This study deals with fixed‐time consensus problems of second‐order multi‐agent systems with uncertain bounded disturbances. Instead of the time‐triggered control algorithm, a distributed event‐triggered control algorithm is developed in the presence of uncertain disturbance. By designing a novel threshold, a triggering function is proposed, which is fully distributed and does not require continuous communication. To tackle the chattering problem, a saturation function is defined to improve the control algorithm. Several conditions are derived and the rigorous proof is given by using Lyapunov stability theory and fixed‐time stability theory. Then, to reduce the disturbance effect, an event‐triggered control algorithm is proposed by using a disturbance observer. Finally, two simulation examples are given to verify the efficiency of the proposed control method.

With the continuous development of industrial intelligence, the integration of cyber–physical components creates a need for effective attack detection methods to mitigate potential DDoS threats. Although several DDoS attack detection modeling approaches have been proposed, few effectively incorporate the unique characteristics of industrial control system (ICS) architectures and traffic patterns. This paper focuses on DDoS attack detection within cloud–edge collaborative ICSs and proposes a novel detection model called FedDynST. This model combines federated learning and deep learning to construct feature graphs of traffic data. Introducing dynamic and static adjacency matrices, this work reveals the interactions between long-term industrial traffic data and short-term anomalies associated with DDoS attacks. Convolutional neural networks are utilized to capture distinctive temporal features within industrial traffic, thereby improving the detection precision. Moreover, the model enables continuous optimization of the global detection framework through a federated learning-based distributed training and aggregation mechanism, ensuring the privacy and security of industrial client data. The effectiveness of the FedDynST model was validated on the CICDDoS2019 and Edge-IIoTset datasets. The simulation results validated the superiority of the proposed approach, and thus, demonstrated significant improvements in both detection accuracy and convergence.

This paper focuses on event-triggered finite-time consensus problem of second-order multi-agent system, which is subjected to external bounded disturbance. First, a novel finite-time consensus control algorithm based on the event-triggering control scheme is proposed. The proposed algorithm contains a saturation function that is disturbance rejection and aims at eliminating the chattering problem caused by the discontinuity of the control algorithm in some existing work. Further, the utilization of saturation function reduces damages to the actuators and decreases energy consumptions in practical applications. Second, an event-triggering function is developed to generate the control event sequences, which is fully continuous communication free and avoids continuous update of the controller by contrast with real-time control method and continuous communication event-triggered control scheme. Third, finite-time bounded consensus can be reached with the scale of the convergence region adjusted by appropriate parameter selecting. A rigorous proof based on Lyapunov stability analysis is given to verify that the event-triggered control algorithm, under the derived conditions, solves the second-order finite-time consensus with chattering free and being robust to external disturbances as well as excluding the Zeno behavior. Finally, two simulation examples are performed to validate the effectiveness of the results.