Output feedback averaged sub-gradient integral sliding mode control to regulate the tridimensional autonomous motion of autonomous submersible vehicles

This study presents the development of an output feedback control for regulating the movement of an autonomous submersible vehicles in the tridimensional space. The controller formulation applies the Averaged Sub-Gradient Integral Sliding Mode which is fed with the estimation of the translational velocity states by a distributed super-twisting algorithm. The structure of the autonomous submersible vehicles dynamics permits the implementation of the ASG algorithm using the estimates of translation velocity. The proposed scheme solves a non-linear extremum seeking problem that aims to minimize a non-strictly convex function that depends on the tracking error defined by the difference of some suitable reference trajectories and the coordinates of the submarine center of mass. The desired reference trajectories were designed to force the autonomous submersible vehicles three-dimensional motion to a continuous circuit in an oscillating shape over the horizontal plane combined with a submersion on the z-axis. The comparison between the proposed controller, the ASG with complete knowledge of the states and the state feedback controller is presented. This comparison confirms the output feedback ASG controller forced the autonomous submersible vehicles to the desired trajectory with a notable difference in the magnitude of the control given the estimation of the states. These outcomes justify the potential contributions of the suggested ASG integrated with the super-twisting algorithm to obtain the local minimization of the evaluated functional depending on the tracking error. The results justify the potential contributions of the suggested ASG with the super-twisting algorithm to regulate the position of the autonomous submersible vehicles to the desired trajectory.