Journal
INTERNATIONAL JOURNAL OF CONTROL
Volume 92, Issue 1, Pages 2-11Publisher
TAYLOR & FRANCIS LTD
DOI: 10.1080/00207179.2017.1286691
Keywords
Distributed parameter systems; infinite-dimensional backstepping; boundary control; boundary observer; reaction-diffusion system
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Funding
- Ministerio de Economia y Competitividad [MTM2015-65608-P]
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Recently, the problem of designing boundary controllers and observers for unstable linear constant-coefficient reaction-diffusion equation on N-balls has been solved by means of the backstepping method. However, the extension of these results to spatially varying coefficients is far from trivial. This work deals with radially varying reaction coefficients under revolution symmetry conditions on a sphere (the three-dimensional case). Under these conditions, the equations become singular in the radius. When applying the backstepping method, a similar type of singularity appears in the backstepping control and observer kernel equations. However, with a simple scaling transformation, we are able to reduce the singular equation to a regular equation, which turns out to be the same kernel equations appearing when using the one-dimensional backstepping method. In addition, the scaling transformation allows us to prove stability in the H-1 space.
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