Observers are well known in the theory of dynamical systems. They are used to estimate the states of a system from some measurements. However, recently observers have also been developed to estimate some unknowns for systems governed by Partial differential equations.
Our aim is to design an observer to solve inverse source problem for a one dimensional wave equation. Firstly, the problem is discretized in both space and time and then an adaptive observer based on partial field measurements (i.e measurements taken form the solution of the wave equation) is applied to estimate both the states and the source. We see the effectiveness of this observer in both noisefree and noisy cases. In each case, numerical simulations are provided to illustrate the effectiveness of this approach. Finally, we compare the performance of the observer approach with Tikhonov regularization approach.
Date of Award  May 25 2013 

Original language  English 

Awarding Institution   Computer, Electrical and Mathematical Science and Engineering


Supervisor  Meriem Laleg (Supervisor) 

 Inverse Problem
 Wave Equation
 Tikhonov Regularization
 Observer