This article investigates the exponential synchronization issue for networks of variable-order fractional piecewise-smooth systems with short memory, where each node is modeled to satisfy $\sigma $ -QUAD condition, and possess the incommensurate order. First, the generalized Caputo variable-order fractional derivative (VOFD) operator is defined, and some properties and lemmas with respect to VOFD are developed. Second, the dynamic event-triggered control mechanism is designed, where the additional internal dynamic variable is subject to the nonlinear variable-order fractional dynamical system with incommensurate order. Third, by exploiting the Lyapunov stability theory and some auxiliary inequality techniques, the exponential synchronization criteria are established in terms of linear matrix inequalities (LMIs) under the designed control scheme. In addition, the nonexistence of Zeno behavior is proved by contradiction. Finally, a numerical example is given to illustrate the effectiveness of the main results.

This article aims to address the fixed-time optimal leader-following consensus issue for unknown multiagent systems (MASs) under Denial of Service (DoS) and false data injection (FDI) attacks. A novel fixed-time stability theorem under DoS attacks is presented to simplify the stability conditions and decrease the computational complexity of the settling time. Simultaneously, the deep neural networks (DNNs) structure with the projection operator are adopted in real-time to approximate the unknown system dynamics. To achieve the optimal consensus under cyber-attacks, a hierarchical control approach is presented, which includes a reference signal generation layer and a tracking control layer. Specifically, the distributed and Luenberger-based observers are designed in the reference signal generation layer to solve the fixed-time state estimation issues of leader and followers under multiple malicious attacks, respectively. Then, the optimal control strategy based on the event-triggered mechanism (ETM) is designed in the tracking control layer to track the reference signal and minimize the cost consumption. Due to the difficulty in obtaining explicit expressions of the optimal control mechanisms, a critic-only reinforcement learning (RL)-based algorithm is presented for online learning the unknown weight within a fixed time. By rigorous proof, the developed observers can achieve the fixed-time state reconstruction and the optimal control policy can track observation states after a fixed time. Finally, simulation results about platooning control of automated vehicles are given to demonstrate the efficacy of the developed technique.

This article focuses on the leader–following consensus in fixed time for multiagent systems under denial-of-service (DoS) attacks. First, the node-based distributed DoS attack model is developed, where multiple adversaries launch different attack strategies working together on nodes of the system. Second, a novel fixed-time stability theorem is presented, where an index function is introduced to decrease the complexity of the stability condition and achieve the stability goal under node-based distributed DoS attacks. Third, based on this index function, the resilient dynamic event-triggered mechanism (DETM) is designed by utilizing the DoS attacks detection signals to reduce the consumption of computational costs and save the system resources. With the assistance of Lyapunov stability theory, some consensus conditions are established and the Zeno behavior is excluded. Finally, the autonomous swarm systems, including autonomous aerial vehicles and autonomous ground vehicles, are applied to illustrate the effectiveness of control strategy.

This article aims to address the finite-time consensus issue for variable-order fractional multiagent systems (MASs) under denial of serve (DoS) attacks. First, the framework of node-based DoS attack is introduced, including its influences, detection, and recovery mechanisms. Second, a new variable-order fractional difference (VO-FD) inequality is proposed to accurately evaluate the variable-order fractional derivative of the power function. Based on the developed inequality, two novel finite-time stability theorems are presented based on the developed inequality, which fill up the gap in variable-order fractional finite-time stability without and with DoS attacks, respectively. Third, a resilient distributed control protocol is proposed, where the dynamic event-triggered mechanism (DETM) is introduced based on the detected signal of attack to ensure the desired control performance and economize system resources. According to the Lyapunov stability theory, the consensus can be achieved within the settling time, and some linear matrix inequality (LMI)-based conditions are obtained. Finally, the feasibility and validity of theoretical analysis is illustrated by simulation example.