TY - JOUR A2 - Kunze, Herb AU - Asiri, Sharefa AU - Zayane-Aissa, Chadia AU - Laleg-Kirati, Taous-Meriem PY - 2015 DA - 2015/10/19 TI - An Adaptive Observer-Based Algorithm for Solving Inverse Source Problem for the Wave Equation SP - 796539 VL - 2015 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. SN - 1024-123X UR - https://doi.org/10.1155/2015/796539 DO - 10.1155/2015/796539 JF - Mathematical Problems in Engineering PB - Hindawi Publishing Corporation KW - ER -