Synchronization of circular restricted three body problem with lorenz hyper chaotic system using a robust adaptive sliding mode controller

Khan, Ayub; Shahzad, Mohammad

doi:10.1002/cplx.21459

Cited by 69 publications

(55 citation statements)

References 34 publications

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“…In this section, we synchronize the identical and non-identical pairs of Φ 6 -VDPO and DO using RASMC technique that has a very quick response in stabilizing the synchronization of chaotic systems [32][33][34][35][36]. Below we describe the technique in details.…”

Section: Synchronization Using Rasmcmentioning

confidence: 99%

Improved Time Response of Stabilization in Synchronization of Chaotic Oscillators Using Mathematica

Shahzad

Ahmad

Saaban

et al. 2016

Systems

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Abstract:Chaotic dynamics are an interesting topic in nonlinear science that has been intensively studied during the last three decades due to its wide availability. Motivated by much researches on synchronization, the authors of this study have improved the time response of stabilization when parametrically excited Φ 6 -Van der Pol Oscillator (VDPO) and Φ 6 -Duffing Oscillator (DO) are synchronized identically as well as non-identically (with each other) using the Linear Active Control (LAC) technique using Mathematica. Furthermore, the authors have synchronized the same pairs of the oscillators using a more robust synchronization with faster time response of stability called Robust Adaptive Sliding Mode Control (RASMC). A comparative study has been done between the previous results of Njah's work and our results based on Mathematica via LAC. The time response of stabilization of synchronization using RASMC has been discussed.

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Section: Synchronization Using Rasmcmentioning

confidence: 99%

Improved Time Response of Stabilization in Synchronization of Chaotic Oscillators Using Mathematica

Shahzad

Ahmad

Saaban

et al. 2016

Systems

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“…The prominent characteristic of a chaotic system is its extreme sensitivity to initial conditions and the system's parameters. Over the past decades, chaos control has been widely investigated and many researches have been studied in this field [1][2][3][4][5][6][7][8][9][10][11][12][13][14]. In [1], a linear feedback control method is proposed for controlling uncertain L€ u system.…”

Section: Introductionmentioning

confidence: 99%

“…In [9], a linear active control technique is developed for the global chaos synchronization problem of two identical chaotic systems and two nonidentical chaotic systems. However, these methods [1][2][3][4][5][6][7][8][9] can not deal with the effects caused by input dead-zone nonlinearity and timedelays. In practice, the problem of input dead-zone nonlinearity and time-delays is often encountered in various engineering systems, and the existence of input dead-zone nonlinearity and time-delays frequently becomes a source of instability and poor performance.…”

Section: Introductionmentioning

confidence: 99%

“…In practice, the problem of input dead-zone nonlinearity and time-delays is often encountered in various engineering systems, and the existence of input dead-zone nonlinearity and time-delays frequently becomes a source of instability and poor performance. Hence, chaos control with input dead-zone nonlinearity and time-delays is more important than that of without input dead-zone nonlinearity and time-delays [1][2][3][4][5][6][7][8][9].…”

Section: Introductionmentioning

confidence: 99%

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Chaos control of uncertain time‐delay chaotic systems with input dead‐zone nonlinearity

Pai

2014

Complexity

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This article presents an adaptive sliding mode control (SMC) scheme for the stabilization problem of uncertain time-delay chaotic systems with input dead-zone nonlinearity. The algorithm is based on SMC, adaptive control, and linear matrix inequality technique. Using Lyapunov stability theorem, the proposed control scheme guarantees the stability of overall closed-loop uncertain time-delay chaotic system with input dead-zone nonlinearity. It is shown that the state trajectories converge to zero asymptotically in the presence of input dead-zone nonlinearity, time-delays, nonlinear real-valued functions, parameter uncertainties, and external disturbances simultaneously. The selection of sliding surface and the design of control law are two important issues, which have been addressed. Moreover, the knowledge of upper bound of uncertainties is not required. The reaching phase and chattering phenomenon are eliminated. Simulation results demonstrate the effectiveness and robustness of the proposed scheme.

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“…As a result, a variety of control methods and techniques have been developed to study the chaos synchronization. These include the adaptive control strategy [9], projective synchronization [10], sliding mode control [11], nonlinear control techniques [12], and active control method [13], which are well-known synchronization control techniques among others. Among these techniques, the active control (AC) and adaptive synchronization control (ASC) strategies have attracted a great interest in the literature concerned because of their easy implementation to practical systems [14][15][16][17][18][19][20][21][22].…”

Section: Introductionmentioning

confidence: 99%

Controller Parameter Optimization for the Robust Synchronization of Chaotic Systems with Known and Unknown Parameters

Ahmad

Saaban

Ibrahim

2017

J. Uncertain. Anal. Appl.

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In this paper, a synchronization problem of a three-dimensional (3-D) Coullete chaotic system using the active-and adaptive-based synchronization control techniques is addressed. Based on the Routh-Hurwitz criterion and using the active control algorithm, a single control function is considered and a computational study is performed to identify the correct balance between the converging rates of the synchronization error signals to the origin and magnitude of the linear controlling parameters (LCPs) for the globally exponential synchronization (GES) between two identical 3-D Coullete chaotic systems. In order to achieve the complete synchronization (CS) objective with unknown model uncertainties, external disturbances, and unknown time-varying parameters, a novel nonlinear adaptive synchronous controller is proposed and suitable adaptive laws of time-varying parameters are designed that accomplish the asymptotic synchronization between two identical uncertain 3-D Coullete chaotic systems. The two synchronizing controlling approaches are applied to investigate the CS phenomenon, and the results are compared. Open research problems are also discussed. All simulations results are carried out to validate the effectiveness of the proposed synchronization control approaches by using Mathematica 10.0.

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Synchronization of circular restricted three body problem with lorenz hyper chaotic system using a robust adaptive sliding mode controller

Cited by 69 publications

References 34 publications

Improved Time Response of Stabilization in Synchronization of Chaotic Oscillators Using Mathematica

Improved Time Response of Stabilization in Synchronization of Chaotic Oscillators Using Mathematica

Chaos control of uncertain time‐delay chaotic systems with input dead‐zone nonlinearity

Controller Parameter Optimization for the Robust Synchronization of Chaotic Systems with Known and Unknown Parameters

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