Article
2022
·
3 citations
Sidewise Profile Control of 1-D Waves
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 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.
Keywords
1-D wave equations
Sidewise profile controllability
Nodal profile control
BV-coefficients
Sidewise observability
Sidewise energy estimates
EXACT BOUNDARY CONTROLLABILITY
NODAL PROFILE
NULL CONTROLLABILITY
HEAT-EQUATION
OBSERVABILITY
NETWORK
WoS Categories
Operations Research & Management Science
Mathematics, Applied
Citation
- Journal
- JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS
- Year
- 2022
- Volume
- 193
- Issue
- 1-3
- Pages
- 931-949
- ISSN
- 0022-3239
- eISSN
- 1573-2878
- DOI
- 10.1007/s10957-021-01986-w
- WoS UID
- WOS:000739270900001