Sliding mode projective synchronization for fractional-order coupled systems based on network without strong connectedness

2021 ◽  
pp. 014233122110009
Author(s):  
Xin Meng ◽  
Baoping Jiang ◽  
Cunchen Gao
Keyword(s):  
Fractional Order ◽  
Sliding Mode ◽  
Coupled Systems ◽  
Projective Synchronization ◽  
Slave System ◽  
Complete Synchronization ◽  
Synchronization Problem ◽  
Strong Connectedness ◽  
Master System ◽  
Error System

This paper considers the Mittag-Leffler projective synchronization problem of fractional-order coupled systems (FOCS) on the complex networks without strong connectedness by fractional sliding mode control (SMC). Combining the hierarchical algorithm with the graph theory, a new SMC strategy is designed to realize the projective synchronization between the master system and the slave system, which covers the globally complete synchronization and the globally anti-synchronization. In addition, some novel criteria are derived to guarantee the Mittag-Leffler stability of the projective synchronization error system. Finally, a numerical example is given to illustrate the validity of the proposed method.

scholarly journals Sliding Mode Control and Modified Generalized Projective Synchronization of a New Fractional-Order Chaotic System

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
Junbiao Guan ◽  
Kaihua Wang
Keyword(s):  
Sliding Mode Control ◽  
Fractional Order ◽  
Chaotic System ◽  
Secure Communication ◽  
Sliding Mode ◽  
Projective Synchronization ◽  
Control Technique ◽  
Order System ◽  
Mode Control ◽  
The Stability

A new fractional-order chaotic system is addressed in this paper. By applying the continuous frequency distribution theory, the indirect Lyapunov stability of this system is investigated based on sliding mode control technique. The adaptive laws are designed to guarantee the stability of the system with the uncertainty and external disturbance. Moreover, the modified generalized projection synchronization (MGPS) of the fractional-order chaotic systems is discussed based on the stability theory of fractional-order system, which may provide potential applications in secure communication. Finally, some numerical simulations are presented to show the effectiveness of the theoretical results.

Synchronization of Liu Chaotic System with Fractional-Order

2013 ◽  
Vol 336-338 ◽  
pp. 467-470
Author(s):  
Su Hai Huang
Keyword(s):  
Fractional Order ◽  
Chaotic System ◽  
Stability Theory ◽  
Unknown Parameter ◽  
Chaos Synchronization ◽  
Sliding Mode ◽  
Projective Synchronization ◽  
Sliding Mode Controller ◽  
Adaptive Sliding Mode ◽  
Adaptive Sliding Mode Controller

This paper deals with chaos synchronization of the Liu chaotic system with fractional-order. Based on the fractional-order stability theory, an adaptive sliding mode controller has been constructed to realize projective synchronization of fractional-order Liu chaotic system with unknown parameter. An illustrative simulation result is given to demonstrate the effectiveness of the proposed sliding mode controller.

scholarly journals Robust Synchronization of Fractional-Order Hyperchaotic Systems Subjected to Input Nonlinearity and Unmatched External Perturbations

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Teh-Lu Liao ◽  
Jun-Juh Yan ◽  
Jen-Fuh Chang
Keyword(s):  
Fractional Order ◽  
Sliding Mode ◽  
Input Nonlinearity ◽  
Synchronization Problem ◽  
Robust Synchronization ◽  
Single Controller ◽  
Unmatched Uncertainties ◽  
The Cost ◽  
Hyperchaotic Systems ◽  
Control Implementation

This paper investigates the robust synchronization problem for a class of fractional-order hyperchaotic systems subjected to unmatched uncertainties and input nonlinearity. Based on the sliding mode control (SMC) technique, this approach only uses a single controller to achieve chaos synchronization, which reduces the cost and complexity for synchronization control implementation. As expected, the error states can be driven to zero or into predictable bounds for matched and unmatched perturbations, respectively, even with input nonlinearity.

scholarly journals Finite-Time Projective Synchronization of Fractional-Order Memristive Neural Networks with Mixed Time-Varying Delays

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-27
Author(s):  
Meng Hui ◽  
Chen Wei ◽  
Jiao Zhang ◽  
Herbert Ho-Ching Iu ◽  
Ni Luo ◽  
...  
Keyword(s):  
Neural Networks ◽  
Lyapunov Function ◽  
Fractional Order ◽  
Finite Time ◽  
Settling Time ◽  
Projective Synchronization ◽  
Time Varying ◽  
Memristive Neural Networks ◽  
Synchronization Problem ◽  
Fractional Differential

This paper is concerned with the finite-time projective synchronization problem of fractional-order memristive neural networks (FMNNs) with mixed time-varying delays. Firstly, under the frame of fractional-order differential inclusion and the set-valued map, several criteria are derived to ensure finite-time projective synchronization of FMNNs. Meanwhile, three properties are established to deal with different forms of the finite-time fractional differential inequation, which greatly extend some results on estimation of settling time of FMNNs. In addition to the traditional Lyapunov function with 1-norm form in Theorem 1, a more general and flexible Lyapunov function based on p-norm is constructed in Theorem 2 to analyze the finite-time projective synchronization problem, and the estimation of settling time has been verified less conservative than previous results. Finally, numerical examples are provided to demonstrate the effectiveness of the derived theoretical results.

scholarly journals Synchronization of Coupled Chaotic Systems with Ring Connection Based on Special Antisymmetric Structure

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Xiangyong Chen ◽  
Jianlong Qiu ◽  
Qiang Song ◽  
Ancai Zhang
Keyword(s):  
Theoretical Analysis ◽  
Chaotic Systems ◽  
Design Method ◽  
Stable System ◽  
Stability Criteria ◽  
Complete Synchronization ◽  
Numerical Examples ◽  
Synchronization Problem ◽  
Direct Design ◽  
Error System

This paper considers the complete synchronization problem for coupled chaotic systems with ring connections. First, we use a direct design method to design a synchronization controller. It transforms the error system into a stable system with special antisymmetric structure. And then, we get some simple stability criteria of achieving the complete synchronization. These criteria are not only easily verified but also improve and generalize previous known results. Finally, numerical examples are provided to demonstrate the effectiveness of the theoretical analysis.

scholarly journals Projective Synchronization of Nonidentical Fractional-Order Memristive Neural Networks

2019 ◽  
Vol 2019 ◽  
pp. 1-11 ◽  
Author(s):  
Chong Chen ◽  
Zhixia Ding
Keyword(s):  
Neural Networks ◽  
Fractional Order ◽  
Sliding Mode ◽  
Direct Method ◽  
Projective Synchronization ◽  
Sliding Mode Controller ◽  
Memristive Neural Networks ◽  
Lyapunov Direct Method ◽  
Sliding Motion ◽  
Fractional Order Integral

This paper investigates projective synchronization of nonidentical fractional-order memristive neural networks (NFMNN) via sliding mode controller. Firstly, based on the sliding mode control theory, a new fractional-order integral sliding mode controller is designed to ensure the occurrence of sliding motion. Furthermore, according to fractional-order differential inequalities and fractional-order Lyapunov direct method, the trajectories of the system converge to the sliding mode surface to carry out sliding mode motion, and some sufficient criteria are obtained to achieve global projective synchronization of NFMNN. In addition, the conclusions extend and improve some previous works on the synchronization of fractional-order memristive neural networks (FMNN). Finally, a simulation example is given to verify the effectiveness and correctness of the obtained results.

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