Reinforcement learning-based event-triggered finite-time lag optimal consensus for uncertain multi-agent systems under hybrid attacks

This paper focuses on achieving practical finite-time lag consensus (PFTLC) for uncertain nonlinear multi-agent systems (MASs) subjected to hybrid cyber-physical attacks, including denial-of-service (DoS) and false data injection (FDI). First, deep neural networks (DNNs) are incorporated to approximate unknown nonlinearities, and Lyapunov-based adaptive learning laws with projection modification ensure bounded parameter updates. Second, a distributed observer and a Luenberger-type observer integrated with dynamic event-triggered (DET) mechanisms are constructed to estimate the leader’s lag state under DoS disruptions and the followers’ local states affected by FDI attacks, respectively. These schemes effectively reduce communication and computational loads while ensuring the practical finite-time convergence of all estimation errors. Third, a DET finite-time optimal control strategy is proposed to address the observer state consensus, where a reinforcement learning (RL) framework is applied to approximate the optimal value function online without solving the HJB equation explicitly. Finally, simulation results on a multi-UAVs formation scenario validate the proposed framework’s effectiveness and resilience, demonstrating accurate state estimation, consensus convergence, and significant communication efficiency under hybrid attacks.