Premium
Adaptive synchronization of new fractional‐order chaotic systems with fractional adaption laws based on risk analysis
Author(s) -
Behinfaraz Reza,
Ghaemi Sehraneh,
Khanmohammadi Sohrab
Publication year - 2019
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.5471
Subject(s) - synchronization (alternating current) , control theory (sociology) , mathematics , lyapunov stability , chaotic , stability (learning theory) , fractional calculus , order (exchange) , adaptive control , synchronization of chaos , fractional order system , reliability (semiconductor) , lyapunov function , mathematical optimization , computer science , control (management) , topology (electrical circuits) , nonlinear system , artificial intelligence , power (physics) , physics , finance , combinatorics , machine learning , quantum mechanics , economics
In this paper, a new fractional‐order chaotic system and an adaptive synchronization of fractional‐order chaotic system are proposed. Parameters adaption laws are obtained to design adaptive controllers using Lyapunov stability theory of fractional‐order system. Finally, reliability of designed controllers and risk analysis of adaptive synchronization problem are formulated and, risk of using the proposed controllers in presences of external disturbances are demonstrated. Also, risk of controllers are reduced using an optimizing method. Numerical examples are used to verify the performance of the proposed controllers.