# IJPAM: Volume 89, No. 2 (2013)

IDENTIFICATION OF FRACTIONAL-ORDER DYNAMICAL
SYSTEMS BASED ON NONLINEAR FUNCTION
OPTIMIZATION

Ľubomír Dorčák, Emmanuel A. Gonzalez, Ján Terpák,
Institute of Control and Informatization of Production Processes
Faculty BERG, Technical University of Košice, B. Němcovej 3
042 00 Košice, Slovakia
Department of Computer Technology, College of Computer Studies
De La Salle University Manila, 1004 Manila, Philippines
Faculty of Electrical Engineering and Computer Science
Brno University of Technology, Czech Republic
Technical University of Košice, Computing Center, B. Němcovej 3
042 00 Košice, Slovakia

Abstract. In general, real objects are fractional-order systems and also dynamical processes taking place in them are fractional-order processes, although in some types of systems the order is very close to an integer order. So we consider dynamical system whose mathematical description is a differential equation in which the orders of derivatives can be real numbers. With regard to this, in the task of identification, it is necessary to consider also the fractional order of the dynamical system. In this paper we give suitable numerical solutions of differential equations of this type and subsequently an experimental method of identification in the time domain is given. We will concentrate mainly on the identification of parameters, including the orders of derivatives, for a chosen structure of the dynamical model of the system. Under mentioned assumptions, we would obtain a system of nonlinear equations to identify the system. More suitable than to solve the system of nonlinear equations is to formulate the identification task as an optimization problem for nonlinear function minimization. As a criterion we have considered the sum of squares of the vertical deviations of experimental and theoretical data and the sum of squares of the corresponding orthogonal distances. The verification was performed on systems with known parameters and also on a laboratory object.

AMS Subject Classification: 26A33, 37N35

Key Words and Phrases: identification, control, fractional calculus, fractional-order system and model, optimization, orthogonal regression, total least squares method

DOI: 10.12732/ijpam.v89i2.8 How to cite this paper?
Source:
International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2013
Volume: 89
Issue: 2