## 4 Application
### Control Implementation and Test Results
Lastly, the advantages and disadvantages of the MBSE/MDA approach were discussed with respect to this AUV control application (Table 5). In this case study, the above-described MBSE methodology, combined with MDA concepts, was only applied to simple test scenarios for a miniature torpedo-shaped AUV running on the free surface. We are yet to fine-tune parameters with respect to the process and measurement noise and the evolutionary optimization for noise parameters for this application. Thus, these important further developments are scheduled for the future. Firstly, the EKF/UKF-based navigation filters will be simulated online within a complete AUV combined with depth control and a suitable environment. Then, the new controller will be implemented on the AUV and tested online through fast frequency disturbances. The performances of the different Kalman filter extensions in terms of accuracy will be carefully investigated in different scenarios. In further MBSE/MDA studies, we will also follow our application strategy to specify, in detail, the patterns of model transformations using the different MDA transformation types, and we will compare them to cases using OPM, such as those described in [54; 55]. Conceptualization, N.V.H. ([PERSON]), N.V.H. ([PERSON]), V.-T.T. and N.-T.B., methodology, N.V.H. ([PERSON]), N.V.H. ([PERSON]), V.-T.T. and N.-T.B., software, N.V.H. ([PERSON]), N.V.H. ([PERSON]), and V.-T.T. ; validation, N.V.H. ([PERSON]), N.V.H. ([PERSON]), V.-T.T. and N.-T.B., writing--original draft preparation, N.V.H. ([PERSON]), N.V.H. ([PERSON]), and V.-T.T. ; writing--review and editing N.V.H. ([PERSON]), N.V.H. ([PERSON]), V.-T.T. and N.-T.B. ; visualization, N.V.H. ([PERSON]), N.V.H. ([PERSON]), V.-T.T. and N.-T.B. ; supervision, N.V.H. ([PERSON]); project administration, N.V.H. ([PERSON]); funding acquisition, N.-T.B. All authors have read and agreed to the published version of the manuscript. Vietnam National Foundation for Science and Technology Development (NAFOSTED). This research was funded by the Vietnam National Foundation for Science and Technology Development (NAFOSTED) under grant number 107.03-2019.302. The authors would like to warmly express their thanks for the support. The authors declare no conflict of interest. ## Abbreviations \begin{tabular}{l l l l} AUV & Autonomous underwater vehicle & MES & Marine environment system \\ CIM & Computation independent model & MOF & Meta Object Facility \\ CLF & Control Lyapunov functions & OMG & Object Management Group \\ DoF & Degrees of freedom & OOSEM & Object-Oriented Systems Engineering Method \\ EKF & Extended Kalman filter & OPM & Object Process Methodology \\ GPS & Global positioning system & PID & Proportional-integral-derivative \\ HA & Hybrid automata & PIM & Platform independent model \\ _Harmony_-SE & _Harmony_ for systems engineering & PSM & Platform specific model \\ HDS & Hybrid dynamic system & RPY & Roll, pitch, and yaw \\ \end{tabular} 



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