Identification of fractional-order dynamical systems based on nonlinear function optimization

• Main Authors: Dorćak, Luboḿir, Gonzalez, Emmanuel A., Terṕak, J́an, Valsa, Juraj, Pivka, Ladislav
• Format: text
• Published: Animo Repository 2013
• Subjects: Fractional calculus; Least squares; Nonlinear functional analysis; Time-domain analysis; Electric controllers; Electrical and Electronics
• Online Access: https://animorepository.dlsu.edu.ph/faculty_research/3006
• Institution: De La Salle University

In general, real objects are fractional-order systems and also dy- namical 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 con- sider dynamical system whose mathematical description is a differential equa- tion 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 assump- tions, 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 mini- mization. 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.