<p>In this paper, the optimal consensus problem of nonlinear multi-agent systems is investigated via the self-triggered adaptive dynamic programming method. First, the Hamilton-Jacobi-Bellman equation for the state error of multi-agent systems is established, which provides the foundation for deriving the optimal consensus control. Then, the critic-only adaptive dynamic programming approach based on particle swarm optimization is proposed to obtain the approximate solution of the Hamilton-Jacobi-Bellman equation. Furthermore, the event-triggered condition is designed of which the triggering threshold value depends solely on the state error at the triggering instant. The self-triggered control mechanism is further constructed to predict the next triggering instant and update the corresponding control strategy utilizing the current system state, reducing the consumption of computing and communication resources. Finally, Lyapunov-based analysis proves that the proposed control scheme can ensure the uniform ultimate boundedness of consensus error in multi-agent systems, and the efficacy of the self-triggered adaptive control approach is further validated through numerical simulations.</p>