scholarly journals Adaptive controllability of microscopic chaos generated in chemical reactor system using anti-synchronization strategy

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Taqseer Khan ◽  
Harindri Chaudhary
Keyword(s):  
Chaos Control ◽  
Control Method ◽  
Lyapunov Stability Theory ◽  
Chemical Reactor ◽  
Reactor System ◽  
State Variables ◽  
Unknown Parameters ◽  
Control Functions ◽  
Synchronization Scheme ◽  
The Given

<p style='text-indent:20px;'>In this manuscript, we design a methodology to investigate the anti-synchronization scheme in chaotic chemical reactor system using adaptive control method (ACM). Initially, an ACM has been proposed and analysed systematically for controlling the microscopic chaos found in the discussed system which is essentially described by employing Lyapunov stability theory (LST). The required asymptotic stability criterion of the state variables of the discussed system having unknown parameters is derived by designing appropriate control functions and parameter updating laws. In addition, numerical simulation results in MATLAB software are performed to illustrate the effective presentation of the considered strategy. Simulations outcomes correspond that the primal aim of chaos control in the given system have been attained computationally.</p>

scholarly journals Hybrid projective combination–combination synchronization in non-identical hyperchaotic systems using adaptive control

2020 ◽  
Vol 9 (3) ◽  
pp. 597-611
Author(s):  
Ayub Khan ◽  
Harindri Chaudhary
Keyword(s):  
Adaptive Control ◽  
Secure Communication ◽  
Chaos Control ◽  
Control Method ◽  
Lyapunov Stability Theory ◽  
Projective Synchronization ◽  
Unknown Parameters ◽  
Combination Synchronization ◽  
Synchronization Scheme ◽  
Hyperchaotic Systems

Abstract In this paper, we investigate a hybrid projective combination–combination synchronization scheme among four non-identical hyperchaotic systems via adaptive control method. Based on Lyapunov stability theory, the considered approach identifies the unknown parameters and determines the asymptotic stability globally. It is observed that various synchronization techniques, for instance, chaos control problem, combination synchronization, projective synchronization, etc. turn into particular cases of combination–combination synchronization. The proposed scheme is applicable to secure communication and information processing. Finally, numerical simulations are performed to demonstrate the effectivity and correctness of the considered technique by using MATLAB.

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.

Difference Synchronization of Identical and Nonidentical Chaotic and Hyperchaotic Systems of Different Orders Using Active Backstepping Design

2018 ◽  
Vol 13 (5) ◽  
Author(s):  
Eric Donald Dongmo ◽  
Kayode Stephen Ojo ◽  
Paul Woafo ◽  
Abdulahi Ndzi Njah
Keyword(s):  
Chaotic System ◽  
Initial Conditions ◽  
Lyapunov Stability Theory ◽  
The State ◽  
State Variables ◽  
State Variable ◽  
New Type ◽  
The Difference ◽  
Synchronization Scheme ◽  
Hyperchaotic Systems

This paper introduces a new type of synchronization scheme, referred to as difference synchronization scheme, wherein the difference between the state variables of two master [slave] systems synchronizes with the state variable of a single slave [master] system. Using the Lyapunov stability theory and the active backstepping technique, controllers are derived to achieve the difference synchronization of three identical hyperchaotic Liu systems evolving from different initial conditions, as well as the difference synchronization of three nonidentical systems of different orders, comprising the 3D Lorenz chaotic system, 3D Chen chaotic system, and the 4D hyperchaotic Liu system. Numerical simulations are presented to demonstrate the validity and feasibility of the theoretical analysis. The development of difference synchronization scheme has increases the number of existing chaos synchronization scheme.

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.

PROJECTIVE SYNCHRONIZATION OF DIFFERENT CHAOTIC SYSTEMS WITH NONLINEARITY INPUTS

2012 ◽  
Vol 26 (11) ◽  
pp. 1250059 ◽  
Author(s):  
YUJUN NIU ◽  
XINGYUAN WANG
Keyword(s):  
Chaotic Systems ◽  
Control Method ◽  
Sliding Mode ◽  
External Noise ◽  
Projective Synchronization ◽  
Adaptive Technique ◽  
Noise Disturbances ◽  
Different Chaotic Systems ◽  
Synchronization Scheme ◽  
The Given

In this paper, projective synchronization of different chaotic systems is studied, in the presence of uncertainties of system parameter variation, external noise disturbance and nonlinearity inputs. Using adaptive technique, sliding mode control method and pole assignment technique, an adaptive projective synchronization scheme is proposed to ensure the drive system and the response system with nonlinearity inputs can be rapidly synchronized up to the given scaling factor, without requiring the bounds of the system uncertainties and external noise disturbances be known in advance. The results of numerical simulation further verify the effectiveness and feasibility of the proposed scheme.

scholarly journals Compound Synchronization of Four Chaotic Complex Systems

2015 ◽  
Vol 2015 ◽  
pp. 1-11 ◽  
Author(s):  
Junwei Sun ◽  
Yi Shen ◽  
Guangzhao Cui
Keyword(s):  
Complex System ◽  
Complex Systems ◽  
Complex Space ◽  
Control Method ◽  
Lyapunov Stability Theory ◽  
Control Scheme ◽  
Compound Synchronization ◽  
Chaotic Complex System ◽  
Synchronization Scheme ◽  
Novel Design

The chaotic complex system is designed from the start of the chaotic real system. Dynamical properties of a chaotic complex system in complex space are investigated. In this paper, a compound synchronization scheme is achieved for four chaotic complex systems. According to Lyapunov stability theory and the adaptive control method, four chaotic complex systems are considered and the corresponding controllers are designed to realize the compound synchronization scheme. Four novel design chaotic complex systems are given as an example to verify the validity and feasibility of the proposed control scheme.

Anti-Control of Chaos of Linear Continuous-Time Systems with Unknown Parameters Using Adaptive Control

2011 ◽  
Vol 403-408 ◽  
pp. 4806-4813
Author(s):  
Farzaneh Akhgari ◽  
Zahra Rahmani ◽  
Behrooz Rezaie
Keyword(s):  
Linear System ◽  
Control Method ◽  
Reference Model ◽  
Lyapunov Stability Theory ◽  
Model Matching ◽  
Control Of Chaos ◽  
Unknown Parameters ◽  
Feedback Control Method ◽  
The Stability ◽  
Controllable Systems

In this paper, a feedback control method is proposed for the anti-control of chaos of linear controllable systems based on model-matching. First, it is considered that the linear system is completely known and an anti-control method is designed. Then, the parameters of the linear controllable system in companion form are assumed to be unknown. The chaotification is achieved choosing an appropriate control law and a parametric updating law based on Lyapunov stability theory, which provides the stability of the resulting adaptive system and the convergence of the tracking errors to zero. The proposed method is applied to anti-control of chaos of a linear system, while the Rössler chaotic system is the reference model. The numerical simulation results show the effectiveness of the proposed method.

scholarly journals Parameter Identification and The Multi-Switching Sliding Mode Combination Synchronization of Fractional Order Non-Identical Chaotic System Under Stochastic Disturbances

2021 ◽  
Author(s):  
Weiqiu Pan ◽  
Tianzeng Li ◽  
Yu Wang
Keyword(s):  
Fractional Order ◽  
Sliding Mode ◽  
Lyapunov Stability Theory ◽  
Control Technique ◽  
State Variables ◽  
Stochastic Disturbances ◽  
Unknown Parameters ◽  
Combination Synchronization ◽  
Special Cases ◽  
Drive Systems

Abstract This paper deals with the issue of the multi-switching sliding mode combination synchronization (MSSMCS) of fractional order (FO) chaotic systems with different structures and unknown parameters under double stochastic disturbances (SD) utilizing the multi-switching synchronization method. The stochastic disturbances are considered as nonlinear uncertainties and external disturbances. Our theoretical part is divided into two cases, namely, the dimension of the drive-response system are different (or same). Firstly, a FO sliding surface was established in term of fractional calculus. Secondly, depended on the FO Lyapunov stability theory, the adaptive control technology and sliding mode control technique, the multi-switching adaptive controllers (MSAC) and some suitable multi-switching adaptive updating laws (MSAUL) are designed, so that the state variables of the drive systems are synchronized with the different state variables of the response systems. Simultaneously, the unknown parameters are assessed and the upper bound of stochastic disturbances are examined. Selecting the suitable scale matrices, the multi-switching projection synchronization, multi-switching complete synchronization, and multi-switching anti-synchronization will become special cases of MSSMCS. Finally, examples are displayed to certify the usefulness and validity of the demonstrated scheme via MATLAB.

scholarly journals Exponential Synchronization of Two Nonlinearly Coupled Complex Networks with Time-Varying Delayed Dynamical Nodes

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Wei Shao
Keyword(s):  
Complex Networks ◽  
Chaotic Systems ◽  
Control Method ◽  
Lyapunov Stability Theory ◽  
Exponential Synchronization ◽  
Time Varying ◽  
Time Varying Delay ◽  
Coupled Networks ◽  
Synchronization Scheme ◽  
Varying Delay

This paper investigates the exponential synchronization between two nonlinearly coupled complex networks with time-varying delay dynamical nodes. Based on the Lyapunov stability theory, some criteria for the exponential synchronization are derived with adaptive control method. Moreover, the presented results here can also be applied to complex dynamical networks with single time delay case. Finally, numerical analysis and simulations for two nonlinearly coupled networks which are composed of the time-delayed Lorenz chaotic systems are given to demonstrate the effectiveness and feasibility of the proposed complex network synchronization scheme.

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