This paper focuses on the distributed model predictive control (DMPC) method for nonlinear multi-autonomous underwater vehicle (AUV) systems. Firstly, it extends the requirement of unidirectional topology to directed acyclic graphs (DAG). The newly proposed DMPC algorithm eliminates the need for a priori knowledge of all node information, thus eliminating the need for a universally accessible and entirely connected leader across various communication topologies.Next, a distributed model predictive formation controller based on switching topologies is proposed. To minimize the discrepancy between the anticipated and actual state trajectories of AUVs at successive sampling moments, a self-deviation constraint approach is implemented within the open-loop optimization framework. Then, a common Lyapunov function (CLF) based on joint neighbor sets is put forward for the stability analysis of the multi-AUV system under switching communication topologies. Finally, the effectiveness and superiority of the proposed strategies are verified through numerical simulation experiments.