Stabilizing periodic orbits of fractional order chaotic systems via linear feedback theory

Rahimi, Maryam; Salarieh, Hassan; Alasty, Aria

doi:10.1016/j.apm.2011.07.019

Cited by 9 publications

(4 citation statements)

References 21 publications

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“…By setting α = 0.98, θ 1 = −1, θ 2 = 1, θ 3 = 0.15, ω = 1 and θ 4 = 0.3, the fractional-order Duffing equation shows chaotic behavior. Moreover, existence of an unstable periodic orbit in the fractional-order Duffing system with these parameter values is proven in the literature [15]. Adding the external disturbance d(t) and control input u(t) to the system dynamics gives:…”

Section: A Fractional-order Duffing Systemmentioning

confidence: 93%

“…Moreover, it is demonstrated that UPO can be found in these systems as integer order ones. Some control techniques have been applied for stabilizing the UPO of fractional-order chaotic systems such as linear feedback control [15], delayed feedback method [16], predictionbased feedback control [17], fuzzy prediction-based feedback control [18], State feedback with fractional P I λ D µ control [19], [20], and impulsive control [21]. These algorithms Bahram Yaghooti is with the Department of Electrical and Systems Engineering, Washington University in St. Louis, St. Louis, MO, USA 63130.…”

Section: Introductionmentioning

confidence: 99%

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Stabilizing Unstable Periodic Orbit of Unknown Fractional-Order Systems via Adaptive Delayed Feedback Control

Yaghooti¹,

Safavigerdini²,

Hajiloo³

et al. 2022

Preprint

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This paper presents an adaptive nonlinear delayed feedback control scheme for stabilizing the UPO of unknown fractional-order chaotic systems. The proposed control scheme uses the Lyapunov approach and sliding mode control technique to ensure that the closed-loop control system is asymptotically stable on a periodic trajectory sufficiently close to the UPO of the fractional-order chaotic system. It is guaranteed that the closed-loop system will be robust to external disturbances with unknowable bounds. Finally, the proposed method is used to stabilize the UPO of the fractional-order Duffing and Gyro systems, and extensive simulation results are used to evaluate its performance.

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Section: A Fractional-order Duffing Systemmentioning

confidence: 93%

Section: Introductionmentioning

confidence: 99%

Stabilizing Unstable Periodic Orbit of Unknown Fractional-Order Systems via Adaptive Delayed Feedback Control

Yaghooti¹,

Safavigerdini²,

Hajiloo³

et al. 2022

Preprint

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“…A linear feedback control method is developed for stabilizing the UPO of FO chaotic systems by Rahimi et al 31 We have applied the linear feedback control method to the duffing system and compared the results to our proposed algorithm. As Figure 1 illustrates, our method converges to the main UPO of the system faster than the linear feedback method.…”

Section: Fo Duffing Systemmentioning

confidence: 99%

“…29,30 Some control techniques have been applied for stabilizing the UPO of FO chaotic systems such as linear feedback control. Rahimi et al 31 represented techniques for finding unstable periodic orbits in chaotic FO systems and for the stabilization of founded UPOs. Sadeghian et al 32 illustrated a method to apply feedback of measured states using the period of fixed points (in discrete systems) and periodic orbits (in continuous systems), in which there is no need for information for fixed point and periodic orbits.…”

Section: Introductionmentioning

confidence: 99%

Stabilizing unstable periodic orbit of unknown fractional-order systems via adaptive delayed feedback control

Yaghooti,

Safavigerdini,

Hajiloo

et al. 2023

Proceedings of the Institution of Mechanical Engineers, Part I:

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This article presents an adaptive nonlinear delayed feedback control scheme for stabilizing the unstable periodic orbit of unknown fractional-order chaotic systems. The proposed control framework uses the Lyapunov approach and sliding mode control technique to guarantee that the closed-loop system is asymptotically stable on a periodic trajectory sufficiently close to the unstable periodic orbit of the system. The proposed method has two significant advantages. First, it employs a direct adaptive control method, making it easy to implement this method on systems with unknown parameters. Second, the framework requires only the period of the unstable periodic orbit. The robustness of the closed-loop system against system uncertainties and external disturbances with unknown bounds is guaranteed. Simulations on fractional-order duffing and gyro systems are used to illustrate the effectiveness of the theoretical results. The simulation results demonstrate that our approach outperforms the previously developed linear feedback control method for stabilizing unstable periodic orbits in fractional-order chaotic systems, particularly in reducing steady-state error and achieving faster convergence of tracking error.

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Lyapunov-based fractional-order controller design to synchronize a class of fractional-order chaotic systems

Chen

2013

Nonlinear Dyn

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Stabilizing periodic orbits of fractional order chaotic systems via linear feedback theory

Cited by 9 publications

References 21 publications

Stabilizing Unstable Periodic Orbit of Unknown Fractional-Order Systems via Adaptive Delayed Feedback Control

Stabilizing Unstable Periodic Orbit of Unknown Fractional-Order Systems via Adaptive Delayed Feedback Control

Stabilizing unstable periodic orbit of unknown fractional-order systems via adaptive delayed feedback control

Lyapunov-based fractional-order controller design to synchronize a class of fractional-order chaotic systems

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