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Szász–Mirakyan ‐based adaptive controller design for chaotic synchronization
Author(s) -
Izadbakhsh Alireza,
Zamani Iman,
Khorashadizadeh Saeed
Publication year - 2020
Publication title -
international journal of robust and nonlinear control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.361
H-Index - 106
eISSN - 1099-1239
pISSN - 1049-8923
DOI - 10.1002/rnc.5380
Subject(s) - control theory (sociology) , operator (biology) , synchronization (alternating current) , controller (irrigation) , bounded function , duffing equation , polynomial , chaotic , computer science , stability (learning theory) , mathematics , topology (electrical circuits) , control (management) , nonlinear system , mathematical analysis , physics , biochemistry , chemistry , repressor , combinatorics , artificial intelligence , quantum mechanics , machine learning , biology , transcription factor , agronomy , gene
Abstract This article presents a robust adaptive controller for chaos synchronization using the Szász–Mirakyan operator as a universal approximator. In accordance with the universal approximation theorem, the Szász–Mirakyan operator, an extended version of the Bernstein polynomial, can approximate uncertainties, including unmodeled dynamics and external disturbances. This fact is completely discussed in this article. It is shown that using the Szász–Mirakyan operator as basis functions and tuning the polynomial coefficients by the adaptive laws calculated in the stability analysis, uniformly ultimately bounded stability can be assured. Performance evaluation has also been carried out to confirm the satisfactory performance of transient response of the controller. Numerical simulations on the Duffing–Holmes oscillator are provided in order to demonstrate the effectiveness of this approach.