# Artificial Neural Networks in Coordinated Control of Multiple Hovercrafts with Unmodeled Terms
## 1 Introduction  
In recent years, Wireless Sensor Networks (WSNs) have attracted growing interests from researchers, because they have merits, compared with traditional networking solutions, such as reliability, flexibility, and an ease of deployment, that enable their use in a wide range of varied application scenarios [1]. They can be applied to track moving objects, to monitor special areas so as to trigger alarm systems when some dangerous signals are detected, etc. As the eyes and ears of the IoT, WSNs can work as bridges to build connections between the real-world and the digital-world. In light of this promising application scenario, this paper mainly focuses on a case study of mobile WSNs, where a group of hovercrafts equipped with specific sensors are chosen as test platforms. The objective is to enable them to move around and interact with the physical environment [2] and thus execute a mission of mapping, searching, and monitoring in a specific area. Coordinated control of a fleet of hovercrafts is challenging, especially when we take into account their complex dynamic models. Until now, for a single surface vehicle, many research results have been reported. For example, a linear fuzzy-PID controller was proposed in [3]. Compared with the ordinary PID controller, the proposed controller therein performs better in term of improving settling time and reducing overshoot of the control signal. However, their works just consider the kinematic models of the vehicle without considering the dynamic models, which is not realistic in real operation scenarios. Another weakness of the linear controller is that it usually achieves local stability, e.g., [4], where velocity and position controllers were developed based on a linearized system, which is controllable only when the angular velocity is nonzero. Considering the limitations of linear controllers, in [5, 6], nonlinear controllers for underactuated ships were designed, and global asymptotic stability is achieved. In [7], a nonlinear Lyapunov-based tracking controller was presented, and it was able to exponentially stabilize the position tracking error to a neighborhood of the origin that can be madearbitrarily small. A method of incorporating multiobjective controller selection into a closed-loop control system was presented in [8], where the authors designed three controllers so as to capture three \"behaviors\" representative of typical maneuvers that would be performed in a port environment. However, none of the works mentioned above consider disturbances and unmodeled terms of the vehicle. In order to ensure that the vehicle is robust to external disturbances, in [9], two controllers with application to a surface vehicle (named Qboat) and a hovercraft were proposed, and the authors designed disturbance estimators to estimate external constant disturbances. The disadvantage of this control strategy is that they did not consider unmodeled terms involved in the dynamic model of the vehicle. Considering this constraint, an estimator was developed in [10], where a fuzzy system was used to approximate unknown kinetics. A fault tolerant tracking controller was designed in [11] for a surface vessel. In addition, a self-constructing adaptive robust fuzzy neural control scheme for tracking surface vessels was proposed in [12], where simulation results were shown to testify the efficiency of the proposed method therein. With respect to coordinated control strategy for multiple vehicles, many authors have presented their own approaches. In [13], a cooperative path following methodology was proposed under the assumption that the communication among a group of fully-actuated surface vehicles is undirected and continuous. A coordinated path following with a switching communication topology was designed in [14], while a null-space-based behavioral control technique was proposed in [15; 16]. In [17; 18; 19], a leader-follower control strategy was presented.