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By constructing a dynamic state space model of the ship, this research integrates two advanced adaptive algorithms, namely adaptive gradient moment estimation (AMSGrad) and adaptive gradient algorithm (AdaGrad), within the linear quadratic regulator (LQR) framework. These algorithms can be used to enhance on-the-fly convergence of control parameters, ensure robust system performance under dynamic conditions, and reduce modeling errors or installation errors. Unlike traditional control methods that rely heavily on exhaustive modeling and lack on-the-fly adaptability, elastic and flexible systems for autonomous ship operations can be achieved. Research results show that this technology has made a significant contribution to unmanned navigation technology, achieving reliable control, precise navigation, and expanding the scope of applications such as automatic transportation and environmental monitoring. 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