Autonomous underwater vehicles (AUVs) equipped with active or passive sonars are vital for underwater acoustic surveillance missions. Effective onboard autonomous control of AUVs is essential for adapting to real-time environmental conditions and dynamic tracking scenarios to enhance mission performance. This paper presents the development of an advanced onboard autonomous control system for AUVs, specifically designed to enhance acoustic target tracking performance. The system employs a modular architecture and behavior-based control method, enabling the AUV to execute tasks such as area approach, area search, target tracking, and optimal acoustic communication. Control commands—including heading, speed, and depth—are generated using an interval programming method to solve the multi-objective optimization problem involving multiple activated behaviors. To achieve necessary acoustic predictions, the system incorporates a data-driven environmental prediction model based on the multiresolution dynamic mode decomposition method. The BELLHOP ray-tracing acoustic model is integrated to predict acoustic transmission loss. Additionally, the control system features a reinforcement learning module that optimizes the weights of individual behaviors to ensure optimal coordination. The effectiveness of the developed system is demonstrated and validated through computer simulations involving two cooperative AUVs tracking an underwater dynamic target.