Tracking control of fully actuated ocean vehicles in a viscous incompressible fluid

This paper addresses the problem of tracking control with a position tracking error constraint of ocean vehicles inside a viscous incompressible fluid, which is described by Navier–Stokes equations (NSEs) perturbed by fluid body force within a bounded domain in three-dimensional space. Since only weak solutions of the NSEs exist globally while global existence of their strong/smooth solutions is a millennium problem, point-wise fluid forces and moments acting on the ocean vehicle are not able to bound. This difficulty is overcome by an appropriate design of control laws and stability analysis of the closed-loop system including the NSEs using a proper extension of the vehicle body. The proposed control design ensures existence of a weak solution and practical exponential stability of the closed-loop system. A simulation on an omni-directional intelligent navigator illustrates the results.