**6. Conclusions**

In this study, we proposed a SIFOFLC algorithm for an AUV motion control system. Unlike a conventional FLC algorithm, this is reduced to a SISO controller by using the signed distance method, which provides a significant reduction to parameter tuning and computation burden. In addition, a fractional derivative operator was applied to increase degrees of freedom of the controller, hence the proposed control algorithm is more flexible and adaptive to the AUV motion control system. Furthermore, we developed an HPSO algorithm and applied it to optimize the controller parameters. The simulation results show that the proposed controller enhances the stability and transient performance of the controlled AUV motion system, which manifests in less oscillations of angular velocity, shorter dynamic settling time, and higher control accuracy. In future studies, we will perform experiments using the proposed controller to verify its practicability.

**Author Contributions:** Conceptualization, Z.C. and B.Z.; methodology and software, Z.C. and Z.Z.; validation, S.L. and M.L.; writing—original draft preparation, Z.C. and L.L.; writing—review and editing, L.L. and B.Z.; supervision, L.L., L.Z. and Y.Y. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by the Shenzhen Science and Technology Program under Grant JCYJ20210324122010027; the Science and Development Program of Local Lead by Central Government, Shenzhen Science and Technology Innovation Committee under Grant 2021Szvup111; the Guangdong Basic and Applied Basic Research Foundation under Grant 2019A1515111073; the National Natural Science Foundation of China under Grant 52001259, 11902252; the Young Talent fund of University Association for Science and Technology in Shaanxi, China under Grant 20200502; Science and Technology on Avionics Integration Laboratory and Aeronautical Science Foundation of China under Grant 201955053003; Maritime Defense Technology Innovation Center Innovation Fund under Grant JJ-2021-702-09; National Research and Development Project under Grant 2021YFC2803000.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** The data presented in this study are available in the article.

**Conflicts of Interest:** The authors declare no conflict of interest.
