Solving Inverse IVPs and BVPs

real-time solution of inverse problems for embedded systems

Supplemental Material to the Paper:

"An Algebraic Framework for the Real-Time Solution of Inverse Problems on Embedded Systems"

by: Matthew Harker, Christoph Gugg, Paul O'Leary and Gerhard Rath

March 2014

These scripts require our Discrete Orthogonal Polynomial Toolbox:

http://www.mathworks.com/matlabcentra /fileexchange/41250

and the function to convert figures to eps:

http://www.mathworks.com/matlabcentral/fileexchange/42388

This paper presents a new approach to solving inverse IVPs and BVPs. The solution is optimized for applications where the inverse problem must be solved repeatedly with every new sensor measurement. The new method reduces the run-time solution of the inverse problem to a single matrix multiplication. The paper derives all the necessary theory for the new solution method. The MATLAB files presented here implement the numerical testing of the method with specific examples. Additionally, the paper presents a laboratory verification by applying the method to the reconstruction of a deformation curve from inclinometer measurements. The automatic generation of code for the
implementation on an embedded system is demonstrated.

A preprint of the paper can be found at <www.arxiv.org>