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Pinning synchronization of fractional‐order complex networks with adaptive coupling weights
Author(s) -
Ding Xiaoshuai,
Cao Jinde,
Alsaadi Fuad E.
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.3043
Subject(s) - synchronization (alternating current) , correctness , eigenvalues and eigenvectors , control theory (sociology) , lyapunov function , coupling (piping) , topology (electrical circuits) , mathematics , network topology , complex network , verifiable secret sharing , matrix (chemical analysis) , adaptive control , computer science , control (management) , nonlinear system , algorithm , artificial intelligence , engineering , mechanical engineering , physics , materials science , set (abstract data type) , quantum mechanics , combinatorics , composite material , programming language , operating system
Summary This work studies the issue of synchronization control for a type of fractional‐order complex networks, in which the adaptive coupling matrix is considered under the directed topology structure. A pinning control strategy, with the free selection of pinning nodes, is adopted for the synchronization goal. Then, by absorbing the information of eigenvectors and adaptive laws for the coupling matrix, a new Lyapunov function is constructed, by which, and with the assistance of Gronwall inequality and network features, the sufficient condition for Mittag‐Leffler synchronization of the fractional‐order network is established. Accordingly, an easy verifiable algebraic criterion is further derived by means of some matrix inequalities. Besides, we also discuss the effect of outer coupling strength on the achievement of network synchronization. Finally, a numerical experiment is performed to show the evidence of the correctness and effectiveness of the proposed results.