Finite-time Synchronization of a Class of Coupled Memristor-based Recurrent Neural Networks: Static State Control and Dy
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ISSN:1598-6446 eISSN:2005-4092 http://www.springer.com/12555
Finite-time Synchronization of a Class of Coupled Memristor-based Recurrent Neural Networks: Static State Control and Dynamic Control Approach Chao Yang, Yicheng Liu*, Fangmin Li, and Yangfan Li Abstract: This paper investigates the problem of the finite-time synchronization of a class of coupled memristorbased recurrent neural networks (MRNNs) with time delays. Based on the drive-response concept and differential inclusions theory, several sufficient assumptions are given to ensure the finite-time synchronization of MRNNs. In order to realize the finite-time synchronization between the drive system and the response system, we design three classes of novel control rules such as static state controller, static output controller, dynamic state controller. Using the theory of differential inclusion, a generalized finite-time convergence theorem and Lyapunov method, the conditions herein are easy to be verified. Moreover, the upper bounds of the settling time of synchronization are estimated and the designed dynamic state controllers have good anti-interference capacity. Finally, two numerical examples are presented to illustrate the effectiveness and the validity of theoretical results. Keywords: Differential inclusion, finite-time synchronization, memristor, nonlinear coupling, recurrent neural networks.
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INTRODUCTION
The term memristor theory was first investigated by Chua in 1971 [1]. Kennedy in [2] revealed that one circuit element of memristor was a new nonlinear electric circuit element which could reveal the relationship between magnetic flux and electric charge. Then in 2008, HewlettPackard Laboratories and Mathur prototyped the memristor as the fourth circuit element [3, 4]. Nowdays, memristive neural networks (MNNs) have great potential in new generation of brain-like neural computers [5–11]. Different from traditional neural network, a memristor connect two neurons in the MNNs, which would significantly improve the adhibition of neural networks for information processing and associative memory. For example, when the voltage is turned off, the memristor can remember the most recent value until the voltage is turned on next time. Up to now, synchronization and control of MNNs have attracted more and more attention because of the wellknown physical properties of memristor [12–16]. Synchronization, can help to understand an unknown dynamic neuron system from one or more well-know dynamic neuron. In the control field of artifical neural neuron system,
synchronization of MNNs has a great feature to control the trajectories of the error states converge to zero. In addition, many works need to be improved by neural networks through communication or interaction with another one. Then in real experiments, neural networks with coupling have played an important role due to their broad range of experiments and the coupled neuron system could be effectively applied to storage technologies based on synchronization [17–22]. Since Pecora and Carroll in [23]
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