Sidewise Profile Control of 1-D Waves

Yeşim Saraç () and Enrique Zuazua ()
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Yeşim Saraç: Atatürk University
Enrique Zuazua: Friedrich-Alexander University, Erlangen-Nürnberg

Journal of Optimization Theory and Applications, 2022, vol. 193, issue 1, No 38, 949 pages

Abstract: 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; Primary: 35L05; 93B05 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s10957-021-01986-w

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