## 1 Introduction  
Underwater vehicles have been extensively developed for many military applications in recent decades. In particular, autonomous underwater vehicles (AUVs) are of interest with respect to developing civil applications for enhancing economic effectiveness, e.g., ocean exploration, environmental monitoring, mapping, and disaster and tsunami warnings [1; 2; 3; 4; 5; 6; 7; 8]. Controller design for AUVs has been a challenge because controllers are closely linked to AUV dynamics in complex underwater environments [9; 10; 11]. The AUV controller can consist of discrete models, continuous models, and their interaction in a hybrid dynamic system (HDS), as modeled by hybrid automata (HA) [12; 13; 14; 15]. Traditional control methods have often been used for implementing complex systems to make them more effective for their controllers [16; 17; 18]. They have also been used for building AUV controllers. Some traditional control techniques applied for AUV applications are described below. Lyapunov stability [19; 20; 21; 22] was demonstrated to be very reactive. However, the stability of the desired waypoint was not suitable enough to track horizontal planar trajectories. The proportional-integral-derivative (PID) regulator [23; 24; 25; 26] proved to be well suited for use in AUVs when tracking horizontal planar trajectories. It was possible to successfully perform the first autonomous trip using this method. Nevertheless, the PID controller was implemented to control the AUV in the absence of large disturbances. The linear quadratic (LO) [27; 28] controller presented average stabilization results. Backstepping methods [29; 30] were shown to be able to control the Euler roll, pitch, and yaw (RPY) angles in conditions of high environmental noise. The sliding-mode controller (SMC) [31; 32; 33] did not give good results when applied alone, as it seemed to be short of adaptation for the dynamics of AUVs. Hence, in some studies investigating backstepping [34; 35], neural networks [36; 37; 38; 39], the computed torque method [40; 41], and digital filters such as extended/unscented Kalman filters (EKF/UKF), the SMC has been improved by using control techniques to improve its performance for AUVs. The above assessment led to us choosing a combination of PID and backstepping to perform a continuous model evolution of the AUV controller, called the integral backstepping (IB) technique. Reusability must also be considered in the development of new AUV applications with respect to their lifecycle in an effort to reduce their cost and resources. The Object Management Group (OMG) [42] standardized the unified modeling language (UML), which is as an industry standard used to visualize, specify, construct, and document the artefacts of a software-intensive system. The system modeling language (SysML) [43] was standardized by the OMG for systems engineering. SysML is a UML profile that can provide simple but powerful constructs for modeling a wide range of systems engineering problems. However, the drawback of UML and SysML is that they lack the ability to model the evolution of internal continuous behavior for developed systems. On the other hand, the model-based systems engineering (MBSE) approach was formalized by INCOSE [44; 45] to robustly model whole artefacts in the development lifecycle of unintelligible systems. Examples of systems engineering methods [46] were identified in a survey of MBSE methodologies [47], including _Harmony_ for systems engineering (_Harmony_-SE) [48; 49], the object-oriented systems engineering method (OOSEM) [50; 51], the rational unified process for systems engineering (RUP-SE) [52], the state analysis method [53], and the object process methodology (OPM) [54; 55]. The model-driven architecture (MDA) [56; 57] was standardized by the OMG for separating the specification of system operations from the details of how a system uses the capabilities of its platform. The three main goals of MDA are portability, interoperability, and reusability through an architectural separation of concerns.