High gain observer design for fractional‐order non‐linear systems with delayed measurements: application to synchronisation of fractional‐order chaotic systems

Bettayeb, Maâmar; Al‐Saggaf, Ubaid M.; Djennoune, Saïd

doi:10.1049/iet-cta.2017.0396

Cited by 16 publications

(8 citation statements)

References 44 publications

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“…The synchronization of a chaotic system is essential when two chaotic systems must be synchronized. Chaotic synchronization can be categorized as identical and non-identical [19][20][21][22][23][24][25]. There are plenty of papers in the literature in which this kind of synchronization controller strategy is evinced.…”

Section: Introductionmentioning

confidence: 99%

Robust Stabilization and Synchronization of a Novel Chaotic System with Input Saturation Constraints

Azar

Serrano

Zhu

et al. 2021

Entropy

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In this paper, the robust stabilization and synchronization of a novel chaotic system are presented. First, a novel chaotic system is presented in which this system is realized by implementing a sigmoidal function to generate the chaotic behavior of this analyzed system. A bifurcation analysis is provided in which by varying three parameters of this chaotic system, the respective bifurcations plots are generated and evinced to analyze and verify when this system is in the stability region or in a chaotic regimen. Then, a robust controller is designed to drive the system variables from the chaotic regimen to stability so that these variables reach the equilibrium point in finite time. The robust controller is obtained by selecting an appropriate robust control Lyapunov function to obtain the resulting control law. For synchronization purposes, the novel chaotic system designed in this study is used as a drive and response system, considering that the error variable is implemented in a robust control Lyapunov function to drive this error variable to zero in finite time. In the control law design for stabilization and synchronization purposes, an extra state is provided to ensure that the saturated input sector condition must be mathematically tractable. A numerical experiment and simulation results are evinced, along with the respective discussion and conclusion.

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Section: Introductionmentioning

confidence: 99%

Robust Stabilization and Synchronization of a Novel Chaotic System with Input Saturation Constraints

Azar

Serrano

Zhu

et al. 2021

Entropy

Self Cite

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“…Fractional high-gain observer is an algorithm processed by several authors to solve the problem of estimation [20,21]. It was shown that when using high-gain observers, the state estimate converges to the actual state rapidly.…”

Section: Introductionmentioning

confidence: 99%

A Proposed High-Gain Observer for a Class of Nonlinear Fractional-Order Systems

Etlili

Khedher

Errachdi

2021

Mathematical Problems in Engineering

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This paper proposes a high-gain observer for a class of nonlinear fractional-order systems. Indeed, this approach is based on Caputo derivative to solve the estimation problem for nonlinear systems. The proposed high-gain observer is used to estimate the unknown states of a nonlinear fractional system. The use of Lyapunov convergence functions to establish stability of system is detailed. The influence of different fractional orders on the estimation is presented. Ultimately, numerical simulation examples demonstrate the efficiency of the proposed approach.

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“…Since introduced by Leibniz and L'Hopital in 1860s [1], the fractional calculus theory has achieved rapid development and aroused great attention among some realms of science, such as chaotic systems [2,3], secure communication [4], digital signal processor [5], diffusion equation [6,7], control fields [8][9][10] and so on. In [2], Boubellouta et al have studied the chaos synchronisation problem of the uncertain optical chaotic systems by designing a fractional-order controller.…”

Section: Introductionmentioning

confidence: 99%

“…In [2], Boubellouta et al have studied the chaos synchronisation problem of the uncertain optical chaotic systems by designing a fractional-order controller. Meanwhile, Bettayeb et al have also investigated the synchronisation problem of fractional-order chaotic systems with time delay by designing a new observer with high gain in [3].…”

Section: Introductionmentioning

confidence: 99%

Projective synchronisation of variable‐order systems via fractional sliding mode control approach

Meng

Kao

Gao

et al. 2020

IET Control Theory & Applications

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High gain observer design for fractional‐order non‐linear systems with delayed measurements: application to synchronisation of fractional‐order chaotic systems

Cited by 16 publications

References 44 publications

Robust Stabilization and Synchronization of a Novel Chaotic System with Input Saturation Constraints

Robust Stabilization and Synchronization of a Novel Chaotic System with Input Saturation Constraints

A Proposed High-Gain Observer for a Class of Nonlinear Fractional-Order Systems

Projective synchronisation of variable‐order systems via fractional sliding mode control approach

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