Open AccessReduced‐order fractional integral observer for synchronisation and anti‐synchronisation of fractional‐order chaotic systems
Author(s) -
MeléndezVázquez Fidel,
MartínezGuerra Rafael
Publication year - 2018
Publication title -
iet control theory and applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.059
H-Index - 108
eISSN - 1751-8652
pISSN - 1751-8644
DOI - 10.1049/iet-cta.2017.1117
Subject(s) - fractional calculus , observability , control theory (sociology) , observer (physics) , chaotic , mathematics , chaotic systems , extension (predicate logic) , mittag leffler function , algebraic number , computer science , mathematical analysis , control (management) , physics , quantum mechanics , artificial intelligence , programming language
In this study, the problems of synchronisation and anti‐synchronisation are solved for commensurate and incommensurate fractional chaotic systems. A reduced‐order fractional integral observer is proposed for fractional systems satisfying a fractional algebraic observability condition, which is shown to be Mittag–Leffler stable. This observer is used as a slave system, whose states are synchronised with the states of the chaotic system, which acts as a master. The observer uses a reduced set of measurable signals from the master system, solving the anti‐synchronisation problem as a straightforward extension of the synchronisation one. Numerical simulations on the fractional Lorenz and Rössler systems assess the performance of the proposed methodology.