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Boundary control method to identification of elastic modulus of string equation from Neumann-Dirichlet map

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Abstract

This paper considers identification for the spatial variable coefficient of a vibrating string with Neumann boundary control from the measured boundary displacement. The reconstruction algorithm consists of two steps: The first step is to recover the spectral data from the measured boundary displacement by showing that the system is spectral controllable; the second step is to reconstruct the coefficient from the recovered spectral data using the boundary control method, for which the required exact controllability is also verified.

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Authors and Affiliations

  1. School of Mathematical Sciences, Tianjin Normal University, Tianjin, 300387, China

    Zhixue Zhao

  2. Academy of Mathematics and Systems Science, Academy Sinica, Beijing, 100190, China

    Baozhu Guo

  3. School of Computational and Applied Mathematics, University of the Witwatersrand, Wits, 2050, South Africa

    Baozhu Guo

Authors
  1. Zhixue Zhao
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  2. Baozhu Guo
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Corresponding author

Correspondence to Zhixue Zhao.

Additional information

This research was supported by the National Natural Science Foundation of China under Grant No. 11326196 and the Doctoral Fund Program of Tianjin Normal University under Grant No. 52XB1413.

This paper was recommended for publication by Editor ZHANG Bingyu.

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Zhao, Z., Guo, B. Boundary control method to identification of elastic modulus of string equation from Neumann-Dirichlet map. J Syst Sci Complex 29, 1212–1225 (2016). https://doi.org/10.1007/s11424-015-4235-5

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  • DOI: https://doi.org/10.1007/s11424-015-4235-5

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