Synchronization analysis for fractional order memristive Cohen–Grossberg neural networks with state feedback and impulsive control

2018 ◽  
Vol 506 ◽  
pp. 644-660 ◽  
Author(s):  
Lingzhong Zhang ◽  
Yongqing Yang ◽  
Xianyun Xu
Keyword(s):  
Neural Networks ◽  
Fractional Order ◽  
State Feedback ◽  
Impulsive Control

scholarly journals Mittag-Leffler synchronization of delayed fractional-order bidirectional associative memory neural networks with discontinuous activations: state feedback control and impulsive control schemes

2017 ◽  
Vol 473 (2204) ◽  
pp. 20170322 ◽  
Author(s):  
Xiaoshuai Ding ◽  
Jinde Cao ◽  
Xuan Zhao ◽  
Fuad E. Alsaadi
Keyword(s):  
Neural Networks ◽  
Fractional Order ◽  
Associative Memory ◽  
State Feedback ◽  
Impulsive Control ◽  
State Feedback Control ◽  
Bidirectional Associative Memory ◽  
Discontinuous Activations ◽  
The Fixed Point Theorem ◽  
Discontinuous Activation Functions

This paper is concerned with the drive–response synchronization for a class of fractional-order bidirectional associative memory neural networks with time delays, as well as in the presence of discontinuous activation functions. The global existence of solution under the framework of Filippov for such networks is firstly obtained based on the fixed-point theorem for condensing map. Then the state feedback and impulsive controllers are, respectively, designed to ensure the Mittag-Leffler synchronization of these neural networks and two new synchronization criteria are obtained, which are expressed in terms of a fractional comparison principle and Razumikhin techniques. Numerical simulations are presented to validate the proposed methodologies.

scholarly journals Global Mittag–Leffler Stability and Stabilization Analysis of Fractional-Order Quaternion-Valued Memristive Neural Networks

Mathematics ◽  
2020 ◽  
Vol 8 (3) ◽  
pp. 422 ◽  
Author(s):  
Grienggrai Rajchakit ◽  
Pharunyou Chanthorn ◽  
Pramet Kaewmesri ◽  
Ramalingam Sriraman ◽  
Chee Peng Lim
Keyword(s):  
Neural Networks ◽  
Fractional Order ◽  
Differential Inclusions ◽  
State Feedback ◽  
Control Law ◽  
Memristive Neural Networks ◽  
Numerical Examples ◽  
Quaternion Multiplication ◽  
Stabilizing Control ◽  
Stability And Stabilization

This paper studies the global Mittag–Leffler stability and stabilization analysis of fractional-order quaternion-valued memristive neural networks (FOQVMNNs). The state feedback stabilizing control law is designed in order to stabilize the considered problem. Based on the non-commutativity of quaternion multiplication, the original fractional-order quaternion-valued systems is divided into four fractional-order real-valued systems. By using the method of Lyapunov fractional-order derivative, fractional-order differential inclusions, set-valued maps, several global Mittag–Leffler stability and stabilization conditions of considered FOQVMNNs are established. Two numerical examples are provided to illustrate the usefulness of our analytical results.

scholarly journals New Results on Synchronization of Fractional-Order Memristor‐Based Neural Networks via State Feedback Control

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Xiaofan Li ◽  
Yuan Ge ◽  
Hongjian Liu ◽  
Huiyuan Li ◽  
Jian-an Fang
Keyword(s):  
Neural Networks ◽  
Feedback Control ◽  
Fractional Order ◽  
Nonsmooth Analysis ◽  
State Feedback ◽  
Direct Method ◽  
Young Inequality ◽  
State Feedback Control ◽  
Feedback Controllers ◽  
Theoretical Results

This paper addresses the synchronization issue for the drive-response fractional-order memristor‐based neural networks (FOMNNs) via state feedback control. To achieve the synchronization for considered drive-response FOMNNs, two feedback controllers are introduced. Then, by adopting nonsmooth analysis, fractional Lyapunov’s direct method, Young inequality, and fractional-order differential inclusions, several algebraic sufficient criteria are obtained for guaranteeing the synchronization of the drive-response FOMNNs. Lastly, for illustrating the effectiveness of the obtained theoretical results, an example is given.

scholarly journals Global Mittag–Leffler Stabilization of Fractional-Order BAM Neural Networks with Linear State Feedback Controllers

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Hongyun Yan ◽  
Yuanhua Qiao ◽  
Lijuan Duan ◽  
Ling Zhang
Keyword(s):  
Neural Networks ◽  
Lyapunov Function ◽  
Fractional Order ◽  
State Feedback ◽  
Control Strategies ◽  
Sufficient Conditions ◽  
State Feedback Control ◽  
Bam Neural Networks ◽  
Linear State ◽  
The Stability

In this paper, the global Mittag–Leffler stabilization of fractional-order BAM neural networks is investigated. First, a new lemma is proposed by using basic inequality to broaden the selection of Lyapunov function. Second, linear state feedback control strategies are designed to induce the stability of fractional-order BAM neural networks. Third, based on constructed Lyapunov function, generalized Gronwall-like inequality, and control strategies, several sufficient conditions for the global Mittag–Leffler stabilization of fractional-order BAM neural networks are established. Finally, a numerical simulation is given to demonstrate the effectiveness of our theoretical results.

scholarly journals Almost Periodic Synchronization of Fuzzy Cellular Neural Networks with Time–Varying Delays via State–Feedback and Impulsive Control

2019 ◽  
Vol 29 (2) ◽  
pp. 337-349 ◽  
Author(s):  
Yongkun Li ◽  
Huimei Wang ◽  
Xiaofang Meng
Keyword(s):  
Neural Networks ◽  
State Feedback ◽  
Impulsive Control ◽  
Cellular Neural Networks ◽  
Banach Fixed Point Theorem ◽  
Time Varying ◽  
Fuzzy Cellular Neural Networks ◽  
Almost Periodic ◽  
Response Systems ◽  
Linear Differential

Abstract In this paper, we are concerned with drive-response synchronization for a class of fuzzy cellular neural networks with time varying delays. Based on the exponential dichotomy of linear differential equations, the Banach fixed point theorem and the differential inequality technique, we obtain the existence of almost periodic solutions of this class of networks. Then, we design a state feedback and an impulsive controller, and construct a suitable Lyapunov function to study the problem of global exponential almost periodic synchronization for the drive-response systems considered. At the end of the paper, we provide an example to verify the effectiveness of the theoretical results.

scholarly journals Finite-Time Mittag–Leffler Synchronization of Neutral-Type Fractional-Order Neural Networks with Leakage Delay and Time-Varying Delays

Mathematics ◽  
2020 ◽  
Vol 8 (7) ◽  
pp. 1146
Author(s):  
Călin-Adrian Popa ◽  
Eva Kaslik
Keyword(s):  
Neural Networks ◽  
Feedback Control ◽  
Fractional Order ◽  
Finite Time ◽  
State Feedback ◽  
Neutral Type ◽  
Leakage Delay ◽  
State Feedback Control ◽  
Time Varying ◽  
Control Scheme

This paper studies fractional-order neural networks with neutral-type delay, leakage delay, and time-varying delays. A sufficient condition which ensures the finite-time synchronization of these networks based on a state feedback control scheme is deduced using the generalized Gronwall–Bellman inequality. Then, a different state feedback control scheme is employed to realize the finite-time Mittag–Leffler synchronization of these networks by using the fractional-order extension of the Lyapunov direct method for Mittag–Leffler stability. Two numerical examples illustrate the feasibility and the effectiveness of the deduced sufficient criteria.

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