Stabilization and Decay Rate Estimation of Nonlinear Flexible Marine Riser System With the Rotational Inertia Under Nonlinear Boundary Controls

This article investigates the boundary stabilization of a flexible marine riser system that takes rotational inertia into account. This system is described using a nonlinear partial differential equation under the nonlinear controls. Specifically, we focus on applying nonlinear boundary feedback control forces and torques at the top end of the riser. Utilizing measurements of boundary velocity and angular velocity, we devise nonlinear feedback mechanisms aimed at mitigating vibrations within the flexible marine riser system. Our approach encompasses a broad range of nonlinear feedback scenarios. To establish the well-posedness of the resulting closed-loop system, we employ the nonlinear semigroup method. Furthermore, we leverage the integral multiplier technique to demonstrate that the stability characteristics of the closed-loop system are dictated by a dissipative ordinary differential equation. As the nonlinear feedback functions exhibit distinct growth patterns in proximity to the origin, we identify three primary types of decay behaviors. These are subsequently estimated through solutions of the ordinary differential equation and validated through numerical simulations.