TY - JOUR

T1 - An Adaptive Observer-Based Algorithm for Solving Inverse Source Problem for the Wave Equation

AU - Asiri, Sharefa M.

AU - Zayane, Chadia

AU - Laleg-Kirati, Taous-Meriem

N1 - KAUST Repository Item: Exported on 2020-10-01

PY - 2015/10/19

Y1 - 2015/10/19

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.

UR - http://hdl.handle.net/10754/581311

UR - http://www.hindawi.com/journals/mpe/2015/796539/

UR - http://www.scopus.com/inward/record.url?scp=84946908853&partnerID=8YFLogxK

U2 - 10.1155/2015/796539

DO - 10.1155/2015/796539

M3 - Article

VL - 2015

SP - 1

EP - 8

JO - Mathematical Problems in Engineering

JF - Mathematical Problems in Engineering

SN - 1024-123X

ER -