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In this paper, the finite-time output feedback trajectory tracking control problem for autonomous underwater vehicles (AUVs) is investigated. The vehicle model is constructed in six degrees of freedom and the vehicle attitude is represented by quaternions to avoid representation singularities. The control design consists of three steps. First, by using the finite-time control technique, two global finite-time stabilizing controllers based on state feedback are proposed for the vehicle translational and rotational tracking error subsystems, respectively. Second, considering the estimation problem of the vehicle translational velocities, a global finite-time convergent observer is employed to reconstruct the information of the vehicle translational velocities. Finally, based on the proposed state feedback controllers and the finite-time convergent observer, a finite-time output feedback trajectory tracking control scheme for AUVs is derived. Global finite-time stability of the closed-loop system is rigorously proved by using Lyapunov theory. Compared with the conventional backstepping control scheme via output feedback, the proposed finite-time output feedback control scheme offers not only a faster convergence rate but also a higher tracking accuracy for trajectory tracking control of AUVs. Simulations demonstrate the effectiveness of the proposed control scheme.
Li et al. (2014) studied this question.