Abstract: Aiming at the key challenges of limited control accuracy and insufficient robustness in the cooperative control of Autonomous Surface Vessels (ASVs) and Autonomous Underwater Vehicles (AUVs) heterogeneous formations—stemming from the inherent large time delay and high packet loss rate of underwater acoustic communication—this paper proposes a cooperative control method based on Augmented State Linear Time-Varying Model Predictive Control (LTV-MPC). The core objective is to achieve high-precision and stable formation maintenance under weak communication constraints. First, a long-horizon state prediction and compensation mechanism is constructed based on the Cooperative Turn and Velocity (CTRV) model. By integrating historical motion trajectory estimation, the nonlinear error accumulation induced by pure dead reckoning during extended communication interruption intervals is effectively suppressed. Second, a trajectory smoother with velocity feedforward and an augmented state space are designed. Real-time correction of the predictive model is realized via online Jacobian linearization, which not only mitigates the model nonlinear mismatch problem in high-maneuver scenarios but also suppresses control input chattering. Numerical simulation results over partial cycles demonstrate that, under conditions of high packet loss rate and random long time delay in underwater acoustic communication, the root mean square error (RMSE) of position tracking for the proposed method is 1.401 m. This represents a 78.6% and 23.2% improvement in accuracy compared to traditional PID control and sliding mode control algorithms, respectively. Furthermore, while maintaining control accuracy highly consistent with the standard MPC algorithm, the control output commands are significantly smoother and more stable. This study effectively addresses the dual challenges posed by weak communication constraints and nonlinear dynamics, significantly enhancing the robustness and stability of ASV-AUV heterogeneous formation cooperative control. It provides a theoretical foundation for the cooperative control of cross-domain heterogeneous clusters under weak communication conditions.