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

Asiri Sharefa; Zayane-Aissa Chadia; Laleg-Kirati Taous-Meriem

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

机译：基于自适应观测器的波动方程反源算法

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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 algorithmis emphasized in noise-free and noisy cases and an insight on the impact ofmeasurements' size and location is provided.

机译：观察者在控制理论中是众所周知的。最初设计用于在给定某些测量值的情况下估计动态系统的隐藏状态，但对于由偏微分方程控制的系统，观察者的范围最近已扩展到某些未知数的估计。在本文中，观察者被用来解决一维波动方程的反源问题。自适应观察器旨在估计完全离散系统的状态和源组件。在无噪声和高噪声的情况下强调了该算法的有效性，并提供了对测量尺寸和位置的影响的见解。

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《Mathematical Problems in Engineering》 |2015年第21期|796539.1-796539.8|共8页
作者
Asiri Sharefa; Zayane-Aissa Chadia; Laleg-Kirati Taous-Meriem;
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King Abdullah Univ Sci & Technol, Comp Elect & Math Sci & Engn, Thuwal 239556900, Saudi Arabia;

King Abdullah Univ Sci & Technol, Comp Elect & Math Sci & Engn, Thuwal 239556900, Saudi Arabia;

King Abdullah Univ Sci & Technol, Comp Elect & Math Sci & Engn, Thuwal 239556900, Saudi Arabia;

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1. An Adaptive Observer-Based Algorithm for Solving Inverse Source Problem for the Wave Equation [J] . SharefaAsiri, ChadiaZayane-Aissa, Taous-MeriemLaleg-Kirati Mathematical Problems in Engineering: Theory, Methods and Applications . 2015,第5期

机译：基于自适应观测器的波动方程反源算法
2. Efficient algorithm for solving inverse source problems of a nonlinear diffusion equation in microwave heating [J] . X.Chen, Y.M.Chen Journal of Computational Physics . 1997,第2期

机译：求解微波加热非线性扩散方程逆源问题的高效算法
3. Direct algorithms for solving some inverse source problems in 2D elliptic equations [J] . Abdelaziz Batoul, El Badia Abdellatif, El Hajj Ahmad Inverse Problems: An International Journal of Inverse Problems, Inverse Methods and Computerised Inversion of Data . 2015,第10期

机译：解决二维椭圆方程中某些逆源问题的直接算法
4. A fast and adaptive algorithm for the inverse medium problem with multiple frequencies and multiple sources for the time-harmonic wave equation [C] . S. Chaillat, G. Biros International Conference on Structural Dynamics . 2011

机译：具有多频率的逆介质问题的快速和自适应算法及其多谐波方程的多源
5. An approximation method for solving nonhomogeneous wave equations and related inverse problems [D] . Macias, Jose M. 1999

机译：一种求解非均匀波动方程和相关逆问题的近似方法
6. Matrix algorithms for solving (in)homogeneous bound state equations [O] . M. Blank, A. Krassnigg -1

机译：求解（内部）齐次约束状态方程的矩阵算法
7. An Adaptive Observer-Based Algorithm for Solving Inverse Source Problem for the Wave Equation [O] . Asiri Sharefa M., Zayane Chadia, Laleg-Kirati Taous-Meriem 2015

机译：基于自适应观测器的波动方程反源算法

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

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