scholarly journals Sliding Mode Matrix-Projective Synchronization for Fractional-Order Neural Networks

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Jinman He ◽  
Tengfei Lei ◽  
Limin Jiang
Keyword(s):  
Neural Networks ◽  
Fractional Order ◽  
Sliding Mode ◽  
Scaling Factor ◽  
Projective Synchronization ◽  
Constant Matrix ◽  
Numerical Application ◽  
The Matrix ◽  
Response Systems ◽  
Integral Sliding Surface

This work generalizes the projection scaling factor to a general constant matrix and proposes the matrix-projection synchronization (MPS) for fractional-order neural networks (FNNs) based on sliding mode control firstly. This kind of scaling factor is far more complex than the constant scaling factor, and it is highly variable and difficult to predict in the process of realizing the synchronization for the driving and response systems, which can ensure high security and strong confidentiality. Then, the fractional-order integral sliding surface and sliding mode controller for FNNs are designed. Furthermore, the criterion for realizing MPS is proved, and the reachability and stability of the synchronization error system are analyzed, so that the global MPS is realized for FNNs. Finally, a numerical application is given to demonstrate the feasibility of theory analysis. MPS is more general, so it is reduced to antisynchronization, complete synchronization, projective synchronization (PS), and modified PS when selecting different projective matrices. This work will enrich the synchronization theory of FNNs and provide a feasible method to study the MPS of other fractional-order dynamical models.

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.

Mixed H∞ and passive projective synchronization for fractional-order memristor-based neural networks with time delays via adaptive sliding mode control

2017 ◽  
Vol 31 (14) ◽  
pp. 1750160 ◽  
Author(s):  
Shuai Song ◽  
Xiaona Song ◽  
Ines Tejado Balsera
Keyword(s):  
Neural Networks ◽  
Sliding Mode Control ◽  
Fractional Order ◽  
Time Delays ◽  
Closed Loop ◽  
Sliding Mode ◽  
Projective Synchronization ◽  
Adaptive Sliding Mode Control ◽  
Closed Loop System ◽  
Mode Control

This paper investigates the mixed [Formula: see text] and passive projective synchronization problem for fractional-order (FO) memristor-based neural networks with time delays. Our aim is to design a controller such that, though the unavoidable phenomena of time delay and external disturbances is fully considered, the resulting closed-loop system is stable with a mixed [Formula: see text] and passive performance level. By combining sliding mode control and adaptive control methods, a novel adaptive sliding mode control strategy is designed for the synchronization of time-delayed FO dynamic networks. Via the application of FO system stability theory, the projective synchronization conditions are addressed in terms of linear matrix inequalities. Based on the conditions, a desired controller which can guarantee the stability of the closed-loop system and also ensure a mixed [Formula: see text] and passive performance level is designed. Finally, two simulation examples are given to illustrate the effectiveness of the proposed method.

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.

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