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Composite learning fuzzy synchronization for incommensurate fractional‐order chaotic systems with time‐varying delays
Author(s) -
Zhou Yan,
Liu Heng,
Cao Jinde,
Li Shenggang
Publication year - 2019
Publication title -
international journal of adaptive control and signal processing
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.73
H-Index - 66
eISSN - 1099-1115
pISSN - 0890-6327
DOI - 10.1002/acs.2967
Subject(s) - control theory (sociology) , tracking error , controller (irrigation) , parametric statistics , fuzzy logic , lyapunov stability , synchronization (alternating current) , convergence (economics) , fuzzy control system , chaotic , mathematics , stability (learning theory) , nonlinear system , interval (graph theory) , adaptive control , computer science , control (management) , artificial intelligence , topology (electrical circuits) , statistics , physics , combinatorics , quantum mechanics , machine learning , agronomy , economics , biology , economic growth
Summary This paper presents a composite learning fuzzy control to synchronize two different uncertain incommensurate fractional‐order time‐varying delayed chaotic systems with unknown external disturbances and mismatched parametric uncertainties via the Takagi‐Sugeno fuzzy method. An adaptive controller together with fractional‐order composite learning laws is designed based on both a parallel distributed compensation technology and a fractional Lyapunov criterion. The boundedness of all variables in the closed‐loop system and the Mittag‐Leffler stability of tracking error can be guaranteed. T‐S fuzzy systems are provided to tackle unknown nonlinear functions. The distinctive features of the proposed approach consist in the following: (1) a supervisory control law is designed to compensate the lumped disturbances; (2) both the prediction error and the tracking error are used to estimate the unknown fuzzy system parameters; (3) parameter convergence can be ensured by an interval excitation condition. Finally, the feasibility of the proposed control strategy is demonstrated throughout an illustrative example.