Adaptive type‐2 fuzzy system for synchronisation and stabilisation of chaotic non‐linear fractional order systems

Jafari, Pouria; Teshnehlab, Mohammad; Tavakoli-Kakhki, Mahsan

doi:10.1049/iet-cta.2017.0785

Cited by 24 publications

(11 citation statements)

References 56 publications

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“…Also, studies on FO system have recently gained significant attention from control research communities because of their potential applications in various engineering systems and control processes, such as stabilization, synchronization, state estimation and reference tracking [21][22][23][24][25][26]. Although many useful research works have been constructed based on fuzzy approach, most of them are concerned with integer-order systems and only a little amount of them are dealt with FO fuzzy systems [27,28].…”

Section: Introductionmentioning

confidence: 99%

Robust tracking control design for fractional-order interval type-2 fuzzy systems

et al. 2022

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This paper is concerned with an uncertainty and disturbance estimator-based tracking control problem for a class of interval type-2 fractional-order Takagi-Sugeno fuzzy systems subject to time-varying delays. The footprints of the uncertainty of the underlying fuzzy systems are taken into account to capture and model different levels of uncertainties. The uncertainty and disturbance estimator is used to promote the tracking behavior of rejecting disturbance in the control system. First, by applying the Lyapunov approach, we focus on the examination of stability and performance of the fractional-order tracking error system. Next, unknown system uncertainties, external disturbances and nonlinearities are accurately estimated via an appropriate filter design. Especially, the proposed control technique does not require any prior knowledge about above said unknown factors and it only requires the bandwidth information about the lowpass filter. Then, four numerical examples with simulation results are presented in the end, to show the potential of the theoretical results of the proposed control method.Keywords Fractional-order systems • Interval type-2 fuzzy model • Robust control design • Stability analysis.

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Section: Introductionmentioning

confidence: 99%

Robust tracking control design for fractional-order interval type-2 fuzzy systems

et al. 2022

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“…Among the latest published studies concerned with the robust stability of linear time invariant (LTI) fractional order systems and nonlinear fractional order systems. The works 26–29 have made effort to analyze the robust stability of fractional order systems. Based on the zero exclusion principle, the robust stability of LTI delayed fractional order system in the presence of real parametric uncertainties has been studied in the works of Moornani and Haeri 30 and Ghorbani et al 31 Analogously, Zheng and Li 32 presented necessary and sufficient criteria to analyze the robust stability of an interval fractional order plant in the presence of uncertain orders and uncertain coefficients.…”

Section: Introductionmentioning

confidence: 99%

Robust stability analysis of a general class of interval delayed fractional order plants by a general form of fractional order controllers

Ghorbani

Tavakoli-Kakhki

2021

Math Methods in App Sciences

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In this paper, the robust stability of interval fractional order plants with one time delay controlled by fractional order controllers is investigated in a general form. For robust stability analysis of the closed loop system by the zero exclusion principle, the distance between the origin and the value set of the characteristic function needs to be checked. It is known that the outer vertices of this value set may change at some switching frequencies and the repetitive calculation of these vertices at switching frequencies leads to additional calculations. In this study initially, new necessary and sufficient conditions are proposed to check the robust stability of a delayed fractional order closed loop system. Then, a novel robust stability testing function is presented based on some vertices, which are fixed for all positive frequencies. Therefore, no additional calculation is needed to obtain the outer vertices of the characteristic function value set for any pair of the switching frequencies. Also, a finite frequency range is presented to reduce the computational cost noticeably. Eventually, three numerical examples are given to verify the efficiency of the results of this paper.

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“…Some related works can be mentioned as follows: a dynamic general type-2 fuzzy system with optimized secondary membership for online frequency regulation is studied in [19], a hybridized forecasting method based on weight adjustment of neural network using generalized type-2 fuzzy set was outlined in [20], parameter adaptation in the imperialist competitive algorithm using generalized type-2 fuzzy logic was described in [21], the optimization of fuzzy controller design using a differential evolution algorithm with dynamic parameter adaptation based on type-1 and interval type-2 fuzzy systems was put forward in [22], a comprehensive review on type 2 fuzzy logic applications was outlined in [23], a dynamic general type-2 fuzzy system has been used with optimized secondary membership for online frequency regulation [24], while an intelligent oversampling approach based upon general type-2 fuzzy Sets was adopted to detect web spam [25]. A novel intuitionistic based interval type-2 fuzzy similarity measures with application to clustering in [26], a dynamic event-triggered sliding mode control for interval type-2 fuzzy systems with fading channels is shown in [27], a general type-2 fuzzy gain scheduling PID controller with application to power-line inspection robots in [28], an online general type-2 fuzzy classifier using evolving type-1 rules is shown in [29], input-to-state stabilization of interval type-2 fuzzy systems subject to cyberattacks with an observer-based adaptive sliding mode approach are studied in [30], general type-2 fuzzy logic systems based on shadowed sets are presented in [31], an adaptive type-2 fuzzy system is used for the synchronization and stabilization of chaotic non-linear fractional order systems in [32], and general interval approach for encoding words into interval type-2 fuzzy sets based on normal distribution and free parameter is adopted in [33].…”

Section: Introductionmentioning

confidence: 99%

Differential Evolution with Shadowed and General Type-2 Fuzzy Systems for Dynamic Parameter Adaptation in Optimal Design of Fuzzy Controllers

Ochoa

Castillo

Melín

et al. 2021

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This work is mainly focused on improving the differential evolution algorithm with the utilization of shadowed and general type 2 fuzzy systems to dynamically adapt one of the parameters of the evolutionary method. Previously, we have worked with both kinds of fuzzy systems in different types of benchmark problems and it has been found that the use of fuzzy logic in combination with the differential evolution algorithm gives good results. In some of the studies, it is clearly shown that, when compared to other algorithms, our methodology turns out to be statistically better. In this case, the mutation parameter is dynamically moved during the evolution process by using shadowed and general type-2 fuzzy systems. The main contribution of this work is the ability to determine, through experimentation in a benchmark control problem, which of the two kinds of the used fuzzy systems has better results when combined with the differential evolution algorithm. This is because there are no similar works to our proposal in which shadowed and general type 2 fuzzy systems are used and compared. Moreover, to validate the performance of both fuzzy systems, a noise level is used in the controller, which simulates the disturbances that may exist in the real world and is thus able to validate statistically if there are significant differences between shadowed and general type 2 fuzzy systems.

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Adaptive type‐2 fuzzy system for synchronisation and stabilisation of chaotic non‐linear fractional order systems

Cited by 24 publications

References 56 publications

Robust tracking control design for fractional-order interval type-2 fuzzy systems

Robust tracking control design for fractional-order interval type-2 fuzzy systems

Robust stability analysis of a general class of interval delayed fractional order plants by a general form of fractional order controllers

Differential Evolution with Shadowed and General Type-2 Fuzzy Systems for Dynamic Parameter Adaptation in Optimal Design of Fuzzy Controllers

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