Year: 2021
Type: preprint
Abstract: We analyze the sidewise controllability for the variable coefficients one-dimensional wave equation. The control is acting on one extreme of the string with the aim that the solution tracks a given path at the other free end. This sidewise control problem is also often referred to as nodal profile or tracking control. First, the problem is reformulated as a dual observability property for the corresponding adjoint system. Using sidewise energy propagation arguments the sidewise observability is shown to hold, in a sufficiently large time, in the class of BV-coefficients. We also present a number of open problems and perspectives for further research.
Source: arXiv (Cornell University)
Authors: Sarac, Yesim, Zuazua, Enrique
Language: English
Subfield: Control and Systems Engineering
Field: Engineering
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W3119429486