Stabilization of a fluid-solid system, by the deformation of the self-propelled solid. Part II: The nonlinear system

TL;DR

This paper demonstrates the stabilization of a complex nonlinear fluid-solid interaction system through boundary feedback control of the solid's deformation, ensuring physical constraints and self-propulsion.

Contribution

It introduces a method to stabilize a nonlinear fluid-solid system using boundary feedback and deformation constraints, extending previous linear results to the nonlinear case.

Findings

Nonlinear system stabilization achieved via boundary feedback.

Constructed deformation satisfies physical and self-propulsion constraints.

Fixed point method used for proof of stabilization.

Abstract

In this second part we prove that the full nonlinear fluid-solid system introduced in Part I is stabilizable by deformations of the solid that have to satisfy nonlinear constraints. Some of these constraints are physical and guarantee the self-propelled nature of the solid. The proof is based on the boundary feedback stabilization of the linearized system. From this boundary feedback operator we construct a deformation of the solid which satisfies the aforementioned constraints and which stabilizes the nonlinear system. The proof is made by a fixed point method.