Fixed-Time Optimal Consensus of Multiagent Systems Under Cyber-Attacks: A Hierarchical Control Approach.

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.