Stabilization of the Marine Riser model by controllers depending on finitely many parameters

TL;DR

This paper presents a feedback control method for globally stabilizing marine riser models using finitely many parameters and observables, inspired by dissipative PDE control techniques, ensuring practical and computationally feasible stabilization.

Contribution

It introduces a novel feedback control strategy for marine riser models that depends on finitely many parameters and observables, inspired by dissipative PDE control methods.

Findings

Achieves global stabilization of marine riser models.

Ensures asymptotic stabilization with computational feasibility.

Provides a control approach suitable for practical applications.

Abstract

We prove global stabilization of the marine riser models using a feedback controller that depend on finitely many finite-volume elements and finitely many nodal observables. Our approach is based on a feedback control design for dissipative nonlinear partial differential equations, inspired by the methodology introduced in [Evol. Equ. Control Theory, Vol. 3 (2014), 579-594]. The proposed control strategy ensures asymptotic stabilization while maintaining computational feasibility, making it suitable for practical applications.