Resilient optimal consensus control for second-order nonlinear multi-agent systems under DoS attacks

This article addresses the resilient adaptive fuzzy optimal consensus tracking control problem for uncertain nonlinear multi-agent systems under intermittent denial-of-service (DoS) attacks and external disturbances. To address the challenge of reconstructing the leader's dynamics when its system matrix is unavailable to followers, a distributed dynamic compensator is designed to estimate the unknown matrix, based on which a distributed adaptive observer is developed to recover the leader's state. An adaptive nonlinear compensation filter is further introduced to mitigate the influence of external disturbances and FLS approximation errors without requiring derivative information of virtual control laws. Subsequently, an actor-critic fuzzy adaptive optimal controller is developed by integrating the reinforcement learning framework with the backstepping technique, which achieves consensus tracking while minimising the predefined cost function. Finally, simulation results are provided to demonstrate the effectiveness of the proposed scheme.