Boundary Control Method to Identification of Elastic Modulus of String Equation from Neumann-Dirichlet Map

ZHAO Zhixue1 , GUO Baozhu2

1. 1.School of Mathematical Sciences, Tianjin Normal University, Tianjin 300387, China.;2.Academy of Mathematics and Systems Science, Academy Sinica, Beijing 100190, China; School of Computational and Applied Mathematics, University of the Witwatersrand, Wits 2050, South Africa.
• Online:2016-10-25 Published:2016-10-11

ZHAO Zhixue,GUO Baozhu. Boundary Control Method to Identification of Elastic Modulus of String Equation from Neumann-Dirichlet Map[J]. Journal of Systems Science and Complexity, 2016, 29(5): 1212-1225.

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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