Adaptive tracking control of underactuated AUV with historical navigation information and piecewise weighted fractional order integration

In this study, a piecewise adaptive weighted fractional order integration (PAWFOI) is introduced in cascade-backstepping control, which improves the effectiveness of autonomous underwater vehicles (AUVs) in suppressing navigation errors during long-duration operations. Additionally, PAWFOI significantly reduces the computational complexity compared to conventional fractional order integration, ensuring a consistent computational speed. The adaptive weight selector dynamically adjusts the weights based on the AUV state information, achieving enhanced tracking performance. Based on Lyapunov's theory, the results demonstrated that AUV tracking control can be achieved by selecting appropriate control parameters. Finally, an example is presented to verify the correctness and validity of the theoretical results.