Experimental Study of the HUM Control Operator for Linear Waves

TL;DR

This paper investigates the numerical approximation of wave controllability using spectral Galerkin methods, providing experimental insights that support theoretical results and raise new questions for wave control analysis.

Contribution

It introduces a Galerkin spectral approach to approximate the control operator for linear wave equations, bridging theory and numerical experiments.

Findings

Good numerical illustrations of wave controllability theory

Support for spectral methods in control approximation

New questions raised for future wave control research

Abstract

We consider the problem of the numerical approximation of the linear controllability of waves. All our experiments are done in a bounded domain \Omega of the plane, with Dirichlet boundary conditions and internal control. We use a Galerkin approximation of the optimal control operator of the continuous model, based on the spectral theory of the Laplace operator in \Omega. This allows us to obtain surprisingly good illustrations of the main theoretical results available on the controllability of waves, and to formulate some questions for the future analysis of optimal control theory of waves.