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An Adaptive Observer-Based Algorithm for Solving Inverse Source Problem for the Wave Equation

Author

Listed:
  • Sharefa Asiri
  • Chadia Zayane-Aissa
  • Taous-Meriem Laleg-Kirati

Abstract

Observers are well known in control theory. Originally designed to estimate the hidden states of dynamical systems given some measurements, the observers scope has been recently extended to the estimation of some unknowns, for systems governed by partial differential equations. In this paper, observers are used to solve inverse source problem for a one-dimensional wave equation. An adaptive observer is designed to estimate the state and source components for a fully discretized system. The effectiveness of the algorithm is emphasized in noise-free and noisy cases and an insight on the impact of measurements’ size and location is provided.

Suggested Citation

  • Sharefa Asiri & Chadia Zayane-Aissa & Taous-Meriem Laleg-Kirati, 2015. "An Adaptive Observer-Based Algorithm for Solving Inverse Source Problem for the Wave Equation," Mathematical Problems in Engineering, Hindawi, vol. 2015, pages 1-8, October.
    • Handle: RePEc:hin:jnlmpe:796539
    DOI: 10.1155/2015/796539
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    Cited by:

    1. Hussein, S.O. & Dyhoum, Taysir E., 2022. "Solutions for non-homogeneous wave equations subject to unusual and Neumann boundary conditions," Applied Mathematics and Computation, Elsevier, vol. 430(C).
    2. Litao Shen & Tian-Yi Wang & Haoran Zhang, 2024. "Source Inversion Based on Distributed Acoustic Sensing-Type Data," Mathematics, MDPI, vol. 12(12), pages 1-24, June.

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