This paper presents a hierarchical secure control framework for resilient vehicular platooning under hybrid cyber-physical threats, including coupled false data injection (FDI) and denial-of-service (DoS) attacks, as well as actuator faults. A two-layer architecture is adopted to decouple cyber-layer disruptions from physical-layer execution, thereby enhancing system modularity and fault isolation. At the upper layer, a virtual platoon system is constructed, where a distributed resilient controller integrated with an event-triggered mechanism (ETM) is developed to ensure coordinated behavior while reducing communication overhead. At the lower layer, an adaptive fault-tolerant tracking controller is designed to compensate for actuator degradation and external disturbances, enabling each physical vehicle to follow its virtual reference independently. A layer-wise Lyapunov-based analysis is conducted to guarantee the practical exponential stability of the hierarchical control framework, where tractable LMI conditions are derived for both the cyber coordination and physical tracking components. Simulation results demonstrate that the proposed architecture effectively mitigates fault propagation, maintains robust performance under concurrent cyber and physical threats, and outperforms non-hierarchical benchmarks in terms of system stability.

This paper investigates the platoon control of heterogeneous vehicular cyber-physical systems (VCPSs) subject to external disturbances by using neural network and uniformly quantized communication data. To reduce the adverse effects of quantization errors on system performance, a coupling sliding mode surface is established for each following vehicle. The radial basis function (RBF) neural networks are employed to approximate the unknown external disturbances. Then, a novel platoon control law is proposed for cooperative tracking in which each following vehicle only uses the uniformly quantized data of the neighboring vehicles. And the designed controllers in this paper are fully distributed due to the fact that the selection of each vehicle's controller parameters is independent of the entire communication topology. The string stability of VCPSs in the entire control process is ensured rather than only ensuring the string stability after the sliding mode surface converges to zero. Compared with the existing controller design methods and quantization mechanisms, the neural adaptive sliding-mode platoon controller proposed in this paper is superior in performances including tracking errors, driving comfort and fuel economy. Numerical simulations illustrate the effectiveness and superiority of the designed control strategy.

This study investigates the problem of event-based privacy-preserving platooning control for connected automated vehicles subject to limited communication resources and data falsification attacks. First, a novel dynamic event-triggered mechanism (DETM)-based encryption and decryption strategy is proposed to regulate the frequency of data encryption and transmission in response to real-time network bandwidth occupancy and vehicular states, thereby safeguarding data privacy while improving communication resource utilization. Then, a unified and general attack modeling method is established to characterize various forms of data falsification attacks on sensor measurements and driving commands. Building upon this, a secure observer-based platooning control protocol is derived, where the controller gains, observer parameters, and communication topology are co-designed to ensure the desired secure platooning performance while ensuring vehicular data privacy and efficient utilization of communication resources. Finally, several comparative case studies with quantified metrics are conducted to demonstrate the efficacy and merits of the proposed methods from the perspectives of platoon stability, security, communication efficiency and data privacy.

Practical experience shows that metro-bus composite networks (MBCNs) are irreplaceable for meeting the travel demands of urban residents. In-depth analyses of MBCN dynamic robustness can reveal the mechanisms driving reliable operations. In this paper, we propose a two-layer metro-bus composite network (TL-MBCN) model that integrates the topological structure with its associated passenger flow dynamic. The propagation of cascading failure in the MBCN is then imitated through a linear load-capacity model by considering passengers’ mode choice behavior and rerouting behavior. Three indicators are introduced to assess the dynamic robustness of the MBCN from three perspectives: connectivity, travel time, and passenger flow. Using traffic data from Nanjing, our experiments reveal that (1) the dynamic robustness of the MBCN varies significantly across different periods of the day, and the scale of the cascading failures is strongly correlated with the passenger flow distribution around the attacked station; (2) the dynamic robustness of the network is significantly influenced by the station capacity, passengers’ tolerance threshold, and their prior knowledge of station failures; and (3) the MBCN is more robust under the proposed passenger flow transfer rule.

Shared steering control enables human–machine cooperation in vehicle lateral control. This article develops an asynchronous shared steering control framework with dynamic event triggering and data-driven guarantees. The human–machine steering system is modeled as an asynchronous closed-loop system, where the driver steering action evolves continuously while the automated steering command is updated only at triggered instants. Without explicit model identification, a data-driven synthesis method is established directly from input-state trajectory data via consistency-set characterization, enabling the codesign of the state-feedback controller and the dynamic triggering mechanism under actuator saturation. Sufficient linear matrix inequality conditions are derived to ensure regional stability and discrete-time $H_\infty$ performance under the stated admissibility conditions for all data-consistent system realizations, while the resulting invariant ellipsoids provide certified positively invariant regions in the disturbance-free case. Simulation results verify the effectiveness and robustness of the proposed method under both disturbance-free and disturbed conditions.

This paper introduces a multiplex network model to explore how information dissemination can mitigate cascading failures. The model couples an infrastructure network with an information propagating layer and incorporates a novel, time-varying redistribution coefficient to capture adaptive, self-protective behaviors. It also accounts for the differing time scales of information spread and failure propagation. The analysis reveals that information transmission significantly enhances network robustness. Specifically, a higher information-transmission rate monotonically increases both the number of surviving nodes and the size of the largest connected component. Furthermore, scale-free (BA) information networks are more effective at suppressing cascades than small-world (WS) or random (ER) topologies, and greater disparity between the time scales of information and failure further strengthens this protective effect. These findings underscore the critical role of rapid information flow in designing resilient critical infrastructures.

This article focuses on prescribed-time distributed robust Nash equilibrium seeking for monotone games impacted by unknown and time-varying disturbances. First, a regularization term with a prescribed-time decaying parameter is introduced to compensate for the absence of strong monotonicity in the merely monotone game. Based on the regularization technique, a new prescribed-time signum-based distributed Nash equilibrium seeking algorithm incorporating an integral sliding mode method, a leader-following consensus protocol, and a gradient algorithm is presented for monotone games with unknown but bounded disturbances. Then, to dispose of the unknown bounds of disturbances, a prescribed-time distributed adaptive integral sliding mode based Nash equilibrium seeking strategy is devised. On the basis of the proposed strategies, some sufficient conditions are obtained to guarantee that the players’ actions are capable of converging to the least-norm Nash equilibrium of the monotone games in a prescribed time. In the end, numerical simulations on least-distance formation control of a network of players testify to the performance of the proposed seeking strategies.

This article is concerned with the trajectory tracking problem for autonomous ground vehicles (AGVs) under unknown dynamics and external disturbances. To solve this problem, a tracking control scheme, which integrates recurrent neural network (RNN)-assisted guidance optimization and structured fuzzy uncertainty modeling, is designed. Specifically, an RNN-based velocity optimization mechanism is introduced to reshape velocity commands into smooth, bounded, and learning-friendly signals, thereby smoothing aggressive commands to improve fuzzy system convergence and approximation accuracy at the kinetic layer. Then, a structured fuzzy modeling method is developed to separately approximate state-dependent unknown dynamics and disturbance-related uncertainties, leading to more accurate modeling and enhanced robustness. Based on the optimized velocity commands and fuzzy uncertainty estimates, two kinetic control laws are developed to drive AGVs to track desired trajectories. Subsequently, two stability-oriented fuzzy weight update laws are constructed, which ensure the uniform ultimate boundedness (UUB) of the closed-loop error dynamics. Simulation and experimental results on an AGV platform demonstrate the effectiveness and practical feasibility of the proposed control scheme.

A distributed optimal double-layer formation control problem for multi-cluster systems, which has rarely been reported, is addressed in this paper. Specifically, the agents in each cluster are required to form a desired shape, while the centroids of the clusters must also adhere to a specified geometric pattern. Beyond this double layer formation task, the agents are faced with a global optimization problem, which should be resolved concurrently. The paper mainly faces the following challenges: (1) how to deal with both inter-cluster and intra-cluster formation problems; (2) how to simultaneously achieve the double-layer formation control and global optimization; (3) how to estimate the averaged state of each cluster, which is unknown to all agents. To achieve optimal double-layer formation control, a multi-cluster aggregative double-layer formation (MCADF) game is first formulated. Following the MCADF game formulation, an efficient broadcasting method is developed to estimate and disseminate the averaged state of each cluster. Moreover, distributed Nash equilibrium seeking strategies for multi-cluster aggregative games are established by incorporating regularization techniques, gradient algorithms, dynamic average consensus protocols and “improved” consensus tracking protocols. It is formally proven by Lyapunov stability analysis that the proposed strategies can steer agents to achieve optimal double-layer formation. Finally, a numerical simulation example on a multiple target enclosing problem is given to verify the effectiveness of the proposed method.

This paper considers a multi-Unmanned Surface Vehicle (multi-USV) escort problem, in which a group of slave USVs need to achieve formation and interception of intruders so as to protect the master vessel against the intruders. The mission scope includes maintaining a protective formation around the master vessel, selecting appropriate interceptors upon detect intruders while retaining followers to preserve coverage, and adapting online to uncertain intruder maneuvers through real-time decision making. An Adaptive Model Predictive Control (AMPC) escort model is established for the considered problem, which takes the future maneuvers of the intruders into consideration. An offline-learned, online-corrected maneuver predictor based on a Mixture Density Network (MDN) and a Kalman Filter (KF) is developed: the MDN captures multi-modal uncertainty in intruder strategies, while the KF corrects predictions when strategies shift, thereby providing robustness even with limited historical data. To enhance solution efficiency, the Crested Porcupine Optimizer is improved via chaotic initialization, random restarts and enhanced cyclic population reduction (CPR) mechanism as desensitization strategies, jointly accelerating convergence and strengthening exploration. Numerical simulations show improvements in interception performance, prediction accuracy, generalization to unknown intruder strategies, and computational efficiency.

This paper studies the problem of aggregative optimization in open multi-agent systems (OMAS), where agents are allowed to join and leave the system in a free manner during the decision-making process. A multi-aggregator communication mechanism is proposed to facilitate information exchange among agents, in which the aggregators are responsible for collecting information from agents and exchanging them with neighboring aggregators. Based on the multi-aggregator communication mechanism, a novel semi-distributed algorithm is designed. Dynamic regret is taken as a metric to evaluate the performance of the proposed algorithm. It is analytically shown that the dynamic regret can be bounded by the sum of agents' individual regrets, each of which grows sub-linearly with its active period length under locally diminishing step-sizes and a slowly changing environment. Moreover, to quantify the impact of agents' joining and leaving on algorithm performance, the regret is analyzed in the case of agent replacement, wherein some of the agents are replaced by new ones though the number of agents remains constant over time. Additionally, the algorithm is simplified in some special cases, resulting in a tighter regret bound. Finally, two numerical examples on target surrounding problems and price based energy management are given to verify the effectiveness of the proposed methods.

This paper proposes a novel secure frequency control approach for microgrids with online attack detection-based data scheduling and remedy mechanisms. First, taking into account the dynamics of photovoltaic (PV) units, energy storage systems (ESSs) and electric vehicle (EV) aggregators with state of charge (SOC)-dependent charging/discharging characteristics, a generic frequency control system model of PV-ESS-EV microgrids is established. Second, a two-step state estimation method involving a one-step-ahead state predictor and a measurement-update-based state estimator is proposed to estimate the microgrid system state, generating optimal prediction and estimation ellipsoids enclosing the true states during the whole operation time. Third, an attack detection scheme is provided for online detection of potential attacks by calculating the intersection over union (IOU) of the two generated ellipsoids. Upon successful attack detection, novel active data scheduling and two-stage data remedy mechanisms are derived for responsively reducing the negative effects of adversarial attacks. Then, a co-design approach, dependent on time-varying IOU signals, to the secure frequency controller and the scheduling mechanism parameters is presented. Finally, the efficacy and merits of the proposed frequency control strategy with attack detection-based data scheduling and remedy are verified through several case studies.

This paper formulates a new distributed Nash equilibrium seeking problem with a dynamic set of players in which players are allowed to join and leave the network in a free manner during the decision-making process. To accommodate the dynamic joining and leaving behaviors of the players, a status estimation mechanism, which is capable of estimating in a finite time whether the players are active or inactive, is introduced. Based on the status estimation mechanism, a gradient play based algorithm is developed for distributed Nash equilibrium seeking in the dynamic environment. It is shown that under strongly connected communication graphs, players' actions are convergent to a small neighborhood of the new Nash equilibrium linearly every time the player set changes. Moreover, the convergence accuracy and convergence rate can be adjusted by suitably tuning the step-size. To cover more general communication scenarios, strongly connected graphs are further relaxed to be B-jointly connected graphs, under which the convergence properties of the proposed algorithm are analytically studied. Furthermore, the upper bound of the average tracking error is quantified to evaluate the dynamic performance of the proposed algorithm. In the last, a simulation study on energy consumption games is given to verify the effectiveness of the proposed algorithm. (c) 2025 Elsevier Ltd. All rights are reserved, including those for text and data mining, AI training, and similar technologies.

This article investigates the resilient cooperative maneuvering problem for a group of electric mobile robots (EMRs) subject to falsified motor inputs. A comprehensive EMR dynamic model is first established by explicitly incorporating direct current (dc)-motor characteristics and pulse-width modulation (PWM)-based actuation mechanisms, which enables accurate modeling of low-level motor voltage manipulations. To counteract falsified inputs, a three-layer resilient cooperative control framework is proposed, consisting of: 1) a networked guidance law for kinematic coordination; 2) an adaptive torque control law for dynamic motion control; and 3) a resilient voltage control law for motor voltage regulation and compensation. Rigorous Lyapunov-based analysis proves the stability of the resulting closed-loop system. At last, both simulation and experimental results demonstrate that the proposed control framework reduces trajectory tracking errors by more than 20%-75% under voltage falsification attacks, ensuring accurate formation maintenance.

This paper studies the problem of distributed cooperative control of connected and automated vehicles (CAVs) in the presence of denial-of-service (DoS) attacks in open environments, where vehicles can perform joining and leaving maneuvers freely in the platoon. First, inspired by the framework of switched systems feature multi-mode and multi-dimensional, the characteristic of platoon maneuvers is described by a switching communication topology. The framework allows for concurrent changes in both the number of vehicles and the topology graph at switching instants caused by joining/leaving of vehicles and DoS attacks. Besides, a full-order distributed observer is designed for each follower vehicle to observe its states. Second, a distributed platooning controller suitable for such a dynamic environment is constructed for effective and secure cooperative vehicle tracking control with the exponential convergence of relative positions and velocities to the leader. Finally, numerical simulations are presented to demonstrate the effectiveness of the theoretical results and merits of the proposed cooperative control design approach on maintaining the desired platooning performance.

Distributed fixed-time and prescribed-time optimization has become a key focus in the study of multi-agent systems (MASs), enabling efficient and scalable solutions to optimization problems with guaranteed convergence within fixed-time and prescribed-time frames, respectively. This survey presents a thorough overview of distributed fixed-time and prescribed-time optimization methodologies, focusing on two key paradigms: time-invariant and time-varying cases. Specifically, the survey begins by exploring fundamental principles of fixed-time optimization of MASs, emphasizing their advantages over asymptotic and finite-time methods, particularly in scenarios with strict convergence-time requirements. Then, recent advances are presented in distributed fixed-time optimization, including second-order MASs, event-triggered control, and application to smart grids. Following that, representative results on distributed prescribed-time optimization are provided, which extend the fixed-time counterpart to a problem with user-defined settling time. Finally, some open challenges in the field, such as handling communication delays, cyber-physical threats, and nonconvexities, are identified that deserve further investigation.

In this paper, we consider the Nash equilibrium (NE) seeking problem for a class of high-order uncertain nonlinear multi-agent systems (MASs) under event-triggered communication (ETC). To address this problem, a hierarchical control method is proposed, which includes a fully distributed NE seeking algorithm layer, a seeking variable performance improvement layer, and a decentralized tracking control layer. Specifically, an event-triggered fully distributed NE seeking algorithm is proposed to achieve the NE seeking objective in the fully distributed NE seeking algorithm layer, which composes a gradient term and a consensus term to drive the variable to its N. To enable this approach to accommodate high-order nonlinear MASs, an improved adaptive NE variable generator with the form of lower triangular is proposed in the seeking variable performance improvement layer. Driven by the newly designed variable, an adaptive controller is designed using the backstepping technique in the decentralized tracking control layer. Compared with the existing NE methods, the developed method is applicable to a wider class of high-order uncertain nonlinear MASs under distributed ETC. Finally, a simulation example is given to demonstrate the efficacy of our developed method. (c) 2026 Elsevier Ltd. All rights are reserved, including those for text and data mining, AI training, and similar technologies.

This paper investigates distributed platooning control of connected and autonomous vehicles (CAVs) under practical spacing policies with vehicular data privacy protection. A practical spacing policy is first designed to adaptively regulate inter-vehicle distances by incorporating real-time traffic flow variations, road friction conditions, and safety distance requirements. The resulting spacing-policy-induced uncertainties are then addressed through an augmented system-based estimation approach. To safeguard vehicular privacy, a differential privacy-enhanced encoding-decoding mechanism is developed, enabling protection of both initial vehicular state information and broadcast vehicular data against eavesdropping attacks. Upon that, a co-design strategy is further proposed to jointly synthesize the privacy protection scheme, estimator, and distributed controller, ensuring reliable platoon tracking performance with data confidentiality. Finally, comparative case studies are conducted to validate the enhanced platoon tracking stability, driving safety, and privacy preservation in realistic traffic scenarios.

This paper studies a distributed online optimization problem over partially Free-In and Free-Out (FIFO) networks, in which a set of unfixed agents cooperate to minimize the sum of a group of time-varying functions over a time horizon. To be specific, the agents are divided into static agents and dynamic agents. The static agents are those who remain in the network during the whole time horizon, while the dynamic agents are allowed to join and leave the network freely. Based on the dual averaging technique, two novel distributed algorithms are developed to address the distributed optimization problem in such a dynamic environment. In the case where agents can distinguish whether their out-neighbors are dynamic agents or static agents, a weighting matrix based algorithm is developed. In the case where the identities of out-neighbors are unavailable, a gradient-storage based algorithm is developed, which has higher communication and local storage requirements than the weighting matrix based algorithm. By assuming that each dynamic agent has at least one in-neighbor and one out-neighbor who are static agents, the running average regret is shown to be upper bounded by $\mathcal {O}(\frac{1}{\sqrt{\mathit {T}}})$ under suitable step-sizes, where $\mathit {T}$ is the time horizon. A simulation study on binary classification is given to verify the effectiveness of the developed algorithms. In addition, a numerical example is used to highlight the advantages of the proposed methods over the distributed sub-gradient decent method.

Dear Editor, This letter is concerned with the robust tracking control problem of automated vehicles(AVs).First,the dynamics of an AV is con-structed by taking into account model uncertainties.Then,to guaran-tee the successful completion of tracking tasks,an actor-critic learn-ing-based robust tracking control scheme is designed.At last,formal stability analysis and experiment results are provided to verify the tracking performance of the designed control scheme.