Identification of fractional order systems using modulating functions method

Abstract

Abstract-The modulating functions method has been used for the identification of linear and nonlinear systems. In this paper, we generalize this method to the on-line identification of fractional order systems based on the Riemann-Liouville fractional derivatives. First, a new fractional integration by parts formula involving the fractional derivative of a modulating function is given. Then, we apply this formula to a fractional order system, for which the fractional derivatives of the input and the output can be transferred into the ones of the modulating functions. By choosing a set of modulating functions, a linear system of algebraic equations is obtained. Hence, the unknown parameters of a fractional order system can be estimated by solving a linear system. Using this method, we do not need any initial values which are usually unknown and not equal to zero. Also we do not need to estimate the fractional derivatives of noisy output. Moreover, it is shown that the proposed estimators are robust against high frequency sinusoidal noises and the ones due to a class of stochastic processes. Finally, the efficiency and the stability of the proposed method is confirmed by some numerical simulations.

New Result for the Analysis of Katugampola Fractional-Order Systems—Application to Identification Problems

“…As a conclusion from the two cases (i) and (ii), one has Dealing with the identification task, a very frequent representation used in the literature is given by [22,33]…”

“…Concerning Caputo fractional-order systems, no analogue Barbalat's lemma to the one proved in [21] has been successfully demonstrated in the literature. The closest lemma to the one in [21], ever proved for Caputo fractional-order systems, has been recently developed in [22]. Using another fractional derivative concept, which is the conformable derivative, the authors in [23] proved the existence of an analogue Barbalat's lemma to the one in [21].…”

Using fractional-order differential equations for health monitoring of a system of cooperating robots

“…The method in [5] is motivated similarly but establishes a linear system of equations, yielding a discrete order distribution. A seriesbased approach to identifying governing equation parameters is detailed in [6]. Computational system identification procedures include the iterative optimization approach of [7].…”

Damage Identification for The Tree-like Network through Frequency-domain Modeling

“…Hence, our proposed method is derived from a fractional-order system identification method proposed by Oustaloup (1995). Other fractionalorder system identification methods can be seen in Hartley and Lorenzo (2003), Liu et al (2013), and Zhou et al (2013.…”