Open AccessAdaptive fuzzy synchronization for uncertain fractional-order chaotic systems with unknown non-symmetrical control gain
Author(s) -
Heng Liu,
Shenggang Li,
Yuanyuan Sun,
Hongxing Wang
Publication year - 2015
Publication title -
wuli xuebao
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.199
H-Index - 47
ISSN - 1000-3290
DOI - 10.7498/aps.64.070503
Subject(s) - control theory (sociology) , mathematics , controller (irrigation) , lyapunov function , lyapunov stability , synchronization (alternating current) , adaptive control , nonlinear system , diagonal , matrix (chemical analysis) , lyapunov equation , chaotic , computer science , topology (electrical circuits) , control (management) , physics , geometry , materials science , quantum mechanics , artificial intelligence , combinatorics , agronomy , composite material , biology
In this paper the synchronization problem for the uncertain fractional-order chaotic systems with unknown non-symmetrical control gain matrices is investigated by means of adaptive fuzzy control. Fuzzy logic systems are employed to approximate the unknown nonlinear functions. We decompose the control gain matrix into a positive definite matrix, a unity upper triangular matrix, and a diagonal matrix with diagonal entries +1 or -1. The positive matrix is used to construct the Lyapunov function; the diagonal matrix is employed to design the controller. Based on the fractional Lyapunov stability theorem, an adaptive fuzzy controller, which is accompanied by fractional adaptation laws, is established. The proposed methods can guarantee the boundedness of the involved signals as well as the asymptotical convergence of the synchronization errors. It should be pointed out that the methods for using quadratic Lyapunov function in the stability analysis of the fractional-order chaotic systems are developed in this paper. Based on the results of this paper, many control methods which are valid for integer-order nonlinear systems can be extended to control fractional-order nonlinear systems. Finally, the effectiveness of the proposed methods is shown by simulation studies.