Adaptive fuzzy-based distributed optimization with privacy protection for uncertain high-order nonlinear multi-agent systems against two types of cyber attacks

This paper investigates the adaptive fuzzy distributed optimization with privacy protection for high-order nonlinear multi-agent systems (MASs) with uncertain disturbance under cyber attacks, in which DoS and eavesdropping attacks are considered. A hierarchical architecture for achieving an optimal objective is provided to build a bridge between distributed optimization design and fuzzy tracking control. A visual signal is constructed to ensure the agents cooperatively minimize the objective function when designing a distributed optimization algorithm to defend against DoS attacks. Moreover, the SingleMod cryptosystem-based privacy protection strategy is employed to avoid privacy leakage caused by external eavesdroppers. Then, an adaptive fuzzy controller is developed to guarantee that the output of MASs can converge to the optimal solution by utilizing a fuzzy logic system and adaptive backstepping technique. Finally, a simulation example is provided to illustrate the validity of the obtained results.