Abstract: The distributed optimal cooperative tracking control problem is investigated for a class of high-order nonlinear multi-agent systems (MASs) with uncertainties, external disturbances, unmeasurable states under directed communication topologies. First, a coupled cooperative design integrating radial basis function neural networks (RBFNNs) , nonlinear state observers (NSO), and nonlinear disturbance observers (NDO) is proposed to achieve online approximation and estimation of system uncertainties, dynamic disturbances, and unmeasurable states. On this basis, an output- feedback distributed robust anti-disturbance optimal backstepping cooperative controller for high-oeder nonlinear MASs is designed within the multi-agent consensus framework, by leveraging the Bellman optimality principle and adaptive dynamic programming. Finally, thebounded stability of the closed-loop system is rigorously proven based on Lyapunov stability theory. All agents can accurately track the desired signal while satiffying the predefined performance requirements. Simulation results verify the feasibility and effectiveness of the proposed method.