Exact Bounded Boundary Controllability to Rest for the Two-Dimensional Wave Equation

TL;DR

This paper addresses the problem of precisely controlling the boundary of a 2D wave system to bring it to rest within a finite time, focusing on bounded control forces applied at the boundary.

Contribution

It provides an exact boundary control method for the 2D wave equation to achieve finite-time rest, with bounded control forces, which is a novel approach.

Findings

Control force applied at boundary can drive wave to rest in finite time

Method ensures bounded control forces during the process

Achieves exact boundary controllability for the 2D wave equation

Abstract

The problem of the exact bounded control of oscillations of the two-dimensional wave equation is considered. Control force is applied to the boundary of the membrane, which is located in a domain on a plane. The goal of the control is to drive the system to rest in a finite time.