Abstract
This paper is committed to studying adaptive control design of Mittag-Leffler stabilization and synchronization for delayed fractional-order bidirectional associative memory (BAM) neural networks. Considering better dynamic property and steady state performance of the system, we adopt adaptive control approaches to stabilize and synchronize two types of delayed fractional-order BAM neural network. It is a remarkable fact, based on adaptive control scheme, the method of auxiliary functions, Mittag-Leffler stabilization and synchronization theories with respect to fractional-order systems, the adaptive controllers are very well designed in a controlled system and two coupled systems, separately. Two examples are performed to illustrate the advantage of the presented theoretic analysis and results.
Highlights
The rapid development of fractional calculus has shown that it is an attractive hot research topic, and fractional calculus has been used successfully in different scientific and technological fields [1, 2]
Our main contributions of the paper are summed up into two points: (1) It is the first time that adaptive control design is applied to delayed fractional-order bidirectional associative memory (BAM) neural networks
We focus on the following delayed fractional-order BAM neural networks of the form m m
Summary
The rapid development of fractional calculus has shown that it is an attractive hot research topic, and fractional calculus has been used successfully in different scientific and technological fields [1, 2]. In fractional-order systems, some attractive results regarding stabilization and synchronization phenomena have been introduced [17, 18] From another point of view, talking about fractional-order systems, we know that MittagLeffler function is one of the important functions, and related properties of Mittag-Leffler are often studied [19]. We try to use adaptive control as a kind of better control scheme to explore Mittag-Leffler stabilization and synchronization on two types of delayed fractional-order BAM neural network. Our main contributions of the paper are summed up into two points: (1) It is the first time that adaptive control design is applied to delayed fractional-order BAM neural networks. (2) Several Mittag-Leffler stabilization and synchronization criteria are first put forward in two types of delayed fractional-order BAM neural network on the basis of adaptive control scheme. The exponential function can be replaced by Mittag-Leffler function in fractional-order systems, which is a generally used function that can be widely applied to different types of factional-order system
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