voltage of the converters to dc voltage reference of MTDCTS within a fixed time. Additionally, it also enables power sharing among the converters based on their individual capacities. Compared to conventional distributed consensus control (DCC), fixed-time control (FTC) presented in this article exhibits a shorter convergence time and is unaffected by the initial state of MTDCTS. In this article, each converter communicates exclusively with its adjacent converters via a communication network that may undergo changes over time, which helps alleviate the strain on the communication network. To test the FTSC, a five-terminal MTDCTS with two wind farm converters (WFCs) is created in power systems computer aided design (PSCAD)/electromagnetic transients including DC (EMTDC).

This article is dedicated to solving the cooperative collision-free target fencing control problem for a class of multiple unmanned surface vehicle (multi-USV) systems subject to external disturbances and uncertain dynamics. While existing control strategies often struggle to simultaneously address external disturbances, internal system uncertainties, and safety constraints in real-world applications, this study proposes a robust two-stage control strategy to effectively tackle these challenges. In the first stage, a baseline controller leveraging sliding mode control (SMC) is developed to effectively compensate for external disturbances and establish fundamental target fencing capabilities. Building on this foundation, the second stage introduces an advanced controller enhanced by soft actor–critic (SAC) reinforcement learning (RL) technique, which is specifically tailored to address internal system uncertainties and guarantee collision avoidance. Finally, numerical simulations are performed to validate the proposed approach, demonstrating its advantages over conventional RL-based methods in terms of efficiency.

In this article, we consider the data privacy issue of distributed learning over adaptive networks under zero-mean protection noise. First, using a nonzero-mean protection noise, a new privacy-preserving diffusion adaptive least-mean-squares algorithm is devised, named NZPD-LMS. Different from the existing differential privacy noise, the nonzero-mean protection noise is designed with two noises with zero-mean and nonzero-mean, allowing the zero-mean noise to retain differential privacy properties, and the nonzero-mean noise to prevent the use of a sliding average over time to obtain transmission values. Then, based on mean-square analysis, we evaluate stability conditions and steady-state error bounds for the NZPD-LMS algorithm, as well as how each algorithmic parameter affects steady-state error. Finally, several simulations are conducted to illustrate the theoretical findings and effectiveness of the proposed approach.

This article is devoted to solving the leaderless and leader-following consensus tracking problems for a class of disturbed second-order multiagent systems (MASs) under the influence of actuator attacks. To achieve this, a two-step control strategy is developed, where the effects of disturbances and actuator attacks on the achievement of consensus tracking are addressed in distinct stages. In the first step, a reference system model is constructed for each agent. Upon which a sliding mode control (SMC) protocol is constructed and utilized to resolve the consensus tracking problem of disturbed second-order MASs in the absence of actuator attacks, facilitating the design of a baseline control term for the MASs under consideration. In the second step, a secure control policy is trained using an off-policy soft actor-critic algorithm, aiming at achieving secure consensus tracking in the presence of actuator attacks. Both numerical simulations and a multipendulum consensus example verify that the designed control structure has better control performance than using only the SMC method and also effectively improves the training efficiency over the traditional reinforcement learning (RL) alone method.

This article proposes an extended zero-gradient-sum (EZGS) approach for solving constrained distributed optimization with free initialization and desired convergence properties. A Newton-based continuous-time algorithm is first designed for general constrained optimization, which is adapted to handle inequality constraints by using log-barrier penalty functions. Then, a general class of EZGS dynamics is developed to address equation-constrained distributed optimization, where an auxiliary dynamics is introduced to ensure the final ZGS property from any initialization. It is demonstrated that for typical consensus protocols and auxiliary dynamics, the proposed EZGS dynamics can achieve the performance with exponential/finite/fixed/prescribed-time (PT) convergence. Particularly, the nonlinear consensus protocols for finite-time EZGS algorithms allow for heterogeneous power coefficients. Significantly, the proposed PT EZGS dynamics is continuous, uniformly bounded, and capable of reaching the optimal solution in a single stage. Furthermore, the barrier method is employed to handle the inequality constraints effectively. Finally, the efficiency and performance of the proposed algorithms are validated through numerical examples, highlighting their superiority over existing methods. In particular, by selecting appropriate protocols, the proposed EZGS dynamics can achieve desired convergence performance.

Considering the memory property of the fractional calculus and the potential diverging state of the open-loop mode, existing analysis methods are difficult to solve the finite-time issue of intermittently controlled fractional-order systems (FOSs). This article studies the finite-time synchronization of coupled FOSs with nonlinearity via fuzzy intermittent quantized control and two novel fractional-order differential inequalities. An interval-type 2 Takagi–Sugeno fuzzy technique is introduced, which not only facilitates the handling of the nonlinear term in the error dynamic system, but also greatly simplifies the control design. Synchronization conditions in form of linear matrix inequalities are provided by designing a novel Lyapunov function on the basis of ellipsoidal norm. Moreover, two corollaries show the generality of the new analysis framework. Compared with existing results, it is amazing that the decreasing magnitude of Lyapunov function on the control intervals can be smaller than its increasing magnitude on the subsequent noncontrol interval. Finally, Chua’s system is used to clarify the effectiveness of theoretical outcomes.

This article proposes a novel extended high-gain observer (EHGO). First, we generalize the standard EHGO by augmenting it with anm-order chained integrator, forming the generalized EHGO (GEHGO). This generalization significantly enhances estimation accuracy for both system states and total disturbance. To address the numerical issues arising from the high-gain parameter raised to powern+m, we employ a feedback-cascaded technique. This reconfigures the generalized observer into a series of feedback-cascaded second-order high-gain observers (HGOs), crucially reducing the high-gain exponent to just two and greatly simplifying numerical implementation. Meanwhile, two saturation nonlinearities with suitable thresholds are embedded in each second-order HGO to prevent the peaks of the transient estimates. The global convergence of this novel EHGO is rigorously demonstrated using Lyapunov-based arguments. We also address the issue of sensitivity to high-frequency measurement noise and demonstrate thatmneeds to be constrained to preserve robustness. Finally, numerical simulations illustrate the obtained theoretical results.

This article deals with the optimal super-ellipse formation tracking control problem for multiple unmanned vehicles (MUVs), where each vehicle contains nonlinear uncertainties of unmodeled basic resistance, and the objective of energy optimization includes the super-ellipse orbit tracking energy and formation motion energy on the normal and tangent directions along the super-ellipse orbits, respectively. The communication topology is the directed leader-following structure. To avoid using the inputs of neighboring MUVs and the global communication information, a novel augmented formation input is designed and integrated into the formation motion subsystem. To deal with the uncertain nonlinearity, the uncertain virtual leader information, and the limited information of neighboring MUVs in the Hamilton-Jacobi–Bellman equations, a simplified reinforcement learning (RL) energy optimization method is designed based on identifier neural networks (NNs) and optimized backstepping technique. Theoretical stability analysis of system errors are given in detail. Simulation results show that the super-ellipse formation tracking energy consumption is significantly saved and the algorithm run time is decreased through comparison.

A flight control system acts as a core subsystem in aircraft for the purpose of attitude control and trajectory tracking. Due to the inaccurate system modeling and the internal/external disturbances (e.g., wind disturbance, aerodynamic parameter change, and load perturbation), the performance of controller designed for the typical operating points may be not optimal for the full flight envelope. This article aims to address the control performance optimization problem of flight control system in the presence of an incompletely known aircraft model and real-time flight data. First, the longitudinal aircraft dynamic model is formulated, followed by the establishment of two typical disturbance models, including periodic and constant disturbances. Subsequently, a real-time optimization framework for enhancing flight control performance is introduced, with the aid of residual-driven realization of Youla parameterized controller. Moreover, the gradient-based performance optimization strategy is proposed to mitigate the performance degradation induced by disturbances, using the online monitored actuator and sensor data of flight control system. By developing tools from optimization theory, the convergence and optimality of gradient-based performance optimization method are analyzed comprehensively. Finally, the proposed methods are testified on the model of an aircraft.

This paper delves into a class of distributed nonconvex optimization control (DNOC) problems for multiagent systems (MASs), aiming to attain consensus among agents while minimizing the collective sum of local cost functions, referred to as the global cost function, through local information exchange. To accomplish this objective, it is introduced a novel distributed predefined-time optimal (DPTO) control algorithm. We prove that the proposed DPTO control algorithm guides the system states towards convergence to the global optimal solution within a user-defined time frame, provided that the global cost function satisfies the Polyak-Lojasiewicz condition, which is less stringent than the standard strong convexity condition. Finally, theoretical findings are substantiated through simulation studies.

In this paper, we address a novel and comprehensive social welfare maximization (SWM) problem for the optimal energy management in a smart grid. The objective is to maximize the total social welfare of dispatchable devices in the smart grid while satisfying certain constraints. Each device in the smart grid is required to meet its local power constraints, and the system as a whole maintains supply-demand balance, taking into account transmission losses and stochastic output power. To facilitate distributed algorithm design, we initially transform the SWM problem into an equivalent dual problem, which is a distributed composite optimization problem. Subsequently, a novel fully distributed proximal alternating direction method of multipliers (PADMM) is proposed, where each agent can autonomously select non-coordinated step size parameters based solely on local information, independent of other agents and the network structure. Detailed convergence analysis is provided, and a worst-case$\mathcal{O}(1/k)$convergence rate is established in the non-ergodic sense. Finally, several numerical experiments are conducted to confirm the effectiveness of the proposed algorithm.

In this work, we consider the safe deployment problem of multiple robots in an obstacle-rich complex environment. When a team of velocity and input-constrained robots is required to move from one area to another, a robust collision-avoidance formation navigation method is needed to achieve safe transferring. The constrained dynamics and the external disturbances make the safe formation navigation a challenging problem. A novel robust control barrier function-based method is proposed which enables collision avoidance under globally bounded control input. First, a nominal velocity and input-constrained formation navigation controller is designed which uses only the relative position information based on a predefined-time convergent observer. Then, new robust safety barrier conditions are derived for collision avoidance. Finally, a local quadratic optimization problem-based safe formation navigation controller is proposed for each robot. Simulation examples and comparison with existing results are provided to demonstrate the effectiveness of the proposed controller.

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.

This article addresses the resilient consensus problem of multiagent systems subject to cyber attacks on communication links, where the attacks on different links may collude to maintain undetectable. For the case with noncollusive attacks on links, a distributed fixed-time observer is designed so that the attack on each link can be detected by the two associated agents. A necessary and sufficient condition is derived to ensure the isolation of attacked links and no mistaken isolation of normal ones. For the case with collusive attacks on links, a novel attack isolation algorithm is proposed by constructing extra observers on the basis of the previous designed distributed fixed-time observer via sequentially removing the information associated with one of the links. Based on the isolation of the attacked links, a control algorithm is designed, and a necessary and sufficient condition is provided to achieve resilient consensus. Numerical examples corroborate the effectiveness of the proposed strategies.

Spatiality and temporality represent key features of the real world. A critical hurdle in the application of fuzzy logic systems lies in their limited capability to directly approximate the variables across spatial and temporal scales. This article investigates the fuzzy approximation problem of uncertain nonlinear spatiotemporal systems. A novel multilayer fuzzy supremum approximation (MFSA) is designed to map a spatiotemporal function to a state-based iterative supremum function by separating the time-varying parameters, which can be further approximated using the proposed fuzzy upremum approximation algorithm. It is indicated that MFSA is an effective approximation method for spatiotemporal functions as compared to the references. Subsequently, MFSA is developed into the leader–following synchronization problem of discrete-time multiagent systems. The MFSA-based observer and synchronization control schemes are designed by removing the assumption that either the leader's control input or the bound of the leader's control input is a known prior to each follower. The uniformly ultimate boundedness of the observer estimation errors and synchronization errors are achieved. The corresponding simulations indicate the efficacy of our approach.

This paper focuses on the design of a privacy-preserving distributed Kalman filtering algorithm for a class of linear time-varying systems in signal-to-interference-plus-noise ratio (SINR)-based sensor networks, where packet dropouts may occur in information transmission between neighboring sensor nodes. Considering the potential occurrence of eavesdropping attacks during information transmission, which is common due to the inherent vulnerability of SINR-based sensor networks, a new class of distributed secure Kalman filtering algorithm has been developed. The presented algorithm incorporates a modified ElGamal cryptosystem and adaptive fusion weights to significantly enhance security, resist privacy leakage, and bolster robustness against packet dropping. Then, a detailed performance analysis for the presented distributed secure Kalman filtering algorithm is conducted, where the security and unbiasedness of the designed algorithm are discussed. Sufficient conditions for the stability of the estimation error are further established to ensure that the estimation error is ultimately bounded in the almost sure sense. Finally, numerical examples are given to illustrate the effectiveness of the proposed algorithm.

This article considers the rapid vibration reduction problem of macro–micro composite positioning stage (MMCPS) using an adaptive neural preassigned-time control strategy. Based on Newton's second law, the MMCPS is modeled as an interconnected system with unknown perturbations, and for the first time, the vibration reduction problem of MMCPS is transformed into a displacement constraint problem. Through adaptive neural network approximation and backstepping control, a preassigned-time controller with a novel performance function-related term is developed, which not only significantly improves the positioning accuracy and reduces the vibration amplitude but also ensures that the displacements of the voice coil motor axis and the stage are constrained to a predefined region in a finite time. Another distinguished feature of the proposed controller lies in the fact that the settling time of the displacement signals can be set as an arbitrary positive value. Moreover, all signals of the closed-loop system are proved to be semiglobally uniformly ultimately bounded. Finally, the feasibility of the designed control strategy is demonstrated via a simulation experiment.

In this article, a target protection problem of multiunmanned surface vessels (multiUSVs) with conflicting individual and group goals is formulated and investigated. In the present problem, the group goal of the USVs is to cooperatively protect a given moving global target by maintaining it at the center of the formation formed by the USVs, whereas each USV has an individual goal of tracking its designated target. Striking a balance between inherently conflicting goals poses a significant challenge, especially in the face of the unknown aggregated information about the center of the formation. This article aims to determine trajectories for USVs to achieve a balance between conflicting individual and group goals. To fulfill this objective, the target protection problem is first transformed into a time-varying aggregative game. Then, a distributed multiround prediction-correction algorithm (DMPCA) is designed to track the unique Nash equilibrium trajectory (NET) of the time-varying aggregative game. It is theoretically proved that the trajectory generated by DMPCA could linearly converge to a bounded domain of NET if the underlying undirected communication graph among the USVs is connected and the algorithm parameters are appropriately selected. Finally, experimental studies are performed to verify the effectiveness of the algorithm.

In this article, the collaborative parameter estimation of multiple unmanned surface vessels with model structure uncertainties is studied. The considered parameter estimation problem is first converted into a distributed state and parameter joint estimation problem. Then, the robust distributed estimator is constructed to handle the inevitable model structure uncertainties, and the upper bounds of prediction and estimation error covariance matrices are derived, respectively. In addition, the upper bound of the estimation error covariance matrix is minimized by designing appropriate estimator gains. Finally, the advantages of the proposed distributed parameter estimation approach from the perspectives of information interaction and consideration of model structure uncertainties are verified via simulations and practical experiments.

The high penetration of renewable energy in grid-connected microgrids creates the tie-line power fluctuations, which can increase operating costs and even pose security and stability risks. Yet, we continue to lack efficient tools to smooth the tie-line power fluctuations within the context of microgrids. In this article, a hierarchical regulation strategy is proposed for smoothing the fluctuations of tie-line power flow in grid-connected microgrids equipped with battery storage units (BSUs), where the BSUs are aggregated into several battery storage aggregators (BSAs) to facilitate the management. This strategy comprises two layers: an upper layer employs a multiple-horizon predictive optimization-based approach to compute the required power allocation for each BSA, ensuring smoothed power trajectories while adhering to system constraints. Subsequently, a lower layer employs a distributed fast tracking-based technique to distribute the allocated power among BSUs within each BSA using predefined-time control theory. Case studies validate the effectiveness of our approach.

The Industrial Internet of Things (IIoT) promotes the deep integration of new-generation communication technologies and industrial ecology. However, the popularity of computing and the proliferation of equipment scale make it a meaningful challenge to provide reasonable resource allocation for task offloading. Therefore, this article proposes a novel two-stage coordinated, distributed, and online multidomain virtual network embedding algorithm based on deep reinforcement learning (DRL)-assisted federated learning (FL) for task offloading in the IIoT. We model the IIoT as a dynamic multidomain structure and deploy local DRL servers in each factory domain combined with the distributed paradigm of FL to reduce the local resource fragmentation. Through local and global cooperation, the IIoT environment is controlled in a fine and macroscopic manner. In addition, the mechanisms of FL ensure the privacy of participant data. Finally, a comprehensive evaluation demonstrates the clear superiority of the proposed algorithm, which improves the long-term offloading revenue, resource utilization, and task offloading success rate by average 17.66%, 5.97%, and 4.52% compared to baselines, respectively.

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.

This article focuses on solving the synchronization problem of neural networks (NNs) in the presence of denial-of-service (DoS) attacks and communication delays. Specifically, an attack detection algorithm constructed based upon the acknowledgment (ACK) signal is provided to detect the sleeping and active intervals of DoS attacks. To reduce information transmission during the synchronization-seeking process, a new kind of Lyapunov function-based resilient event-triggered mechanism (ETM) is designed to modulate the information transmission between the master and slave systems. Then, an event-based impulsive controller is designed to achieve synchronization in the master–slave systems with event-triggered communication and communication delay between the event generator and the controller, where the impulsive control instants are produced by the resilient ETM rather than prescribed. Furthermore, a resilient sampled-data-based ETM and an event-based controller consisting of hybrid state feedback and impulsive controllers are developed. Under the proposed ETMs and controllers, some sufficient yet efficient criteria are derived to guarantee the master–slave synchronization of NNs. The influence of the attack parameters and triggering parameters on the synchronization performance is also discussed. Finally, two numerical examples and an application in image encryption and decryption based on the master–slave chaotic systems are given to demonstrate the effectiveness of the theoretical results.

Fast detection of power line outages is critical for maintaining the stable operation of the power system. The aim of this article is to address the real time detection problem of multiple line outages in power systems. To effectively tackle the high-computational complexity issues associated with traditional approaches, we propose a multiple line outages detection algorithm that utilizes a distributed finite-time observer. The proposed method utilizes only local measurements and information from neighboring buses to update local observer for each bus. The proposed observer is mathematically proven to converge in a finite time, ensuring rapid detection of multiple line outages. Finally, simulation results demonstrate the effectiveness and rapidity of the proposed detection algorithm.

Distributed aggregative optimization (DAO) is a special class of optimization problems of networking agents where the local objective function of each agent relies on the aggregation of other agents’ decisions as well as its own. It is widely known that convergence rate is one of the most important evaluation indexes for practical applications of DAO algorithms. However, it is challenging to achieve fast convergence rate for DAO algorithms over a directed graph, owing to the fact that the underlying interaction graph may be unbalanced, and the local objective functions of individual agent depend upon the decisions of other ones. To efficiently solve the DAO problem over directed graphs, a kind of accelerated distributed optimization algorithm with Nesterov momentum and constant step-size is designed and analyzed. To handle the effect of unbalanced property of the directed networks on solving the DAO problem, a consensus iteration law is embedded into the optimization algorithm to estimate the left Perron eigenvector of the weight matrix. Furthermore, a kind of distributed aggregative gradient tracking technology associated with the Nesterov momentum coefficient is developed and employed to construct the accelerated distributed aggregative algorithm. It is theoretically shown that the proposed optimization algorithm could yield a favorable linear convergence rate after limited iterative steps when the global objective function is$\mu$-strongly convex and$L_{1}$-smooth. At last, numerical experiments are provided to confirm the findings.

This article investigates resilient distributed parameter estimation (RDPE) against sensor attacks with variable sparsity. First, the fixed sparsity of attacks is relaxed to variable sparsity over a specific time scale, with a sparse-varying sensor attack model proposed. Then, to counteract such attacks, an improved resilient distributed parameter observer is constructed by following the concept of sliding windows. Without altering the redundancy condition of sensor measurements, a sufficient condition to resist the sparsity-varying attacks is presented. Furthermore, under the assumption of accessible global historical attack detection information, the performance of RDPE is improved. Finally, some numerical simulation examples are presented to demonstrate the effectiveness of the proposed design.

This article proposes an asymptotic consensus control algorithm for a vehicle platoon with time-varying communication delays and external disturbances. To avoid continuously monitoring the state of the vehicles and utilize network communication resources efficiently, an event-triggered control (ETC) with three free parameters based on periodic sampling is designed. Consider a switched topology, a novel method is constructed to make the discretized Lyapunov–Krasovskii functional (LKF) monotonically decreasing at switching instants, which allows for better analysis of nonweighted$\mathcal {L}_{2}$-gain. The main results give the sufficient conditions for global asymptotic consensus by linear matrix inequalities (LMIs). Finally, a numerical simulation is presented to show the validity of the new analysis technique.

This paper is concerned with the distributed stochastic aggregative optimization (DSAO) problem with constraint set, where the local expected-value cost function of each agent depends both on its own decisions and on the aggregation of other agents' decisions, i.e., the aggregation function. For this reason, a distributed aggregative stochastic Frank-Wolfe (DAS-FW) algorithm is designed by introducing the momentum-based variance reduction technique to reduce the variance due to stochastic gradients, introducing the Frank-Wolfe method to deal with constraint. Then, it is theoretically shown that the DAS-FW algorithm owns a sublinear convergence rate of$O(k^{-\frac{1}{2}})$for the convex and smooth cost functions. Finally, simulations are presented to verify the validity of our theoretical results.

This paper focuses on the event-triggered distributed hierarchical filtering over wireless networks consisting of local wireless sensor networks in the first layer and wireless cluster networks in the second layer. To reduce communication consumption over local wireless sensor networks, recursive event-triggered sequential local estimators are first proposed in each cluster head by the co-design of an event-triggered scheduling mechanism and sequential local estimators, with only necessary measurements being transmitted to the cluster head in an individual cluster. A distributed hierarchical estimator is further derived by fusing local estimates over unreliable wireless cluster networks, where interacted estimates may be unavailable due to potential random link failures. It is noted that the designed hierarchical estimator has significant advantages in reducing communication bandwidth and improving execution efficiency. Finally, a target tracking example is shown to verify the proposed results.

The practical output containment problem for heterogeneous nonlinear multiagent systems under external disturbances generated by an exosystem is investigated in this article. It is required that the outputs of followers converge to the predefined convex combination of leaders' outputs. One of the major challenges in solving such a problem lies in dealing with the coupling among different nonlinearities, state dimensions, and system matrices of heterogeneous agents. To overcome the aforementioned challenge, a distributed observer-based control protocol is developed and employed. First, an adaptive state observer for estimating the states of all the leaders is constructed based on the neighboring interactions. Second, two new classes of observers are constructed for each follower exploiting the output information of the follower, in which the adaptive neural networks (NNs)-based approximation is exploited to compensate for the unknown nonlinearity in the followers' dynamics. A practical output containment control protocol is then generated by the proposed observers, where the control parameters are determined by an algorithm including two steps. Furthermore, with the help of the Lyapunov stability theory and the output regulation method, the practical output containment criteria for the considered closed-loop system under the influences of external disturbances are derived on the basis of the presented control protocol. Finally, the derived theoretical results are illustrated by a simulation example.

In this article, both the fixed-time distributed consensus tracking and the fixed-time distributed average tracking problems for double-integrator-type multiagent systems with bounded input disturbances are studied. First, a new practical robust fixed-time sliding-mode control method based on the time-based generator is proposed. Second, two fixed-time distributed consensus tracking observers for double-integrator-type multiagent systems are designed to estimate the state disagreement between the leader and the followers under undirected and directed communication, respectively. Third, a fixed-time distributed average tracking observer for double-integrator-type multiagent systems is designed to measure the average value of multiple reference signals under undirected communication. Note that all the proposed observers are constructed with time-based generators and can be trivially extended to that for high-order integrator-type multiagent systems. Furthermore, by combining the proposed fixed-time sliding-mode control method with the information provided by the fixed-time observers, the fixed-time controllers are designed to solve the fixed-time distributed consensus tracking and the distributed average tracking problems. Finally, a few numerical simulations are shown to verify the results.

This article investigates the event-triggered distributed average tracking (ETDAT) control problems for the Lipschitz-type nonlinear multiagent systems with bounded time-varying reference signals. By using the state-dependent gain design approach and event-triggered mechanism, two types of ETDAT algorithms called: 1) static and 2) adaptive-gain ETDAT algorithms are developed. It is the first time to introduce the event-triggered strategy into DAT control algorithms and investigate the ETDAT problem for multiagent systems with Lipschitz nonlinearities, which is more practical in real physical systems and can better meet the needs of practical engineering applications. Besides, the adaptive-gain ETDAT algorithms do not need any global information of the network topology and are fully distributed. Finally, a simulation example of the Watts-Strogatz small-world network is presented to illustrate the effectiveness of the adaptive-gain ETDAT algorithms.

This article aims to investigate the data-driven attack detection and identification problem for cyber-physical systems under sparse actuator attacks, by developing tools from subspace identification and compressive sensing theories. First, two sparse actuator attack models (additive and multiplicative) are formulated and the definitions of I/O sequence and data models are presented. Then, the attack detector is designed by identifying the stable kernel representation of cyber-physical systems, followed by the security analysis of data-driven attack detection. Moreover, two sparse recovery-based attack identification policies are proposed, with respect to sparse additive and multiplicative actuator attack models. These attack identification policies are realized by the convex optimization methods. Furthermore, the identifiability conditions of the presented identification algorithms are analyzed to evaluate the vulnerability of cyber-physical systems. Finally, the proposed methods are verified by the simulations on a flight vehicle system.

The distributed Nash equilibrium (NE) seeking problem for multicoalition games has attracted increasing attention in recent years, but the research mainly focuses on the case without agreement demand within coalitions. This article considers a class of networked games among multiple coalitions where each coalition contains multiple agents that cooperate to minimize the sum of their costs, subject to the demand of reaching an agreement on their state values. Furthermore, the underlying network topology among the agents does not need to be balanced. To achieve the goal of NE seeking within such a context, two estimates are constructed for each agent, namely, an estimate of partial derivatives of the cost function and an estimate of global state values, based on which, an iterative state updating law is elaborately designed. Linear convergence of the proposed algorithm is demonstrated. It is shown that the consistency-constrained multicoalition games investigated in this article put the well-studied networked games among individual players and distributed optimization in a unified framework, and the proposed algorithm can easily degenerate into solutions to these problems.

In this article, a new kind of adaptive unscented Kalman filter is proposed to deal with the parameter estimation problem for a class of nonlinear unmanned surface vessel (USV) models with unknown statistical characteristics of process noises. Specifically, the considered parameter estimation problem is first transformed into the state estimation problem by extending 18 parameters and 3 unknown inputs into augmented states for the USVs. With the help of such a transformation, the unknown inputs including disturbances and modeling errors are estimated effectively, and employed to construct the estimators such that the effect of these unknown inputs on parameter estimation can be significantly suppressed. Under the condition that the structure of the covariance matrix of the process noise is available, an adaptive law is further designed to estimate such a high-dimensional covariance matrix where the covariance estimation errors can be reduced. Finally, the proposed estimation approach is verified via performing the practical experiment as well as numerical simulations.

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.

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.

This article addresses the dynamic task allocation problem with limited communication and velocity. The main challenge lie in the selection of$k$fittest winner participants and the participant contention that one winner participant may be selected by multiple targets simultaneously. Existing methods take the distance between the targets and participants as the evaluation index to select winners, which may lead to futile selection since the winner participant locating at the opposite direction of the target cannot intercept the target with limited velocity. By carefully considering both the distance between the targets and participants and the motion direction of the targets, an improved evaluation index for each target is proposed and employed such that the futile selection can be avoided in the executing process of the algorithm. Moreover, an extra evaluation index for each winner participant is presented to select one winner target to overcome the participant contention. Based on these, the control protocols are developed for targets interception, and their stability is proven by the Lyapunov theory under some suitable conditions. Finally, simulation examples are presented to illustrate the effectiveness and advantages of the proposed algorithms.

In an aerial hybrid massive multiple-input multiple-output (MIMO) and orthogonal frequency division multiplexing (OFDM) system, how to design a spectral-efficient broadband multi-user hybrid beamforming with a limited pilot and feedback overhead is challenging. To this end, by modeling the key transmission modules as an end-to-end (E2E) neural network, this paper proposes a data-driven deep learning (DL)-based unified hybrid beamforming framework for both the time division duplex (TDD) and frequency division duplex (FDD) systems with implicit channel state information (CSI). For TDD systems, the proposed DL-based approach jointly models the uplink pilot combining and downlink hybrid beamforming modules as an E2E neural network. While for FDD systems, we jointly model the downlink pilot transmission, uplink CSI feedback, and downlink hybrid beamforming modules as an E2E neural network. Different from conventional approaches separately processing different modules, the proposed solution simultaneously optimizes all modules with the sum rate as the optimization object. Therefore, by perceiving the inherent property of air-to-ground massive MIMO-OFDM channel samples, the DL-based E2E neural network can establish the mapping function from the channel to the beamformer, so that the explicit channel reconstruction can be avoided with reduced pilot and feedback overhead. Besides, practical low-resolution phase shifters (PSs) introduce the quantization constraint, leading to the intractable gradient backpropagation when training the neural network. To mitigate the performance loss caused by the phase quantization error, we adopt the transfer learning strategy to further fine-tune the E2E neural network based on a pre-trained network that assumes the ideal infinite-resolution PSs. Numerical results show that our DL-based schemes have considerable advantages over state-of-the-art schemes.

One key factor affecting the distributed Nash equilibrium (NE) seeking in aggregative games is the unbalanced communication structure for multiple players. Although some results on seeking NE over undirected or weight-balanced graphs were established, how to address the distributed NE seeking problem over general directed communication graphs is still an outstanding challenge. This paper addresses the NE seeking problem for a class of aggregative games with general directed communication graphs. To achieve this objective, two new kinds of distributed discrete-time NE seeking algorithms are developed for aggregative games over fixed digraphs and time-varying digraphs, respectively. In particular, motivated by the heavy-ball method in optimization studies, a momentum term is introduced to the update law of the players’ actions and it is numerically verified that this momentum term accelerates the convergence of the proposed algorithms. For both strongly connected fixed graph and$B$-strongly connected time-varying graph, it is theoretically proved that the actions of players will converge to the NE of aggregative games for the case of decreasing step-size implemented by the proposed NE seeking algorithms if the cost functions and the aggregation of players satisfy some certain conditions. Finally, the developed NE seeking algorithms are applied to the energy consumption control of plug-in hybrid electric vehicles (PHEVs), which demonstrates the effectiveness of the theoretical results.

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.

We aim to address the Nash equilibrium (NE) seeking problem for multiple players over Markovian switching communication networks in this article, where a new type of distributed synchronous discrete-time algorithm is proposed and utilized. Specifically, each player in the present game model is assumed to employ a gradient-like projection algorithm to choose its action based upon the estimated ones for all the others. Under the mild condition that the union network of all communication network candidates is connected, we show that the players' actions could converge to an arbitrarily small neighborhood of the NE in the mean-square sense by adjusting the algorithm parameters. It is further found that the unique NE is mean-square stable when it is not restricted by any constraint set. In addition, we show that the proposed distributed discrete-time NE seeking algorithm can be utilized to deal with the energy trading problem in microgrids where each microgrid is modeled as a rational player using a purchase price as its action to buy energy from other microgrids with surplus supplies. The energy market allocates the excess energy according to the principle of proportional distribution. Some numerical simulations are finally presented to verify the validity of the present discrete-time NE seeking algorithm in solving the energy trading problem.

In this article, we consider the distributed formation navigation problem of second-order multiagent systems subject to both velocity and input constraints. Both collision avoidance and connectivity maintenance of the network are considered in the controller design. A control barrier function method is employed to achieve multiple control objectives simultaneously while satisfying the velocity and input constraints. First, a nominal distributed leader-following formation controller is proposed which satisfies the velocity and input constraints uniformly and handles switching communication graphs. A nonsmooth analysis is employed to prove the global convergence of the controller. Then, a topology-based connectivity maintenance strategy using a new notion of the formation-guided minimum cost spanning tree is proposed and the corresponding barrier function-based constraints are derived. The barrier function-based collision-avoidance conditions are also developed. All barrier function-based constraints are then combined to formulate a quadratic programming problem which modifies the nominal controller when necessary to achieve both collision avoidance and connectivity maintenance. Simulation results demonstrate the effectiveness of the proposed control strategy.

This article is devoted to designing distributed adaptive attack-free protocols for the consensus of linear multi-input multioutput multiagent systems under directed graphs, where the appointed-time reduced-order observers are proposed based only upon the relative output information among neighboring agents. One of the distinguishing features of the attack-free protocols lies in the prohibition on information transmission via the communication channel. By viewing the relative control input as the unknown input on the dynamics of each agent, a class of new unknown input observers is introduced with only the relative output measurement involved. The appointed-time estimation of the consensus error is achieved by utilizing jump discontinuity in the observer design and employing the property of the nilpotent matrix. Moreover, a linear transformation is made on the system of consensus error to realize the observer order reduction. Both theoretical analysis and simulation illustration are presented to reveal the effectiveness of the proposed attack-free protocols.

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.

In this article, a periodic self-triggered impulsive (PSTI) control scheme is proposed to achieve synchronization of neural networks (NNs). Two kinds of impulsive gains with constant and random values are considered, and the corresponding synchronization criteria are obtained based on tools from impulsive control, event-driven control theory, and stability analysis. The designed triggering protocol is simpler, easier to implement, and more flexible compared with some previously reported algorithms as the protocol combines the advantages of the periodic sampling and event-driven control. In addition, the chaotic synchronization of NNs via the presented PSTI sampling is further applied to encrypt images. Several examples are also utilized to illustrate the validity of the presented synchronization algorithm of NNs based on PSTI control and its potential applications in image processing.

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.

This work addresses the distributed consensus tracking problem for an extended class of high-order nonlinear multiagent networks with guaranteed performances over a directed graph. The adding one power integrator methodology is skillfully incorporated into the distributed protocol so as to tackle high powers in a distributed fashion. The distinguishing feature of the proposed design, besides guaranteeing closed-loop stability, is that some transient-state and steady-state metrics (e.g., maximum overshoot and convergence rate) can be preselected a priori by devising a novel performance function. More precisely, as opposed to conventional prescribed performance functions, a new asymmetry local tracking error-transformed variable is designed to circumvent the singularity problem and alleviate the computational burden caused by the conventional transformation function and its inverse function, and to solve the nondifferentiability issue that exists in most existing designs. Furthermore, the consensus tracking error is shown to converge to a residual set, whose size can be adjusted as small as desired through selecting proper parameters, while ensuring closed-loop stability and preassigned performances. One numerical and one practical example have been conducted to highlight the superiority of the proposed strategy.

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.

This article aims to establish an appointed-time observer-based framework to efficiently address the resilient consensus control problem of linear multiagent systems with malicious attacks. The local appointed-time state observer is skillfully designed for each agent to estimate the agent's actual state value at the appointed time, even in the presence of unknown malicious attacks. Based on the state estimation, a new kind of resilient control strategy is proposed, where a virtual system is constructed for each agent to generate an ideal state value such that the consensus of normal agents can be achieved with the exchange of ideal state values among neighboring agents. To specify the consensus trajectory while achieving resilient consensus, the leader-follower resilient consensus is further studied, where the leader is assumed to be a trusted agent with a bounded control input. Compared with the existing results on the resilient consensus, the proposed distributed resilient controller design reduces the requirement on communication connectivity significantly, where the allowable communication graph is only assumed to contain a directed spanning tree. To verify the theoretical analysis, numerical simulations are finally provided.

A swarming behavior problem is investigated in this article for heterogeneous uncertain agents with cooperation-competition interactions. In such a problem, the agents are described by second-order continuous systems with different intrinsic nonlinear terms, which satisfies the "linearity-in-parameters" condition, and the agents' models are coupled together through a distributed protocol containing the information of competitive neighbors. Then, for four different types of cooperation-competition networks, a distributed Lyapunov-based redesign approach is proposed for the heterogeneous uncertain agents, where the distributed controller and the estimation laws of unknown parameters are obtained. Under their joint actions, the heterogeneous uncertain multiagent system can achieve distributed stabilization for structurally unbalanced networks and output bipartite consensus for structurally balanced networks. In particular, the concept of coherent networks is proposed for structurally unbalanced directed networks, which is beneficial to the design of distributed controllers. Finally, four illustrative examples are given to show the effectiveness of the designed distributed controller.

This article works on the consensus problem of nonlinear multiagent systems (MASs) under directed graphs. Based on the local output information of neighboring agents, fully distributed adaptive attack-free protocols are designed, where speaking of attack-free protocol, we mean that the observer information transmission via communication channel is forbidden during the whole course. First, the fixed-time observer is introduced to estimate both the local state and the consensus error based on the local output and the relative output measurement among neighboring agents. Then, an observer-based protocol is generated by the consensus error estimation, where the adaptive gains are designed to estimate the unknown neural network constant weight matrix and the upper bound of the residual error vector. Furthermore, the fully distributed adaptive attack-free consensus protocol is proposed by introducing an extra adaptive gain to estimate the communication connectivity information. The proposed protocols are in essence attack-free since no observer information exchange among agents is undertaken during the whole process. Moreover, such a design structure takes the advantage of releasing communication burden.

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.

Distributed stabilization problem is studied in this article for multiple heterogeneous agents in the uncertain strong–weak competition network with exogenous disturbances, where the agents are modeled by the second-order systems with different nonlinear intrinsic dynamics, and the network uncertainty is characterized by unknown nonzero parameters, which contains three different relationships among agents: 1) cooperation; 2) strong competition; and 3) weak competition. To achieve distributed stabilization, the whole network is first divided into two parts: 1) identifiable part and 2) unidentifiable part, and a new distributed robust integral sign of the error (RISE) controller is designed for each agent, where the selection rules of the corresponding parameters are given. It is shown that the heterogeneous multiagent system (MAS) can achieve distributed stabilization no matter whether the identifiable part is structurally balanced or not. Furthermore, it is proved that the global distributed stabilization is achieved for the heterogeneous agents provided that the partial derivatives of the nonlinear intrinsic dynamics are bounded. Finally, two numerical examples are given to demonstrate the effectiveness of the designed controller.

This article addresses the problem of synchronization of impulsive networks with switching topologies. A new synchronization framework is established with an emphasis on settling time estimation. The impulsive networks consist of physical nodes and cyber modules. For physical nodes, states are changed impulsively at discrete time instants due to some switching phenomena or unexpected sudden noises. For cyber modules, two cases of switching scenarios are considered for information exchange patterns during specific time intervals. In the first case, cyber modules lose all the communication links with others, resulting in disconnected topologies. Then, a distributed controller is proposed for nodes without intrinsic nonlinear dynamics. A distinguished feature of this controller is its capability to estimate a bound for settling time, beyond which the synchronization with respect to a virtual target is guaranteed. In the second case, cyber modules lose some communication links but build other new ones with the help of a smart communication center to form connected topologies. A distributed controller is further designed for nodes in the presence of intrinsic nonlinear dynamics. Accordingly, a sufficient condition is derived to achieve synchronization with an estimated settling time bound. For both cases, the estimated bounds are able to reveal the relationship between the impulsive strength and the synchronization performance. Finally, numerical examples including a case study on a modified IEEE 34 bus test feeder are provided to demonstrate the effectiveness of the proposed controllers.

This article investigates the problems of structural balance and distributed control for a high-order signed network with generic linear dynamics. A novel approach is proposed to analyze the structural balance of a general network based on the strongly connected components of the topology graph and the Frobenius normal form of the adjacency matrix. To address the distributed control of high-order signed networks, both state-feedback and observer-type algorithms are developed on the basis of low-gain strategies, where a unified framework is presented to construct full- or reduced-order observers. The dynamical behaviors of the signed network under the proposed algorithms are systematically explored, where the nontrivial final network state is computed by employing an eigenvector-based approach. The theoretical results are illustrated by numerical examples.

This article deals with the distributed$\mathcal {H}_{\infty }$robust control problem for linear multiagent systems perturbed by external disturbances and norm-bounded uncertain parameters over the Markovian randomly switching communication topologies. To tackle this problem, the distributed observer-based controller is proposed, which requires the relative information between neighbors and the absolute information of a subset of the nodes, and thus is intrinsically distributed. It is of great interest to see that the distributed$\mathcal {H}_{\infty }$robust control problem governed by such a controller can be converted to the stabilization with$\mathcal {H}_{\infty }$disturbance attenuation problems of some decoupled linear systems, whose dimensions equal those of a single node. Then, the$\mathcal {H}_{\infty }$stochastic robust performance region is defined to indicate the robustness of this controller against the variation of communication topologies. It is theoretically shown that the distributed observer-based controller yields bounded and connected robust performance region. Finally, the theoretical results are verified by conducting numerical simulations and experiments.

This article aims to realize event-triggered constrained consensus tracking for high-order nonlinear multiagent networks subject to full-state constraints. The main challenge of achieving such goals lies in the fact that the standard designs [e.g., backstepping, event-triggered control, and barrier Lyapunov functions (BLFs)] successfully developed for low-order dynamics fail to work for high-order dynamics. To tackle these issues, a novel high-order event-triggered mechanism is devised to update the actual control input, lowering the communication and computation burden. More precisely, compared with the conventional event-triggered mechanism, not only the amplitudes of control signals and a fixed threshold are considered but a monotonically decreasing function is introduced to allow a relatively big threshold, while guaranteeing consensus tracking error to be small. Then, a high-order tan-type BLF working for both constrained and unconstrained scenarios is incorporated into the distributed adding-one-power-integrator design for the purpose of confining full states within some compact sets all the time. A finite-time convergent differentiator (FTCD) is introduced to circumvent the “explosion of complexity.” The consensus tracking error is shown to eventually converge to a residual set whose size can be adjusted as small as desired through choosing appropriate design parameters. Comparative simulations have been conducted to highlight the superiorities of the developed scheme.

In this study, the security problem of discrete nonlinear systems with injection attacks is discussed by designing two kinds of iterative learning schemes with the partial information and delay. The definitions of security and insecurity are presented and the injection attack is considered in a discrete nonlinear system. The contribution of this study is twofold: 1) two kinds of iterative learning schemes are designed to be with the partial information and delay due to limited bandwidth of networks and 2) two criteria are proposed to analyze the security and insecurity of a discrete nonlinear system with the two kinds of iterative learning schemes. Finally, numerical results are presented to illustrate the validity of the obtained criteria.

In this study, a new learning control scheme is designed to investigate the stability of a multilayer supply chain network (SCN) and to further improve the convergence speed of the nodes’ states of such a multilayer SCN. Specifically, a multilayer SCN model with three layers is first established and some practical constraints on the states of the proposed SCN model are involved and discussed. By taking the quantities of goods transmitted between different nodes as control inputs, a new kind of learning control scheme is subsequently proposed to discuss the stability of the nodes’ states within the SCN. It is further shown that the convergence speed of nodes’ states with this scheme is faster than that yielded by using some traditional schemes. The contributions of our scheme are twofold: 1) it can save the limited control resource and 2) it can improve the convergence speeds of the states of all nodes. Numerical simulations are finally given to illustrate the effectiveness and advantages of the designed learning scheme.

This article investigates the distributed optimal cooperation problems for multiple high-order systems, in which the dynamics of each agent is allowed to be subject to unknown nonlinearities. To eliminate the effect caused by unknown nonlinearities, a nonlinearity estimator is developed based on agents’ states, which successfully reconstructs the nonlinear dynamics if the unknown nonlinearities are bounded. And to minimize the sum of multiple local nonlinear cost functions with Lipschitz-type gradients, a couple of static and adaptive state-dependent algorithms are designed, respectively, where each agent may only have access to its own local cost function. It is challenging to solve such an optimal cooperation problem as the performance of the whole multiagent network is evaluated by the sum of all local performance functions. In order to fulfill the goal of cooperative optimization, a state-dependent distributed optimal cooperation algorithm is proposed first. By utilizing tools from the Lyapunov stability theory and convex optimization analysis, it is proven that the considered distributed optimal cooperation problem for high-order nonlinear systems can be solved by the proposed optimal cooperation algorithm if the state-dependent parameters are suitably selected. It is noted that the selections of the state-dependent parameters depend on some global information of the multiagent systems. Furthermore, by incorporating the proposed optimal cooperation algorithm with adaptive parameters strategy, the optimal cooperation problem is solved in a fully distributed manner. Finally, a numerical simulation is shown to verify the effectiveness of the proposed algorithms.

This article presents a novel technique for terminal-time synchronization of multivehicle systems. Taking sampled-data communications into account, the terminal-time synchronization problem of multivehicle systems is formulated as three demands. An estimation of terminal time is introduced for each vehicle, and a cooperative algorithm is designed based on motion planning to synchronize all estimated terminal times by using only local sampled-data information. The proposed algorithm not only can ensure the consensus of estimated terminal times at appointed time, but also can make the estimates finally be equal to the actual terminal times. To avoid Zeno behavior, the explicit expression of the norm of the consensus error is formulated, based on which the sampling interval sequence is modified to realize appointed-time approximate consensus of the actual terminal times. Local controller is also designed for each vehicle to ensure the fixed-time convergence of the relative velocity normal to the line of sight, and thus the singularity of control input at terminal time instant is successfully avoided. Experiments are performed to verify the effectiveness of the algorithms.

Designing an efficient distributed economic dispatch (DED) strategy for the smart grid (SG) in the presence of multiple generators plays a paramount role in obtaining various benefits of a new generation power system, such as easy implementation, low maintenance cost, high energy efficiency, and strong robustness against uncertainties. It has drawn a lot of interest from a wide variety of scientific disciplines, including power engineering, control theory, and applied mathematics. We present a state-of-the-art review of some theoretical advances toward DED in the SG, with a focus on the literature published since 2015. We systematically review the recent results on this topic and subsequently categorize them into distributed discrete- and continuous-time economic dispatches of the SG in the presence of multiple generators. After reviewing the literature, we briefly present some future research directions in DED for the SG, including the distributed security economic dispatch of the SG, distributed fast economic dispatch in the SG with practical constraints, efficient initialization-free DED in the SG, DED in the SG in the presence of smart energy storage batteries and flexible loads, and DED in the SG with artificial intelligence technologies.

This paper proposes a distributed hierarchical control framework for energy storage systems (ESSs) in DC microgrid clusters, which achieves voltage regulation and current sharing for ESSs in each microgrid as well as the whole microgrid cluster. The primary control stage adopts a droop controller which only requires local information while the secondary control stage provides correction terms for ESSs within microgrids. The tertiary control stage samples the pinned ESSs in different microgrids with low sampling rate to provide the voltage setpoint, which ensures global current sharing among microgrid cluster. The corresponding multilayered event-triggered consensus algorithm for clusters is proposed to reduce the communication cost generated by operation of the distributed controller. Both the control framework and the consensus algorithm can be extended for satisfying higher dimensional regulation needs. The controller is validated in a DC microgrid cluster through simulation under different scenarios, and the results illustrate the effectiveness of the proposed controller.

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.

We aim to solve the consensus problem of linear multiagent systems (MASs) with input saturation under directed interaction graphs in this article, where only local output information of neighbors is available for each agent. By introducing the multilevel saturation feedback control approach, a fully distributed adaptive anti-windup protocol is proposed, where a local observer, a distributed observer, as well as an anti-windup observer are separately constructed for each agent to estimate consensus error, achieve consensus for a certain internal state, and provide anti-windup compensator, respectively. A dual protocol is further presented with the distributed observer designed based on the input matrix, which gives a thorough view on the connection between the distributed observer and the anti-windup observer, and provides the opportunity to reduce the order of the controller by designing the integrated distributed anti-windup observer. Then, three types of distributed anti-windup protocols are proposed based on the integrated distributed anti-windup observer, which requires different assumptions. Specifically, the first protocol needs two-hop relay information to generate the local observer to estimate consensus error; the second protocol designs the local observer with absolute output information to estimate the state instead; while the last protocol introduces certain assumption on transmission zero of agents' dynamics to design the unknown input observer to estimate consensus error. All of the protocols are validated by strictly theoretical proof, and are illustrated by performing simulation examples.

In building-microgrid communities, renewable generation and time-varying load usually cause power fluctuations, which influence the ancillary support to the main grid. Thermostatically controlled loads (TCLs) can be utilized to compensate such power variations due to their aggregated and controllable power consumptions. Meanwhile, one basic requirement for the users' side of TCLs is to realize the fair sharing of power states and comfort states. This article proposes a distributed event-based control strategy, where information of neighboring TCLs is exchanged only when a dynamic event-triggered condition is satisfied, and thus it intelligently determines the necessary transmission frequency to save communication resources. From a cybersecurity perspective, the communication network of TCLs may be subject to hybrid attacks, for example, denial-of-service (DoS) and false data-injection (FDI) attacks. During DoS attack intervals, no information can be communicated even through the event-triggered condition is satisfied. Furthermore, the control inputs may also be tampered by FDI attacks. By utilizing the Lyapunov stability and hybrid control theories, sufficient conditions regarding the attack parameters are derived such that fair sharing of power states and comfort states of all involved TCLs can be achieved exponentially. The exclusion of Zeno behaviors is proved and a corollary for ideal communication situations is also deduced. Finally, simulation examples with various attack parameters are conducted to verify the effectiveness of the main results.

With the incentive to solve Nash equilibrium computation problems for networked games, this article tries to find answers for the following two problems: 1) how to accommodate hybrid games, which contain both continuous-time players and discrete-time players? and 2) are there any other potential perspectives for solving continuous-time networked games except for the consensus-based gradient-like algorithm established in our previous works? With these two problems in mind, the study of this article leads to the following results: 1) a hybrid gradient search algorithm and a consensus-based hybrid gradient-like algorithm are proposed for hybrid games with their convergence results analytically investigated. In the proposed hybrid strategies, continuous-time players adopt continuous-time algorithms for action updating, while discrete-time players update their actions at each sampling time instant and 2) based on the idea of consensus tracking, the Nash equilibrium learning problem for continuous-time games is reformulated and two new computation strategies are subsequently established. Finally, the proposed strategies are numerically validated.

The risk of transmission lines overload in the power grid is increasing with the large-scale integration of fluctuating distributed renewable energies. Meanwhile, the requirement for accommodating more distributed resources in the future smart grids promotes the transition from the current highly centralized control structure toward a distributed one. In this article, we propose a distributed corrective control approach to mitigate line overloads in a real-time and close-loop manner. Unlike the conventional centralized approach, only simple computation and local information exchange are required to update the local corrective control action. This makes it possible to mitigate line overloads timely and adapt to the topology changes of grids. Furthermore, the introduction of system measurements and security constraints in the proposed algorithm ensures an effective and secure corrective control without new line overloads. The performance of the proposed distributed approach is demonstrated in the IEEE 14-Bus and 118-Bus systems.

In this study, the stability of a hierarchical network with delayed output is discussed by applying a kind of optimal periodic control. To reduce the number of the nodes of the original hierarchical network, an aggregation algorithm is first presented to take some nodes with the same information as an aggregated node. Furthermore, the stability of the original hierarchical network can be guaranteed by the optimal periodic control of the aggregated hierarchical network. Then, an optimal control scheme is proposed to reduce the bandwidth waste in information transmission. In the control scheme, the time sequence is separated into two parts: the deterministic segment and the dynamic segment. With the optimal control scheme, two targets are achieved: 1) the outputs of the original and aggregated hierarchical system are both asymptotically stable and 2) the nodes with slow convergent rate can catch up with the convergence speeds of other nodes.

The mining missing links and predicting upcoming links are two important topics in the link prediction. In the past decades, a variety of algorithms have been developed, the majority of which apply similarity measures to estimate the bonding probability between nodes. And for these algorithms, it is still difficult to achieve a satisfactory tradeoff among precision, computational complexity, robustness to network types, and scalability to network size. In this article, we propose a chaotic ant colony optimized (CACO) link prediction algorithm, which integrates the chaotic perturbation model and ant colony optimization. The extensive experiments on a wide variety of unweighted and weighted networks show that the proposed algorithm CACO achieves significantly higher prediction accuracy and robustness than most of the state-of-the-art algorithms. The results demonstrate that the chaotic ant colony effectively takes advantage of the fact that most real networks possess the transmission capacity and provides a new perspective for future link prediction research.

This article investigates the problem of global output feedback stabilization by using aperiodic-sampled-data control, i.e., event-triggered control, for a class of uncertain nonlinear systems under certain assumptions. By employing the technique of output feedback domination, an observer-based event-triggered output feedback control law is explicitly constructed to guarantee the globally asymptotic stabilization. To avoid the Zeno behavior, a combining mechanism with event-triggered and time-triggered is proposed to ensure that the two consecutive updated time for the sampled-data controller is larger than one positive constant. Finally, it is shown that the problem of global output feedback stabilization for a class of uncertain nonlinear systems is solved via the proposed event-triggered control law. Finally, some comparative simulation examples are given to show the efficiency of the introduced method.

Distributed consensus tracking problem of networked agent systems with directed topologies under denial-of-service (DoS) attacks is investigated. The considered networked agent network consists of a physical layer with fixed physical links and a cyber layer with cyber control units. Both the communication network connecting these two layers and the cyber communication network within the cyber layer may subject to malicious DoS attacks. These two types of attacks have different impacts on the networked system; the former one affects the timely update of control inputs, and the latter influences the connection weights of the cyber communication graph. First, for DoS signals occurring in the communication network which transmits the state and control input information between the two layers, the distributed control protocol based on the event-triggered scheme and locally deployed estimators are designed. Efficient algorithms for selecting event-triggered control parameters and Zeno-free triggered parameters are given to ensure the mean-square consensus. The relationships between the system's parameters and the features of DoS attacks are successfully revealed. Second, corresponding theoretical analysis is derived for consensus tracking of the networked systems when DoS attacks are launched within the cyber layer. Conditions concerning the length of repairing time and indexes of DoS attacks are given by utilizing hybrid control theory. At last, the effectiveness of the obtained results is demonstrated by performing simulations on multirobot systems.

This article considers the rendezvous problem of a group of heterogeneous second-order agents subject to information transmission delays. A major challenge to construct a fully distributed rendezvous protocol is to deal with these delays, which are assumed to be nonuniform and time-varying. Inspired by the fact that a large enough damping coefficient can improve the robustness of a second-order agent against external disturbance, we overcome the above challenge by studying the impact of the damping coefficient on the rendezvous problem. To theoretically analyze the impact, one type of static rendezvous protocol is first proposed and employed. It is interesting to find that agents can reach rendezvous under the static protocol if the damping coefficient is large enough, even though the duration of the time-delay is uncertain. This fact indicates that a large damping coefficient can make the static protocol be robust to the uncertainty of time-delay, which is consistent with the common sense. Then, we apply this impact to deal with the uncertainty introduced by the nonuniform time-varying information delays. To fully apply this impact, we adopt an adaptive approach to making the damping coefficient automatically adapt with the changes of the time-delay. Hence, two classes of fully distributed and adaptive rendezvous protocols are designed, which do not need the global information of the entire communication graph or the value of these time-delays at all. The difference between two classes of protocols is whether it can realize low-frequency learning or not. Finally, some numerical simulations are performed on multiple robots to illustrate the analytical results.

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.

A social cost minimization problem is addressed in this article. In the considered problem, a network of agents work collaboratively to minimize the social cost function, which is defined as the sum of the agents’ local objective functions. The engaged agents are supposed to be equipped with an undirected and connected communication graph. Different from most of the existing works, the social cost function in the considered problem is allowed to be nonconvex and possibly admits local extrema. To avoid local extrema and achieve the global minimization of the social cost function, an extremum-seeking-based approach is proposed by introducing a dynamic average consensus protocol to the sinusoidal-dither-signal-based extremum seeking scheme. The dynamic average consensus protocol is leveraged in the proposed extremum-seeker for information sharing and the sinusoidal probing signal is utilized for information extraction. For the avoidance of local extrema, the amplitude of the dither signal is designed to be adaptive. Through Lyapunov stability analysis, it is shown that the proposed method enables the decision variable to converge to a neighborhood of the global minimum point if the conditions on the network connectivity, the existence of unique global minimum and achievability of the global minimum are satisfied. The theoretical result is verified via simulating a numerical example.

In this paper, the time-varying formation problem is studied under directed topologies. An adaptive approach is utilized to develop a fully distributed formation controller for general linear multiagent systems. To achieve distributed time-varying formations, a feasible formation set is proposed by proposing some conditions. By using adaptive techniques, the main contribution of this paper is that a fully distributed formation algorithm is designed for achieving time-varying formation under directed graphs, which relies only on the local measurements without requiring any global information. By analyzing the Lyapunov stability, the proposed fully distributed formation algorithm can ensure the multiagent systems achieving the goal of time-varying formations. To verify the theoretical results, some simulation examples are shown finally.

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.

This paper considers the output-feedback consensus problem of linear multi-agent systems under directed communication topologies. To avoid the network attack from potential malicious attacker, the concept of attack-free protocol is proposed, wherein the information transmission via communication channel is forbidden. Under this circumstance, only relative output measurement can be utilized to generate the observer and the protocol. In this paper, by viewing the relative input of neighboring agents as the unknown input, novel distributed unknown input observer is presented for each agent to achieve appointed-time estimation of the consensus error, where only measured relative output information is used. The fully distributed adaptive protocol is then designed based on the proposed observer. The distributed observer takes a pulsative form at some time instants, which is noncontinuous; while such form takes the advantage of reducing computational cost, compared with the pairwise observer design structure. Simulation results are also conducted to illustrate the effectiveness of the proposed attack-free protocol.

This paper proposes several hierarchical controller-estimator algorithms (HCEAs) to solve the coordination problem of networked Euler-Lagrange systems (NELSs) with sampled-data interactions and switching interaction topologies, where the cases with both discontinuous and continuous signals are successfully addressed in a unified framework. The HCEAs comprise two main layers (i.e., a control layer and an estimator layer) and one optional layer (i.e., a filter layer), in which the coordination problem is tackled in the main layers and the transient response can be optionally smoothed in the filter layer. For stabilizing the corresponding cascade closed-loop systems, several sufficient conditions on the upper bound of the aperiodic sampling intervals and the lower bound of the control parameters are established. In addition, the HCEAs are extended to address the task-space coordination problem of networked heterogeneous robotic systems, which shows the versatility of the HCEAs. Finally, comparison studies and simulation results are provided to demonstrate the effectiveness, significance, and advantages of the presented algorithms.

Delayed impulsive controllers are proposed in this paper to enable the agents in a class of second-order multiagent systems (MASs) to achieve state consensus, based, respectively, on the relative full-state and partial-state sampled-data measurements among neighboring agents. It is a challenging task to analyze the consensus behaviors of the considered MASs as the dynamics of such MASs will be subjected to joint effects from delay-dependent impulses, aperiodic sampling, and switchings among different communication graphs. A novel analytical approach, based upon the discretization method, state augmentation, and linear state transformation, is developed to establish the sufficient consensus criteria on the range of the impulsive intervals and the control parameters. Remarkably, it is found that consensus in the closed-loop MASs can be always ensured by skillfully selecting the control parameters as long as the nonuniform delays and the impulsive intervals are bounded. A numerical example is finally performed to validate the effectiveness of the proposed delayed impulsive controllers.

The objective of this paper is to design the protocols with a final consensus value and settling time estimations for finite-time consensus of multiagent systems. A couple of new edge-based protocols are developed for multiple second-order nonlinear agents under bounded or Lipschitz-type nonlinear functions, respectively. The final consensus value of the multiagent system is obtained as an average expression. Further, to obtain the estimation of the finite settling time, a special Lyapunov function is constructed. Through the construction processes, both the final consensus value and the settling time are obtained. Finally, as applications, a finite-time formation controller based on the first protocol is designed for multiple mini-spacecraft, verified by simulations.

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.

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 main objective of this article is to explore the issue of how to improve the performance of discrete-time sliding mode control (DSMC) law for a class of discrete-time dynamic systems with both matched and mismatched disturbances. By using tools from mismatched disturbance compensation technique, a new kind of discrete-time sliding surface is constructed and subsequently utilized in designing the desirable DSMC laws. Specifically, two different types of DSMC laws, i.e., the equivalent-control-based DSMC law and the reaching-law-based DSMC law, are respectively constructed based upon the developed sliding surface. Rigorous analysis on stability of the corresponding closed-loop system is performed where it is shown that the mismatched disturbances could be successfully attenuated from the output channel in steady state. The effectiveness of the analytic result is supported by the experimental studies as well as numerical simulations.

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, a controller with multilayer structure is proposed to regulate the thermostatically controlled loads (TCLs), so that power sharing and comfort states consensus can be achieved. Since TCLs have great potential to reduce the fluctuations caused by photovoltaic in the building microgrid community, the control of a cluster of TCLs has practical significance. The multilayer structure can capture the nature of inner and inter communications among the building microgrids. The self-triggered mechanism is adopted to avoid continuous data transmission. The controller is validated through study of two different building microgrid communities with different number of TCLs.

An increasing number of electric vehicles (EVs) make transition energy request from gasoline to electricity possible. As a result, the EVs play a new major role in the smart grid system. Along with the rapid development of energy storage technology, the battery stations constructued for EVs can also provide power to many other applications at lower cost, compared with the power generator, in peak load hours. To achieve such a goal, an efficient collaboration among EVs and battery stations is a new challenge. In this paper, the features of EV charging and battery charging/discharging problems are formulated using a bilevel programming model. The objective is to minimize the EV charging cost, with the maximal battery station operation revenue. The simulation shows the rescheduled charging activities can shift to avoid peak load while the peak load can be shaved by battery discharging.

The problem of distributed formation control for multiple quadrotor aircraft in the form of leader-follower structure is considered in this paper. Based on a nonsmooth backstepping design, a novel consensus formation control algorithm is proposed and utilized. First, for the position control subsystem, based on the linear quadratic regulator optimal design method, a formation control law for multiple quadrotor aircraft is designed such that the positions of all the quadrotor aircraft converge to the desired formation pattern. The designed formation control law for position systems will generate the desired attitude for the attitude control systems. Second, for the attitude control subsystem described by unit quaternion, by employing the technique of finite-time control and switch control, a global bounded finite-time attitude tracking controller is designed such that the desired attitude can be tracked by the multiple quadrotor aircraft in finite time. Finally, numerical example is performed to demonstrate that all quadrotor aircraft converge to the desired formation pattern in the 3-D-space.

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.

In this paper, some efficient criteria for finite-time consensus of a class of nonsmooth opinion dynamics over a digraph are established. The lower and upper bounds on the finite settling time are obtained based respectively on the maximal and minimal cut capacity of the digraph. By using tools of the nonsmooth theory and algebraic graph theory, the Carathéodory and Filippov solutions of nonsmooth opinion dynamics are analyzed and compared in detail. In the sense of Filippov solutions, the dynamic consensus is demonstrated without a leader and the finite-time bipartite consensus is also investigated in a signed digraph correspondingly. To achieve a predetermined consensus, a leader agent is introduced to the considered agent networks. As an application, the nonsmooth compartmental dynamics in the presence of a leader is embedded in the proposed continuous-time protocol to solve the distributed optimization problems over an unbalanced digraph. The convergence to the optimal solution by using the proposed distributed algorithm is guaranteed with appropriately selected parameters. To verify the effectiveness of the proposed protocols, three numerical examples are performed.

In this paper, a distributed average tracking (DAT) problem is studied for Lipschitz-type of nonlinear dynamical systems. The objective is to design DAT algorithms for locally interactive agents to track the average of multiple reference signals. Here, in both dynamics of agents and reference signals, there is a nonlinear term satisfying a Lipschitz-type condition. Three types of DAT algorithms are designed. First, based on state-dependent-gain design principles, a robust DAT algorithm is developed for solving DAT problems without requiring the same initial condition. Second, by using a gain adaption scheme, an adaptive DAT algorithm is designed to remove the requirement that global information, such as the eigenvalue of the Laplacian and the Lipschitz constant, is known to all agents. Third, to reduce chattering and make the algorithms easier to implement, a couple of continuous DAT algorithms based on time-varying or time-invariant boundary layers are designed, respectively, as a continuous approximation of the aforementioned discontinuous DAT algorithms. Finally, some simulation examples are presented to verify the proposed DAT algorithms.

The problem of current sharing controller for parallel dc-dc buck converter system is investigated in this paper. Specifically, to achieve the goal of sharing control and improve the systems dynamic performance, a new finite-time current sharing control algorithm is designed and employed. Under the proposed control algorithm, rigorous proofs show that not only the output voltage of the converter system can reach the desired reference voltage in a finite time, but also the objective of current sharing can be achieved within almost the same time. In addition, when the external load is time-varying and unknown, a finite-time load estimator is given to handle the load variation, and an adaptive finite-time current sharing control algorithm is subsequently developed. Experimental results are presented to verify the effectiveness of the proposed method, and to show its advantages over some traditional control algorithms. It is shown that a faster convergence rate and a better load disturbance rejection performance can be yielded by the present algorithm. Finally, it is shown that the main results can be extended to the case of n parallel dc-dc buck converters.

The safety and stability of modern power systems are undergoing various challenges, introduced by the integration of fluctuating renewable generation. In this paper, we present a hierarchical model predictive power dispatch and control strategy for a class of modern power systems with price-elastic controllable loads (CLs) in energy Internet. In the upper-level optimization, a generalized multiperiod economic dispatch (GMPED) problem is organized within an electricity market environment aiming at maximizing the social welfare. Specifically, the price-elastic CLs are aggregated in controllable load aggregators (CLAs) to participate in the market competition. A novel utility function of the price-elastic CLAs is proposed for market demand response. By solving GMPED, the power setpoints of plants over the further periods are produced, as well as the real-time price for the optimal response of price-elastic CLAs. In the second-level operation, two types of model predictive control-based controllers for both the supply and demand sides are designed for power tracking control by considering the model of the power system and aggregated thermostatically controlled loads. Finally, two case studies are performed on the IEEE 14- and 39-bus system, respectively, which shows that the system-frequency deviation and system cost are reduced significantly with the proposed methods.

This paper studies the distributed average tracking (DAT) problem for multiple reference signals described by the second-order nonlinear dynamical systems. Leveraging the state-dependent gain design and the adaptive control approaches, a couple of DAT algorithms are developed in this paper, which are named finite-time and adaptive-gain DAT algorithms. Based on the finite-time one, the states of the physical agents in this paper can track the average of the time-varying reference signals within a finite settling time. Furthermore, the finite settling time is also estimated by considering a well-designed Lyapunov function in this paper. Compared with asymptotical DAT algorithms, the proposed finite-time algorithm not only solve finite-time DAT problems but also ensure states of physical agents to achieve an accurate average of the multiple signals. Then, an adaptive-gain DAT algorithm is designed. Based on the adaptive-gain one, the DAT problem is solved without global information. Thus, it is fully distributed. Finally, numerical simulations show the effectiveness of the theoretical results.

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 paper, global leader-following consensus problem is investigated for multiple non-holonomic mobile robots subject to input saturation. A globally bounded distributed controller based on only relative state measurements in local coordinate is designed. Under the assumption that the leader's angular velocity is persistently exciting, sufficient conditions for the achievement of consensus tracking in the closed-loop multi-agent systems are established. Finally, simulation examples are provided to illustrate the analytical 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.

In this paper, a quasi-average consensus problem is investigated in the cooperation-competition network, where the elements in the weight matrix of the network can be either positive or negative. To solve this problem, the whole network is firstly divided into two sub-networks, i.e., the cooperation subnetwork and the competition sub-network, and then a novel time-delayed event-triggered control scheme is designed in the competition sub-network. By establishing the solution of the multi-agent system, the ranges of the parameters of the event-triggered controller are determined, and the explicit expression of the error level is derived. Moreover, the convergence rate of quasi-average consensus is provided. It is found that Zeno behavior of the event-triggered controller can be excluded in our framework. Finally, simulation results are presented to validate the effectiveness of the theoretical analysis.

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.

This paper mainly investigates the attitude control problem for a aircraft with quadrotor model. By combining with the physical feature of quadrotor, the attitude trajectory is first planned and divided into different priorities. Then, based on the technique of finite-time control, the finite-time attitude tracking controller is designed such that the attitude decoupled control can be achieved in a finite time. A simulation example is given to demonstrate the efficiency of the proposed method.

In this paper, we analyze stability of incremental exponential stability for switched nonlinear systems with time delay. The continuous contraction theory is generalized to introduce a new type of switching laws. On this basis, the incremental exponential stability is established for both stable and unstable subsystems within the overall switched nonlinear systems with time delay. Computer simulations are presented to validate the theoretical findings.

This paper addresses the consensus tracking problem of multi-agent systems (MASs) with directed switching topologies based on the multiple Lyapunov functions (MLFs) approach. The special feature of Laplacian matrices for topology candidates is explored to construct a new class of MLFs for the tracking error systems of leader-following MASs with directed switching topologies. Then the average dwell time (ADT) method is utilized to establish a sufficient condition that guarantees consensus tracking in the closed-loop MASs. The efficiency of the derived theoretical results and the merits of the proposed MLFs are demonstrated by computer simulations.

This paper considers the event-based containment control problem for second-order multi-agent systems. A novel event-triggered containment control protocol is proposed so as to carry out intermittent examination of the event-triggering condition at sampling instants. One important feature of the designed protocol is that only the sampled position data are used with no utilization of velocity measurements. It is shown that the realization of containment control is guaranteed under a sufficient condition which depends upon the control gains, the sampling period, and the spectrum of the Laplacian matrix among the followers. The effectiveness of the proposed event-triggered containment control protocol is demonstrated by a simulation example.

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.

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.

The distributed synchronization control problem of multiple quadrotor aircraft in the form of leader-follower structure is considered in this paper. Based on the method of backstepping design, a novel distributed consensus control algorithm is proposed. Firstly, for the position control subsystem, by Proportional-Differential control and the theory of communication topology graph, a consensus control law for multiple quadrotor aircraft is designed such that all the quadrotor aircraft can convergence to a leader and move along the desired trajectory asymptotically. The designed distributed consensus control law for position systems will generate the desired attitude for the attitude control subsystems. Secondly, for the attitude control subsystem described by unit quaternion, by employing switch control, a global attitude tracking control law is designed such that the desired attitude can be tracked. Finally, a example is given to demonstrate the efficiency of proposed method.

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 studies a distributed secure consensus tracking control problem for multiagent systems subject to strategic cyber attacks modeled by a random Markov process. A hybrid stochastic secure control framework is established for designing a distributed secure control law such that mean-square exponential consensus tracking is achieved. A connectivity restoration mechanism is considered and the properties on attack frequency and attack length rate are investigated, respectively. Based on the solutions of an algebraic Riccati equation and an algebraic Riccati inequality, a procedure to select the control gains is provided and stability analysis is studied by using Lyapunov's method.. The effect of strategic attacks on discrete-time systems is also investigated. Finally, numerical examples are provided to illustrate the effectiveness of theoretical analysis.

This paper considers the position-based consensus in a network of agents with double-integrator dynamics and directed topology. Two types of distributed observer algorithms are proposed to solve the consensus problem by utilizing continuous and intermittent position measurements, respectively, where each observer does not interact with any other observers. For the case of continuous communication between network agents, some convergence conditions are derived for reaching consensus in the network with a single constant delay or multiple time-varying delays on the basis of the eigenvalue analysis and the descriptor method. When the network agents can only obtain intermittent position data from local neighbors at discrete time instants, the consensus in the network without time delay or with nonuniform delays is investigated by using the Wirtinger's inequality and the delayed-input approach. Numerical examples are given to illustrate the theoretical analysis.

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.

The consensus problem of multiple nonholonomic mobile robots in the form of high-order chained structure is considered in this paper. Based on the model features and the finite-time control technique, a finite-time cooperative controller is explicitly constructed which guarantees that the states consensus is achieved in a finite time. As an application of the proposed results, finite-time formation control of multiple wheeled mobile robots is studied and a finite-time formation control algorithm is proposed. To show effectiveness of the proposed approach, a simulation example is given.

In this paper, the synchronization problem of master-slave chaotic neural networks with remote sensors, quantization process, and communication time delays is investigated. The information communication channel between the master chaotic neural network and slave chaotic neural network consists of several remote sensors, with each sensor able to access only partial knowledge of output information of the master neural network. At each sampling instants, each sensor updates its own measurement and only one sensor is scheduled to transmit its latest information to the controller's side in order to update the control inputs for the slave neural network. Thus, such communication process and control strategy are much more energy-saving comparing with the traditional point-to-point scheme. Sufficient conditions for output feedback control gain matrix, allowable length of sampling intervals, and upper bound of network-induced delays are derived to ensure the quantized synchronization of master-slave chaotic neural networks. Lastly, Chua's circuit system and 4-D Hopfield neural network are simulated to validate the effectiveness of the main results.In this paper, the synchronization problem of master-slave chaotic neural networks with remote sensors, quantization process, and communication time delays is investigated. The information communication channel between the master chaotic neural network and slave chaotic neural network consists of several remote sensors, with each sensor able to access only partial knowledge of output information of the master neural network. At each sampling instants, each sensor updates its own measurement and only one sensor is scheduled to transmit its latest information to the controller's side in order to update the control inputs for the slave neural network. Thus, such communication process and control strategy are much more energy-saving comparing with the traditional point-to-point scheme. Sufficient conditions for output feedback control gain matrix, allowable length of sampling intervals, and upper bound of network-induced delays are derived to ensure the quantized synchronization of master-slave chaotic neural networks. Lastly, Chua's circuit system and 4-D Hopfield neural network are simulated to validate the effectiveness of the main results.

By employing the finite-time control method, the consensus control algorithm for higher-order multiagent systems is designed in this paper. Under a neighbor-based rule, a higher-order finite-time consensus algorithm is explicitly constructed, which only uses local information. The finite-time consensus control algorithm can guarantee that the state consensus is achieved in a finite time. In addition, for multiagent systems having a leader-following structure, the consensus algorithm is also designed. Finally, two examples are presented to show the effectiveness.

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$\mathcal {G}^{(\sigma (t))}$.

In this paper, the problem of attitude synchronization for flexible spacecraft system with actuator faults is investigated. The spacecraft formation is studied in a leader-following architecture and the reference attitude is represented by a virtual leader. A distributed unit quaternion-based synchronization control law is proposed for flexible spacecraft with loss of actuator effectiveness fault. To damp out the induced oscillations of the spacecraft's flexible appendages, an adaptive parameter is introduced. Numerical simulations are presented to demonstrate the effectiveness of the proposed method.

This paper studies the finite-time leader-following tracking problems for a group of autonomous agents modeled by second-order nonlinear dynamics under a dynamic reference leader. First, based on distributed binary measurements, a class of finite-time leader-following tracking algorithms are only requiring a single-bit quantization error relative to each neighbor. Then, by using a topology-dependent Lyapunov function, the finite-time distributed tracking problem can be solved with a finite settling time estimation if the graph of all agents contains a directed spanning tree with the leader as the root and the subgraph among the followers is undirected. Finally, an example is shown to illustrate the effectiveness of the analytical results.

A compound control strategy is proposed for frequency regulation of source-grid-load systems in which power sources, power grids, and loads are all participating in the process. Here, power sources are conventional thermal generators, including new energy power generations, and loads are composed of energy storage units (ESUs) and grid-friendly appliances (GFAs). The proposed control scheme includes two levels of operations, with the upper level to be a model predictive control (MPC) for generators and the lower level to be a distributed leader-following consensus control strategy for multiple ESUs. For new energy power generations, the power outputs are restricted on a constant value during a sampling period based on a predicted generating curve. GFAs respond to the system frequency by regulating their active power consumption. Simulations on a single power system and three interconnected area power systems are provided to verify the effectiveness of the proposed compound control strategy.

This paper studies the stability and Hopf bifurcation in a class of high-dimension neural network involving the discrete and distributed delays under a new framework. By introducing some virtual neurons to the original system, the impact of distributed delay can be described in a simplified way via an equivalent new model. This paper extends the existing works on neural networks to high-dimension cases, which is much closer to complex and real neural networks. Here, we first analyze the Hopf bifurcation in this special class of high dimensional model with weak delay kernel from two aspects: one is induced by the time delay, the other is induced by a rate parameter, to reveal the roles of discrete and distributed delays on stability and bifurcation. Sufficient conditions for keeping the original system to be stable, and undergoing the Hopf bifurcation are obtained. Besides, this new framework can also apply to deal with the case of the strong delay kernel and corresponding analysis for different dynamical behaviors is provided. Finally, the simulation results are presented to justify the validity of our theoretical analysis.

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.

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.

This paper addresses the distributed consensus tracking problem for a class of multi-agent systems with Lipschitz-type node dynamics in the presence of a single leader. The main contribution in the present work is to solve the consensus tracking problem without the over-idealized assumption that the communication topology among dynamic agents is strongly connected and fixed. A distributed protocol based only on the relative states between neighboring agents is designed. Then, by using tools from nonnegative matrix analysis and switching systems theory, it is theoretically shown that consensus tracking in a closed-loop multi-agent network with a switching directed topology can be achieved if there always exists a directed path from the leader to each follower, with the control parameters suitably selected.

This paper concerns the distributed containment problem of multi-agent systems with linear or linearized node dynamics under a directed communication topology. A new class of distributed control protocol based only on the relative outputs of neighboring agents is designed and utilized to achieve containment. Under the assumptions that each agent is stabilizable and detectable, and for each follower there exists at least one leader that has a directed path to that follower, it is theoretically proved that containment in the closed-loop multi-agent system can be guaranteed. A multi-step containment protocol design procedure is further provided. At last, the convergence rate of the containment in multi-agent systems is discussed. Finally, a simulation example is given to verify the effectiveness of the theoretical results.