A distributed adaptive iterative learning control strategy is proposed for the formation problem of nonlinear multi-agent systems with unknown time-varying parameters. Firstly, the uncertain parameters of the system are expanded through Fourier series, and a convergent series sequence is employed to handle the truncation error resulting from the Fourier series expansion. Combined with the formation error during the operation of the multi-agent system, the adaptive iterative learning control law and parameter update law are derived. Secondly, for scenarios where the dynamics of the leader are unknown to most agents, a new auxiliary control is designed to compensate for the unknown dynamics and avoid unknown bounded interference. Then, based on the Lyapunov energy function, it is proved that the formation error of the multi-agent system tends to be zero within a limited time as the number of iterations increases under the action of the designed control law. Finally, this control strategy is applied to multi-UAV formation systems, and its effectiveness is validated through the construction of a semi-physical experimental platform. Experimental results demonstrate that this control method can ensure rapid formation of the required formation by multiple agents, and each agent can accurately track the desired trajectory within a limited time. The proposed method fully considers the parameter uncertainty and anti-interference ability of multi-agent systems, providing an effective approach for the precise control of complex multi-agent systems in practical applications.