scholarly journals Adaptive Synchronization between Fractional-Order Chaotic Real and Complex Systems with Unknown Parameters

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Xiaomin Tian
Keyword(s):  
Complex Systems ◽  
Fractional Order ◽  
Lyapunov Stability Theory ◽  
Order Type ◽  
Robust Adaptive Control ◽  
Projective Synchronization ◽  
Adaptive Synchronization ◽  
Distributed Model ◽  
Unknown Parameters ◽  
Constant Matrix

The complex modified projective synchronization (CMPS) between fractional-order chaotic real and complex systems is investigated for the first time. The parameters of both master and slave systems are assumed to be unknown in advance; moreover, the slave system is perturbed by unknown but bounded external disturbances. The master and slave systems that achieved CMPS can be synchronized up to a complex constant matrix. On the basis of frequency distributed model of fractional integrator and Lyapunov stability theory, a robust adaptive control law is designed to realize the CMPS for two different types of fractional-order chaotic systems. Meanwhile, to deal with these unknown parameters, some fractional-order type parametric update laws are provided. An example is given to demonstrate the effectiveness and feasibility of the proposed synchronization scheme.

‎S‎ynchronization ‎of‎ different ‎dimensions‎ ‎fractional-‎order chaotic ‎systems with uncertain‎‎ ‎ parameters ‎and ‎secure ‎communication‎‎‎‎‎

2021 ◽  
Vol 39 (5) ◽  
pp. 57-72
Author(s):  
Vajiheh Vafaei ◽  
Hossein Kheiri ◽  
Aliasghar Jodayree Akbarfam
Keyword(s):  
Fractional Order ◽  
Secure Communication ◽  
Chaotic Systems ◽  
Security Analysis ◽  
High Sensitivity ◽  
Lyapunov Stability Theory ◽  
Projective Synchronization ◽  
Unknown Parameters ◽  
Function Projective Synchronization ◽  
Fractional Order Controller

In ‎this ‎paper, ‎an‎ adaptive ‎modified‎ function projective synchronization (‎AM‎FPS) ‎scheme‎ ‎of ‎different ‎dimensions‎‎ ‎fractional-‎order ‎chaotic systems with ‎fully ‎unknown parameters is ‎presented‎. ‎On the basis of ‎fractional‎ Lyapunov stability ‎theory ‎and adaptive control law‎,‎ a‎ ‎new‎ fractional-order controller ‎and‎ suitable ‎‎‎‎update ‎rules‎ for unknown parameters are ‎designed‎‎ to realize the ‎AMFPS‎ of different ‎fractional-‎order chaotic systems with ‎non-‎identical ‎orders ‎and different dimensions‎‎. ‎‎Theoretical analysis and numerical simulations are given to verify the validity ‎of ‎the proposed ‎method. ‎Additionally, ‎‎‎‎synchronization results ‎are applied to secure communication via ‎‎ ‎modified ‎‎‎‎masking ‎method. Due to the unpredictability of the scale ‎function ‎matrix‎ and ‎using‎ of ‎fractional-‎order ‎systems with different ‎dimensions ‎and ‎u‎nequal‎ ‎orders,‎‎ the proposed scheme has higher ‎security‎‎. The security analysis ‎‎‎demonstrate that the proposed algorithm ‎has ‎a large key space ‎and‎ high sensitivity to encryption keys ‎and it is ‎‎re‎sistance to all kind of ‎‎attacks‎.

Adaptive Control for Fractional-Order Micro-Electro-Mechanical Resonator With Nonsymmetric Dead-Zone Input

2015 ◽  
Vol 10 (6) ◽  
Author(s):  
Xiaomin Tian ◽  
Shumin Fei
Keyword(s):  
Adaptive Control ◽  
Fractional Order ◽  
Dead Zone ◽  
Lyapunov Stability Theory ◽  
Distributed Model ◽  
Mechanical Resonator ◽  
Unknown Parameters ◽  
The Dead ◽  
Resonator System ◽  
The Stability

This paper deals with the adaptive control of fractional-order micro-electro-mechanical resonator system (FOMEMRS) with nonsymmetric dead-zone nonlinear input. The slope parameters of the dead-zone nonlinearity are unmeasured and the parameters of the controlled systems are assumed to be unknown in advance. To deal with these unknown parameters, some fractional versions of parametric update laws are proposed. On the basis of the frequency distributed model of fractional integrator and Lyapunov stability theory, a robust control law is designed to prove the stability of the closed-loop system. The proposed adaptive approach requires only the information of bounds of the dead-zone slopes and treats the time-varying input coefficient as a system uncertainty. Finally, simulation examples are given to verify the robustness and effectiveness of the proposed control scheme.

Adaptive Synchronization of a Stochastic Fractional-Order System

2015 ◽  
Vol 733 ◽  
pp. 939-942
Author(s):  
Xiao Jun Liu
Keyword(s):  
Numerical Simulations ◽  
Fractional Order ◽  
Stochastic System ◽  
Fractional Order System ◽  
Adaptive Synchronization ◽  
Order System ◽  
Unknown Parameters ◽  
Adaptive Laws

In this paper, adaptive synchronization of a stochastic fractional-order system with unknown parameters is studied. Firstly, the stochastic system is reduced into the equivalent deterministic one with Laguerre approximation. Then, the synchronization for the system is realized by designing appropriate controllers and adaptive laws of the unknown parameters. Numerical simulations are carried out to demonstrate the effectiveness of the controllers and laws.

scholarly journals Universal Projective Synchronization of Two Different Hyperchaotic Systems with Unknown Parameters

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Baojie Zhang ◽  
Hongxing Li
Keyword(s):  
Adaptive Control ◽  
Chaotic Systems ◽  
Control Method ◽  
Scaling Function ◽  
Lyapunov Stability Theory ◽  
Projective Synchronization ◽  
Reference Systems ◽  
Unknown Parameters ◽  
Hyperchaotic Systems ◽  
Function Matrix

Universal projective synchronization (UPS) of two chaotic systems is defined. Based on the Lyapunov stability theory, an adaptive control method is derived such that UPS of two different hyperchaotic systems with unknown parameters is realized, which is up to a scaling function matrix and three kinds of reference systems, respectively. Numerical simulations are used to verify the effectiveness of the scheme.

scholarly journals Adaptive Synchronization for Uncertain Delayed Fractional-Order Hopfield Neural Networks via Fractional-Order Sliding Mode Control

2018 ◽  
Vol 2018 ◽  
pp. 1-8 ◽  
Author(s):  
Bo Meng ◽  
Xiaohong Wang
Keyword(s):  
Neural Networks ◽  
Fractional Order ◽  
Sliding Mode ◽  
Small Region ◽  
Hopfield Neural Networks ◽  
Adaptive Synchronization ◽  
Unknown Parameters ◽  
External Disturbances ◽  
Lyapunov Stability Criterion ◽  
Order Extension

Adaptive synchronization for a class of uncertain delayed fractional-order Hopfield neural networks (FOHNNs) with external disturbances is addressed in this paper. For the unknown parameters and external disturbances of the delayed FOHNNs, some adaptive estimations are designed. Firstly, a fractional-order switched sliding surface is proposed for the delayed FOHNNs. Then, according to the fractional-order extension of the Lyapunov stability criterion, a fractional-order sliding mode controller is constructed to guarantee that the synchronization error of the two uncertain delayed FOHNNs converges to an arbitrary small region of the origin. Finally, a numerical example of two-dimensional uncertain delayed FOHNNs is given to verify the effectiveness of the proposed method.

scholarly journals Adaptive Projective Synchronization between Two Different Fractional-Order Chaotic Systems with Fully Unknown Parameters

2012 ◽  
Vol 2012 ◽  
pp. 1-16 ◽  
Author(s):  
Liping Chen ◽  
Shanbi Wei ◽  
Yi Chai ◽  
Ranchao Wu
Keyword(s):  
Fractional Order ◽  
Chaotic Systems ◽  
Projective Synchronization ◽  
Control Law ◽  
Unknown Parameters ◽  
Chen System ◽  
Fractional Order Differential Equations ◽  
Response Systems ◽  
The Stability ◽  
Adaptive Control Law

Projective synchronization between two different fractional-order chaotic systems with fully unknown parameters for drive and response systems is investigated. On the basis of the stability theory of fractional-order differential equations, a suitable and effective adaptive control law and a parameter update rule for unknown parameters are designed, such that projective synchronization between the fractional-order chaotic Chen system and the fractional-order chaotic Lü system with unknown parameters is achieved. Theoretical analysis and numerical simulations are presented to demonstrate the validity and feasibility of the proposed method.

Adaptive Synchronization of Fractional-Order Coupled Neurons Under Electromagnetic Radiation

2020 ◽  
Vol 30 (03) ◽  
pp. 2050044
Author(s):  
Fanqi Meng ◽  
Xiaoqin Zeng ◽  
Zuolei Wang ◽  
Xinjun Wang
Keyword(s):  
Electromagnetic Radiation ◽  
Fractional Order ◽  
Dynamical Behavior ◽  
Lyapunov Stability Theory ◽  
Neuronal Model ◽  
Adaptive Synchronization ◽  
Dynamical Characteristics ◽  
Single Controller ◽  
Improved Model ◽  
Complex Dynamical Behavior

In this paper, we investigate the dynamical characteristics of four-variable fractional-order Hindmarsh–Rose neuronal model under electromagnetic radiation. The numerical results show that the improved model exhibits more complex dynamical behavior with more bifurcation parameters. Meanwhile, based on the fractional-order Lyapunov stability theory, we propose two adaptive control methods with a single controller to realize chaotic synchronization between two coupled neurons. Finally, numerical simulations show the feasibility and effectiveness of the presented method.

ADAPTIVE SYNCHRONIZATION OF A NOVEL HYPERCHAOTIC SYSTEM WITH FULLY UNKNOWN PARAMETERS

2013 ◽  
Vol 27 (32) ◽  
pp. 1350197
Author(s):  
XING-YUAN WANG ◽  
SI-HUI JIANG ◽  
CHAO LUO
Keyword(s):  
Lyapunov Stability ◽  
Lyapunov Stability Theory ◽  
Adaptive Controller ◽  
Chaotic Synchronization ◽  
Adaptive Synchronization ◽  
Hyperchaotic System ◽  
Unknown Parameters ◽  
Chen System ◽  
Synchronization Scheme ◽  
Hyperchaotic Systems

In this paper, a chaotic synchronization scheme is proposed to achieve adaptive synchronization between a novel hyperchaotic system and the hyperchaotic Chen system with fully unknown parameters. Based on the Lyapunov stability theory, an adaptive controller and parameter updating law are presented to synchronize the above two hyperchaotic systems. The corresponding theoretical proof is given and numerical simulations are presented to verify the effectiveness of the proposed scheme.

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