On the control of chaos via fractional delayed feedback method

Sadeghian, Hoda; Salarieh, Hassan; Alasty, Aria; Meghdari, Ali

doi:10.1016/j.camwa.2011.05.002

Cited by 21 publications

(10 citation statements)

References 28 publications

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“…The design approach consists of two main steps similar as in [28]. The first one is to eliminate the nonlinearity in (6) and the second one is to make the system dynamics asymptotically stable.…”

Section: Elaboration Of a General Methods For Controlling Fo Csmentioning

confidence: 99%

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Controlling and Synchronizing of Fractional- Order Chaotic Systems via Simple and Optimal Fractional-Order Feedback Controller

Soukkou¹,

Leulmi²

2016

IJISA

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In this paper, a simp le and optimal fo rm of fractional-order feedback approach assigned for the control and synchronization of a class of fract ional-order chaotic systems is proposed. The proposed control law can be viewed as a distributed network of linear regulators wherein each node is modeled by a PI controller with moderate gains. The mu ltiobject ive genetic algorithm with chaotic mutation, adopted in this work, can be visualized as a combination of structural and parametric genes of a controller o rchestrated in a hierarchical fashion. Then, it is applied to select an optimal knowledge base, which characterizes the developed controller, and satisfies various design specifications. The proposed design and optimizat ion of the developed controller represents a simp le powerful approach to provide a reasonable tradeoff between computational overhead, storage space, numerical accuracy and stability criterion in control and synchronization of a class of fractional-order chaotic systems. Simu lation results show the satisfactory performance of the proposed approach.

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Section: Elaboration Of a General Methods For Controlling Fo Csmentioning

confidence: 99%

“…In [6], the problem of controlling unstable equilibriu m points and periodic orbits is investigated via the fractional feedback of measured states. In [7], the control and synchronization of the fractional-order Lo renz chaotic system have been addressed via the fractional-order derivative approach.…”

Section:   Smentioning

confidence: 99%

Controlling and Synchronizing of Fractional- Order Chaotic Systems via Simple and Optimal Fractional-Order Feedback Controller

Soukkou¹,

Leulmi²

2016

IJISA

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“…It is only until the most recent decades that many researchers have attached widespread attention to research chaos control of fractionalorder system, in particular, fractional-order Lorenz system [1][2][3][4][5][6], fractional-order financial system [7], fractional-order hyperchaotic system [8], fractional-order Rössler system [9,10], fractional-order Lü system [11] with its findings applied to different areas, such as bridge construction, bioengineering, information engineering and so on. Now, the main method of the chaos control in fractional-order system has adaptive feedback control method [12], linear feedback control method [13], P I λ controller [14], delayed feedback control method [15] and so on. At the moment, the discuss of stochastic system also focuses on integer-order system.…”

Section: Introductionmentioning

confidence: 99%

Chaos Control in a Class of Fractional-order Stochastic Lorenz System

Hou

2012

2012 Fifth International Workshop on Chaos-Fractals Theories and Applications

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This paper briefly introduce the chaos control in a class of fractional-order stochastic Lorenz system. The fractional-order Lorenz system with random parameter can be reduced to its equivalent deterministic one according to orthogonal polynomial approximation principle, and researched by linear feedback method. The numerical results show that this method used in a class of fractional-order stochastic Lorenz system is effective and feasible.

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“…Paula and Savi [10] designed an extended time-delayed feedback control approach to suppress the chaos of a nonlinear pendulum. For more detailed literature on this aspect, one can refer [11][12][13][14].…”

Section: Introductionmentioning

confidence: 99%

Suppressing Chaos for a Fractional‐Order Chaotic Chemical Reaction Model via PD^ζ Controller

Wang

2022

Journal of Mathematics

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In this work, based on the earlier publications, we build a new fractional-order chemical reaction model. Computer simulations manifest that the fractional-order chemical reaction model presents chaotic behavior under a certain parameter condition. To eliminate the chaotic dynamical property, a suitable fractional-order PD ζ controller with time delay is designed. Regarding the time delay as a bifurcation parameter, we set up a novel delay-independent stability and bifurcation criterion guaranteeing the stability and the creation of Hopf bifurcation of the controlled fractional-order chemical reaction model. The influence of time delay on the stability and Hopf bifurcation of the controlled fractional-order chemical reaction model is revealed. At last, numerical simulations are performed to sustain the rationality of the designed PD ζ controller. The obtained conclusions of this work are completely novel and have immense application prospects in the chaos control of chemical reaction systems. Furthermore, the research idea can also be utilized to suppress the chaos of a lot of fractional-order chaotic models.

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On the control of chaos via fractional delayed feedback method

Cited by 21 publications

References 28 publications

Controlling and Synchronizing of Fractional- Order Chaotic Systems via Simple and Optimal Fractional-Order Feedback Controller

Controlling and Synchronizing of Fractional- Order Chaotic Systems via Simple and Optimal Fractional-Order Feedback Controller

Chaos Control in a Class of Fractional-order Stochastic Lorenz System

Suppressing Chaos for a Fractional‐Order Chaotic Chemical Reaction Model via PD^ζ Controller

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On the control of chaos via fractional delayed feedback method

Cited by 21 publications

References 28 publications

Controlling and Synchronizing of Fractional- Order Chaotic Systems via Simple and Optimal Fractional-Order Feedback Controller

Controlling and Synchronizing of Fractional- Order Chaotic Systems via Simple and Optimal Fractional-Order Feedback Controller

Chaos Control in a Class of Fractional-order Stochastic Lorenz System

Suppressing Chaos for a Fractional‐Order Chaotic Chemical Reaction Model via PDζ Controller

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Suppressing Chaos for a Fractional‐Order Chaotic Chemical Reaction Model via PD^ζ Controller