Sidewise control of 1-d waves - Saraç, Yeşim; Zuazua Iriondo, Enrique (Journal of Optimization Theory and Applications, 2022)
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 or profile at the other free end. This sidewise profile control problem is also often referred to as nodal profile or tracking control. The problem is reformulated as a dual observability property for the corresponding adjoint system, which is proved by means of sidewise energy propagation arguments in a sufficiently large time, in the class of BV-coefficients. We also present a number of open problems and perspectives for further research.<br
Keywords: 1-d wave equations; sidewise profile controllability; nodal profile control; BV-coefficients; sidewise observability; sidewise energy estimates

Sidewise Profile Control of 1-D Waves - Saraç, Yeşim; Zuazua Iriondo, Enrique (Journal of Optimization Theory and Applications, 2022)
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 or profile at the other free end. This sidewise profile control problem is also often referred to as nodal profile or tracking control. The problem is reformulated as a dual observability property for the corresponding adjoint system, which is proved by means of sidewise energy propagation arguments in a sufficiently large time, in the class of BV-coefficients. We also present a number of open problems and perspectives for further research.
CRIS-Team Scopus Importer:2022-01-14
Keywords: 1-D wave equations; BV-coefficients; Nodal profile control; Sidewise energy estimates; Sidewise observability; Sidewise profile controllability