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

Sharefa M. Asiri; Chadia Zayane; Taous-Meriem Laleg-Kirati

doi:10.1155/2015/796539

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

Sharefa M. Asiri, Chadia Zayane, Taous-Meriem Laleg-Kirati

Research output: Contribution to journal › Article › peer-review

7 Scopus citations

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.

Original language	English (US)
Pages (from-to)	1-8
Number of pages	8
Journal	Mathematical Problems in Engineering
Volume	2015
DOIs	https://doi.org/10.1155/2015/796539
State	Published - Oct 19 2015

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title = "An Adaptive Observer-Based Algorithm for Solving Inverse Source Problem for the Wave Equation",

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{\textquoteright} size and location is provided.",

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PY - 2015/10/19

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N2 - 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.

AB - 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.

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JO - Mathematical Problems in Engineering

JF - Mathematical Problems in Engineering

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

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