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State estimation for nonlinear conformable fractional‐order systems: A healthy operating case and a faulty operating case
Author(s) -
Jmal Assaad,
Elloumi Mourad,
Naifar Omar,
Ben Makhlouf Abdellatif,
Hammami Mohamed Ali
Publication year - 2020
Publication title -
asian journal of control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.769
H-Index - 53
eISSN - 1934-6093
pISSN - 1561-8625
DOI - 10.1002/asjc.2122
Subject(s) - conformable matrix , fractional calculus , nonlinear system , generalization , convergence (economics) , state (computer science) , order (exchange) , derivative (finance) , stability (learning theory) , lemma (botany) , integer (computer science) , mathematics , computer science , mathematical optimization , control theory (sociology) , algorithm , mathematical analysis , artificial intelligence , ecology , physics , poaceae , control (management) , finance , quantum mechanics , machine learning , financial economics , economics , biology , programming language , economic growth
The issue of estimating states for classical integer‐order nonlinear systems has been widely addressed in the literature. Yet, generalization of existing results to the fractional‐order framework represents a fertile area of research. Note that, recently, a new and advantageous type of fractional derivative, the conformable derivative, was defined. So far, the general query of designing observers for conformable fractional‐order systems has not been investigated. In addition, it has been proved in the literature that some important tools for stability analysis of fractional‐order systems are valid using the conformable derivative concept, but invalid using other fractional derivative concepts. Motivated by the cited facts, this paper presents a first‐state estimation scheme for fractional‐order systems under the conformable derivative concept. A healthy operating case and a faulty operating case are treated. In this paper, a version of Barbalat's lemma, which is invalid using the well‐known Caputo derivative, is exploited to prove the convergence of the estimation errors. In order to validate the theoretical results, a numerical example is studied in the simulation section.