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.

本文针对三维空间有界区域内、受流体力扰动的粘性不可压缩流体中海洋运载器的带位置跟踪误差约束的跟踪控制问题展开研究，该流体运动由纳维-斯托克斯方程（Navier–Stokes Equations, NSEs）描述。由于纳维-斯托克斯方程仅存在全局弱解，而其强/光滑解的全局存在性属于千禧年数学难题之一，因此作用于海洋运载器的逐点流体力与力矩无法被界定。通过合理设计控制律，并借助对运载器本体的适当拓展，对包含纳维-斯托克斯方程的闭环系统开展稳定性分析，可克服该难题。本文提出的控制方案可确保闭环系统存在弱解，并实现其实用指数稳定性。针对全向智能导航平台开展的仿真实验验证了本文所提结果的有效性。