Abstract: In this paper, an adaptive dynamic programming control strategy based on event triggering is designed for the optimal control of a class of nonlinear multi-agent systems. A distributed optimal controller based on event triggering was designed, which not only avoided the transmission of redundant data, but also minimized the performance function of each agent. The performance index function of distributed multi-agent system was designed, and the HJB equation of multi-agent system was obtained by reinforcement learning method, so as to obtain the optimal control strategy of the system. Through Lyapunov method and gradient descent method, the update laws of critic network based on event triggering was obtained, and the stability of closed-loop control system was proved. The effectiveness of the control method was verified by MATLAB simulation.