scholarly journals Adaptive Modified Function Projective Lag Synchronization of Memristor-Based Five-Order Chaotic Circuit Systems

2017 ◽  
Vol 2017 ◽  
pp. 1-8 ◽  
Author(s):  
Qiaoping Li ◽  
Sanyang Liu
Keyword(s):  
Control Method ◽  
Scaling Function ◽  
Control Law ◽  
Chaotic Circuit ◽  
Lmi Approach ◽  
Lag Synchronization ◽  
Bounded Disturbances ◽  
Projective Lag Synchronization ◽  
Adaptive Control Law ◽  
Function Matrix

The modified function projective lag synchronization of the memristor-based five-order chaotic circuit system with unknown bounded disturbances is investigated. Based on the LMI approach and Lyapunov stability theorem, an adaptive control law is established to make the states of two different memristor-based five-order chaotic circuit systems asymptotically synchronized up to a desired scaling function matrix, while the parameter controlling strength update law is designed to estimate the parameters well. Finally, the simulation is put forward to demonstrate the correctness and effectiveness of the proposed methods. The control method involved is simple and practical.

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.

On Complete Control and Synchronization of Zhang Chaotic System with Uncertain Parameters using Adaptive Control Method

2018 ◽  
Vol 7 (1) ◽  
pp. 45-50 ◽  
Author(s):  
Hamed Tirandaz
Keyword(s):  
Adaptive Control ◽  
Chaotic System ◽  
Control Method ◽  
Three Dimensional ◽  
Parameters Estimation ◽  
Control Law ◽  
Complete Control ◽  
Synchronization Problem ◽  
Control And Synchronization ◽  
Adaptive Control Law

Abstract Chaos control and synchronization of chaotic systems is seemingly a challenging problem and has got a lot of attention in recent years due to its numerous applications in science and industry. This paper concentrates on the control and synchronization problem of the three-dimensional (3D) Zhang chaotic system. At first, an adaptive control law and a parameter estimation law are achieved for controlling the behavior of the Zhang chaotic system. Then, non-identical synchronization of Zhang chaotic system is provided with considering the Lü chaotic system as the follower system. The synchronization problem and parameters identification are achieved by introducing an adaptive control law and a parameters estimation law. Stability analysis of the proposed method is proved by the Lyapanov stability theorem. In addition, the convergence of the estimated parameters to their truly unknown values are evaluated. Finally, some numerical simulations are carried out to illustrate and to validate the effectiveness of the suggested method.

Continuous adaptive finite-time modified function projective lag synchronization of uncertain hyperchaotic systems

2016 ◽  
Vol 40 (3) ◽  
pp. 853-860 ◽  
Author(s):  
Xuan-Toa Tran ◽  
Hee-Jun Kang
Keyword(s):  
Finite Time ◽  
Control Method ◽  
Sliding Mode ◽  
External Disturbances ◽  
Lag Synchronization ◽  
Terminal Sliding Mode ◽  
Nonsingular Terminal Sliding Mode ◽  
Projective Lag Synchronization ◽  
Twisting Algorithm ◽  
Hyperchaotic Systems

This paper introduces an adaptive control method for finite-time modified function projective lag synchronization of uncertain hyperchaotic systems. Based upon novel nonsingular terminal sliding mode surfaces and the adaptive super-twisting algorithm, a controller is proposed to provide robustness, high precision and fast and finite-time modified function projective lag synchronization without the knowledge of the upper bound of uncertainties and unknown external disturbances. In addition, chattering is significantly attenuated due to the inherited continuity of the proposed controller. The global stability and finite-time convergence are rigorously proven. Numerical simulation is presented to demonstrate the effectiveness and feasibility of the proposed strategy and to verify the theoretical results.

Projective lag synchronization in drive-response dynamical networks

2014 ◽  
Vol 25 (11) ◽  
pp. 1450068 ◽  
Author(s):  
Ghada Al-Mahbashi ◽  
Mohd Salmi Md Noorani ◽  
Sakhinah Abu Bakar
Keyword(s):  
Chaotic Systems ◽  
Control Method ◽  
Lyapunov Stability Theory ◽  
Scaling Factor ◽  
Lag Synchronization ◽  
Dynamical Networks ◽  
Feedback Control Method ◽  
Projective Lag Synchronization ◽  
Error Dynamics ◽  
The Stability

This paper investigates projective lag synchronization (PLS) behavior between chaotic systems in drive-response dynamical networks (DRDNs) model with nonidentical nodes. A hybrid feedback control method is designed to achieve the PLS with and without mismatched terms. Specially, the coupling matrix in this model is not assumed to be symmetric, diffusive or irreducible. The stability of the error dynamics is proven theoretically using the Lyapunov stability theory. Finally, analytical results show that the states of the dynamical network with non-delayed coupling can be asymptotically synchronized onto a desired scaling factor under the designed controller. Moreover, the numerical simulations results demonstrate the validity of the proposed method.

scholarly journals Adaptive Modified Function Projective Lag Synchronization of Uncertain Hyperchaotic Dynamical Systems with the Same or Different Dimension and Structure

2013 ◽  
Vol 2013 ◽  
pp. 1-15 ◽  
Author(s):  
Xiuli Chai ◽  
Zhihua Gan ◽  
Chunxiao Shi
Keyword(s):  
Dynamical Systems ◽  
Chaotic System ◽  
Control Method ◽  
General Theorem ◽  
Three Dimensional ◽  
Lyapunov Stability Theory ◽  
Hyperchaotic System ◽  
Lag Synchronization ◽  
Projective Lag Synchronization ◽  
Hyperchaotic Systems

Modified function projective lag synchronization (MFPLS) of uncertain hyperchaotic dynamical systems with the same or different dimensions and structures is studied. Based on Lyapunov stability theory, a general theorem for controller designing, parameter update rule designing, and control gain strength adapt law designing is introduced by using adaptive control method. Furthermore, the scheme is applied to four typical examples: MFPLS between two five-dimensional hyperchaotic systems with the same structures, MFPLS between two four-dimensional hyperchaotic systems with different structures, MFPLS between a four-dimensional hyperchaotic system and a three-dimensional chaotic system and MFPLS between a novel three-dimensional chaotic system, and a five-dimensional hyperchaotic system. And the system parameters are all uncertain. Corresponding numerical simulations are performed to verify and illustrate the analytical results.

A general method for projective-lag synchronization of heterogeneous chaotic maps with different dimensions

2021 ◽  
pp. 107754632110264
Author(s):  
Cun-Fang Feng ◽  
Hai-Jun Yang ◽  
Cai Zhou
Keyword(s):  
Discrete Time ◽  
Stability Theory ◽  
Chaotic Systems ◽  
Control Method ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Lag Synchronization ◽  
Different Dimensions ◽  
Projective Lag Synchronization ◽  
General Method

Projective-lag synchronization of complex systems has attracted much attention in the past two decades. However, the majority of previous studies concentrated on continuous-time chaotic systems or discrete-time chaotic systems with the same dimensions. In our present study, a general method for projective-lag synchronization of different discrete-time chaotic systems characterized with different dimensions is first demonstrated. On the basis of stability theory of discrete-time dynamical systems and Lyapunov stability theory, general controllers are designed by using the active control method. The method could achieve projective-lag synchronization in both cases: [Formula: see text] and [Formula: see text]. The effectiveness and feasibility of the proposed method is demonstrated by the projective-lag synchronization between two-dimensional Lorenz discrete-time system and three-dimensional Stefanski map, as well as between the three-dimensional generalized Hénon map and the two-dimensional quadratic map, respectively.

Research of Dynamic Compensation for Hysteresis Nonlinear

2011 ◽  
Vol 128-129 ◽  
pp. 985-989
Author(s):  
Xiang Jiang Wang ◽  
Ji Song Tang
Keyword(s):  
Control Method ◽  
Linear Part ◽  
Control Law ◽  
Hysteresis Model ◽  
Precision Instrument ◽  
Nonlinear Part ◽  
Hysteresis Nonlinearity ◽  
Compensating Operator ◽  
Nonlinear Compensation ◽  
Adaptive Control Law

The hysteresis nonlinearity reduces the accuracy of precision instrument..In order to mitigate the effect of the hysteresis, it is necessary to build hysteresis model and compensate hysteresis nonlinearity.The Krasnosel’skii–Pokrovkii （KP） operator is used to build hysteresis model, which the model is divided into linear part and nonlinear part. The KP compensating operator is proposed to compensate nonlinear part of hysteresis model. The Sliding model adaptive control law for the control method is deduced from the Lyapunov stability theorem. The emulational results confirmed the availability of hysteresis nonlinear compensation control.

LAG SYNCHRONIZATION OF BURSTING NEURON SYSTEMS WITH STOCHASTIC PERTURBATION VIA ADAPTIVE FEEDBACK CONTROL

2014 ◽  
Vol 28 (07) ◽  
pp. 1450022 ◽  
Author(s):  
ZUO-LEI WANG ◽  
XUE-RONG SHI ◽  
YAOLIN JIANG
Keyword(s):  
Feedback Control ◽  
Stochastic Perturbation ◽  
Control Law ◽  
Lag Synchronization ◽  
Theoretical Derivation ◽  
Adaptive Feedback ◽  
Adaptive Feedback Control ◽  
Bursting Neuron ◽  
Control Scheme ◽  
Adaptive Control Law

Lag synchronization of bursting neuron systems is explored when the system is subjected to stochastic perturbation. An adaptive feedback control scheme is presented when the parameters of the neuron systems are unknown. At the same time, an adaptive control law is obtained via theoretical derivation so that two slightly mismatched chaotic systems achieved asymptotically lag synchronization. The effectiveness of the proposed scheme is not only confirmed by theoretical analysis, but also verified by numerical simulations.

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