Identification of systems of arbitrary real order: A new method based on systems of fractional order differential equations and orthogonal distance fitting

Tomas Skovranek*, Vladimir Despotovic

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

1 Citation (Scopus)

Abstract

A new method for identification of systems of arbitrary real order based on numerical solution of systems of nonlinear fractional order differential equations (FODEs) and orthogonal dis-tance fitting is presented. The main idea is to fit experimental or measured data using a solution of a system of fractional differential equations. The parameters of these equations, including the orders of derivatives, are subject to optimization process, where the criterion of optimization is the minimal sum of orthogonal distances of the data points from the fitting line. Once the minimal sum is found, the identified parameters are considered as optimal. The so called orthogonal distance fitting, known also under the names of total least squares or orthogonal regression is naturally used in the fitting criterion, since it is the most suitable tool for fitting lines and surfaces in multidimensional space. The examples illustrating the methods are presented in 2-dimensional and 3-dimensional problems.

Original languageEnglish
Title of host publicationProceedings of the ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference 2009, DETC2009
Pages1063-1068
Number of pages6
EditionPART B
DOIs
Publication statusPublished - 2010
Externally publishedYes
Event2009 ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, DETC2009 - San Diego, CA, United States
Duration: 30 Aug 20092 Sep 2009

Publication series

NameProceedings of the ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference 2009, DETC2009
NumberPART B
Volume4

Conference

Conference2009 ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, DETC2009
Country/TerritoryUnited States
CitySan Diego, CA
Period30/08/092/09/09

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