Implementation of smooth interpolation for optimization
(2015)Department of Automatic Control
 Abstract
 Models of physical systems are often expressed as a system of mathematical expressions derived from first principles. However some of the relationships present in a model are more conveniently expressed as a table, i.e. for certain values of independent variables the values of dependent variables are known. This imposes a limitation on the optimization software to be used, since optimization software is often dependent on all relationships being expressed as mathematical functions. Many useful optimization methods also require that the functions be twice continuously differentiable.
In this thesis software for interpolating table data relationships between two variables as a twice continuously differentiable mathematical function has... (More)  Models of physical systems are often expressed as a system of mathematical expressions derived from first principles. However some of the relationships present in a model are more conveniently expressed as a table, i.e. for certain values of independent variables the values of dependent variables are known. This imposes a limitation on the optimization software to be used, since optimization software is often dependent on all relationships being expressed as mathematical functions. Many useful optimization methods also require that the functions be twice continuously differentiable.
In this thesis software for interpolating table data relationships between two variables as a twice continuously differentiable mathematical function has been developed. This software has also been prototypically made callable from the automatic differentiation tool CasADi. CasADi is used in the optimization tool chain in JModelica.org, an open source platform for optimization and simulation. By implementing support for table based relations a larger range of problems may be solved using CasADi.
The software developed for interpolating tables uses cubic bsplines and de Boor evaluation. Using it one may evaluate the interpolant and its derivatives up to the third order. The resultant function is demonstrated to be twice continuously differentiable and to interpolate the value within machine epsilon range of the correct one at the data points, provided the table data points are equidistantly distributed. The oscillations that occur when interpolating nonequidistant table data points are also examined. (Less)
Please use this url to cite or link to this publication:
http://lup.lub.lu.se/studentpapers/record/8349327
 author
 Larsson, Joakim
 supervisor

 Toivo Henningsson
 Fredrik Magnusson ^{LU}
 Pontus Giselsson ^{LU}
 organization
 year
 2015
 type
 H3  Professional qualifications (4 Years  )
 subject
 other publication id
 ISRN LUTFD2/TFRT59964SE
 language
 English
 id
 8349327
 date added to LUP
 20151218 13:17:48
 date last changed
 20151218 13:17:48
@misc{8349327, abstract = {Models of physical systems are often expressed as a system of mathematical expressions derived from first principles. However some of the relationships present in a model are more conveniently expressed as a table, i.e. for certain values of independent variables the values of dependent variables are known. This imposes a limitation on the optimization software to be used, since optimization software is often dependent on all relationships being expressed as mathematical functions. Many useful optimization methods also require that the functions be twice continuously differentiable. In this thesis software for interpolating table data relationships between two variables as a twice continuously differentiable mathematical function has been developed. This software has also been prototypically made callable from the automatic differentiation tool CasADi. CasADi is used in the optimization tool chain in JModelica.org, an open source platform for optimization and simulation. By implementing support for table based relations a larger range of problems may be solved using CasADi. The software developed for interpolating tables uses cubic bsplines and de Boor evaluation. Using it one may evaluate the interpolant and its derivatives up to the third order. The resultant function is demonstrated to be twice continuously differentiable and to interpolate the value within machine epsilon range of the correct one at the data points, provided the table data points are equidistantly distributed. The oscillations that occur when interpolating nonequidistant table data points are also examined.}, author = {Larsson, Joakim}, language = {eng}, note = {Student Paper}, title = {Implementation of smooth interpolation for optimization}, year = {2015}, }