Almost global practical exponential stabilisation of a floating rigid body

Abstract

This paper designs a control law based on an extension of the forwarding method to solve the problem of almost global practical exponential stabilisation of a rigid body floating on the interface between viscous incompressible air and water governed by Navier–Stokes equations in a bounded domain in three dimensional space, where ‘almost’ means no collision between the rigid body and the domain boundary. Since less regularity of initial data (hence a weak solution) is considered, the forces and moments induced by the air and water on the rigid body are not possible to be bounded. Therefore, we derive the bound of ‘work and power of air and water’ on the rigid body for use in stability and convergence analysis of the closed-loop system.

Keywords:

• Floating rigid body
• stabilisation
• Navier–Stokes equations
• existence
• weak solution

Disclosure statement

No potential conflict of interest was reported by the author(s).