An approach to achieve modified projective synchronization between different types of fractional-order chaotic systems with time-varying delays

Behinfaraz, Reza; Badamchizadeh, Mohammad Ali; Ghiasi, Amir

doi:10.1016/j.chaos.2015.07.008

Cited by 28 publications

(11 citation statements)

References 36 publications

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“…In the synchronization of chaotic system, the main aim of control problem is to achieve zero synchronization error between the drive and response systems by adding a suitable control signal to response system. In this case, we can define the basic type of synchronization error as

E false(t false) = X_{r} false(t false) - X_{d} false(t false),

where E ( t ) shows the synchronization errors, X d = [ x d , y d , z d ] is the state of drive system, and X r = [ x r , y r , z r ] is the state of response system …”

Section: Synchronization Methodsmentioning

confidence: 99%

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Adaptive synchronization of new fractional‐order chaotic systems with fractional adaption laws based on risk analysis

Behinfaraz

Ghaemi

Khanmohammadi

2019

Math Methods in App Sciences

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In this paper, a new fractional‐order chaotic system and an adaptive synchronization of fractional‐order chaotic system are proposed. Parameters adaption laws are obtained to design adaptive controllers using Lyapunov stability theory of fractional‐order system. Finally, reliability of designed controllers and risk analysis of adaptive synchronization problem are formulated and, risk of using the proposed controllers in presences of external disturbances are demonstrated. Also, risk of controllers are reduced using an optimizing method. Numerical examples are used to verify the performance of the proposed controllers.

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E false(t false) = X_{r} false(t false) - X_{d} false(t false),

where E ( t ) shows the synchronization errors, X d = [ x d , y d , z d ] is the state of drive system, and X r = [ x r , y r , z r ] is the state of response system …”

Section: Synchronization Methodsmentioning

confidence: 99%

“…is the state of drive system, and X r = [x r , y r , z r ] is the state of response system. 15 Fractional-order system (9) is considered as drive and response systems in synchronization problem. First, we consider the systems without disturbances, then this problem can be formulate as follows.…”

Section: Synchronization Methodsmentioning

confidence: 99%

Adaptive synchronization of new fractional‐order chaotic systems with fractional adaption laws based on risk analysis

Behinfaraz

Ghaemi

Khanmohammadi

2019

Math Methods in App Sciences

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“….5a n 5a, then the autonomous fractionalorder system (8) is commensurate and if jargðspecðAÞÞ j > ap=2, then system (8) is asymptotically stable [29].…”

Section: Casementioning

confidence: 99%

Optimal synchronization of two different in‐commensurate fractional‐order chaotic systems with fractional cost function

Behinfaraz

Badamchizadeh

2016

Complexity

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This article investigates the optimal synchronization of two different fractional-order chaotic systems with two kinds of cost function. We use calculus of variations for minimizing cost function subject to synchronization error dynamics. We introduce optimal control problem to solve fractional Euler-Lagrange equations. Optimal control signal and minimum time of synchronization are obtained by proposed method. Examples show the optimal synchronization of two different systems with two different cost functions. First, we use an ordinary integer cost function then we use a fractional-order cost function and comparing the results. Finally, we suggest a cost function which has the optimal solution of this problem, and we can extend this solution to solve other synchronization problems.

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“…Many studies have employed the active control method for this purpose. For instance, Behinfaraz et al in [8] and Bhalekar in [9] have used active method for modified projective (MP) synchronization of fractional chaotic systems with time-varying delays and synchronizing two incommensurate Lorenz and Liu chaotic systems, respectively. In [10] and [11], the synchronization of chaotic systems based on an observer design has been studied.…”

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confidence: 99%

A novel continuous time-varying sliding mode controller for robustly synchronizing non-identical fractional-order chaotic systems precisely at any arbitrary pre-specified time

Khanzadeh

Pourgholi

2016

Nonlinear Dyn

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In this paper, attempts are made to design a novel time-varying switching surface in sliding mode control which enables us to synchronize two fractional chaotic systems precisely at any arbitrary pre-specified time. For both Caputo (C) and Riemann-Liuville (RL) derivatives, control laws based on Lyapunov stability theorem are derived. The proposed method is completely robust against existence of uncertainties and exogenous disturbances due to eliminating the reaching phase. Since the sign function is replaced by fractional RL integral of the sign function, the chattering is removed. The simulation results in different scenarios are reported to show the effectiveness of the proposed method.

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An approach to achieve modified projective synchronization between different types of fractional-order chaotic systems with time-varying delays

Cited by 28 publications

References 36 publications

Adaptive synchronization of new fractional‐order chaotic systems with fractional adaption laws based on risk analysis

Adaptive synchronization of new fractional‐order chaotic systems with fractional adaption laws based on risk analysis

Optimal synchronization of two different in‐commensurate fractional‐order chaotic systems with fractional cost function

A novel continuous time-varying sliding mode controller for robustly synchronizing non-identical fractional-order chaotic systems precisely at any arbitrary pre-specified time

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