Robust Adaptive Interval Type-2 Fuzzy Synchronization for a Class of Fractional Order Chaotic Systems

Khettab, Khatir; Bensafia, Yassine; Ladaci, Samir

doi:10.1007/978-3-319-50249-6_7

Cited by 9 publications

(8 citation statements)

References 48 publications

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“…To solve the problem of 𝜑 1 (x 1 , 𝑘) and 𝜑 2 (x 1 , x 2 , 𝑘) , we approximate them by a two-interval type-2 fuzzy adaptive systems. A fuzzy system that uses fuzzy type 2 sets and inference is a fuzzy type 2 system [10][11][12][13][14][15][16]. Type-1 fuzzy set has a crisp membership degree, while type-2 fuzzy set (T2FS) has a fuzzy membership degree.…”

Section: Interval Type-2 Fuzzy Adaptive Controlmentioning

confidence: 99%

“…An adaptive fuzzy backstepping controller (AFBC) 𝑢 𝑎𝑓𝑏 (𝑘) is designed, 𝜑 𝑖 (𝑥̅ 𝑖 , 𝑘) is approximated based on 𝜑 ̂𝑖(𝐱 ̅ ̂, 𝑘|𝜃 𝑖 * ) using a type-2 fuzzy inference approach which is based on extended single-input rule modules, where 𝜃 𝑖 * is the optimal parameter vector defined as follows [14,20]. where, Ω 𝑖 , 𝑈 𝑖 and 𝑉 𝑖 are respectively, suitable compact sets.…”

Section: Interval Type-2 Fuzzy Backstepping Designmentioning

confidence: 99%

“…In addition, the SIRMs model which has a simple structure can relatively reduce the number of IF-THEN inference rules and the adjusted parameters [12]. Consequently, to further improve the traditional SIRMs model because of its performance is still limited to deal with high levels of nonlinear uncertainties, an interval type-2 fuzzy logic system (IT2FLS) has been incorporated to replace the ordinary type-1 fuzzy sets [14]. A novel hybrid interval type-2 fuzzy adaptive backstepping control is developed for a class of discrete-time systems with non-linear uncertainties.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Novel Hybrid Interval Type-2 Fuzzy Adaptive Backstepping Control for a Class of Uncertain Discrete-Time Nonlinear Systems

Boukhalfa¹,

Khettab²,

Essounbouli³

2021

JESA

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A Novel hybrid backstepping interval type-2fuzzy adaptive control (HBT2AC) for uncertain discrete-time nonlinear systems is presented in this paper. The systems are assumed to be defined with the aid of discrete equations with nonlinear uncertainties which are considered as modeling errors and external unknown disturbances, and that the observed states are considered disturbed. The adaptive fuzzy type-2 controller is designed, where the fuzzy inference approach based on extended single-input rule modules (SIRMs) approximate the modeling errors, non-measurable states and adjustable parameters are estimated using derived weighted simplified least squares estimators (WSLS). We can prove that the states are bounded and the estimation errors stand in the neighborhood of zero. The efficiency of the approach is proved by simulation for which the root mean squares criteria are used which improves control performance.

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Section: Interval Type-2 Fuzzy Adaptive Controlmentioning

confidence: 99%

Section: Interval Type-2 Fuzzy Backstepping Designmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Novel Hybrid Interval Type-2 Fuzzy Adaptive Backstepping Control for a Class of Uncertain Discrete-Time Nonlinear Systems

Boukhalfa¹,

Khettab²,

Essounbouli³

2021

JESA

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“…Two important and widely applied definitions are Grunwald-Letnikov definition is perhaps the best known due to its most suitability for the realization of discrete control algorithms [1,12]. The Grunwald-Letnikov definition is expresses as [21,[24][25][26][27]:…”

Section: Definition Of Fractional Calculusmentioning

confidence: 99%

“…For a wide class of functions which appear in real physical and engineering applications, the RiemannLiouville and the Grunwald-Letnikov definitions are equivalent [2,[25][26][27].…”

Section: Definition Of Fractional Calculusmentioning

confidence: 99%

An Improved Robust Fractionalized PID Controller for a Class of Fractional-Order Systems with Measurement Noise

Bensafia¹,

Khettab²,

Idir³

2018

IJIES

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Abstract:Recently, many research works have focused on fractional order control (FOC) and fractional systems. It has proven to be a good mean for improving the plant dynamics with respect to response time and disturbance rejection. In this paper we propose a new approach for robust control by fractionalizing an integer order integrator in the classical PID control scheme and we use the Sub-optimal Approximation of fractional order transfer function to design the parameters of PID controller, after that we study the performance analysis of fractionalized PID controller over integer order PID controller. The implementation of the fractionalized terms is realized by mean of well-established numerical approximation methods. Illustrative simulation examples show that the disturbance rejection is improved by 50%. This approach can also be generalized to a wide range of control methods.

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Design of neural network fractional‐order backstepping controller for MPPT of PV systems using fractional‐order boost converter

Youcef

Khettab

Bensafia

2021

Int Trans Electr Energ Syst

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The main objective of this article is to apply the fractional calculus for establishing a novel design of photovoltaic (PV) system. In order to enhance the efficiency and robustness of the maximum power point tracking (MPPT) approach, a fractional-order (FO) DC-DC boost converter is proposed for a PV system. Due to the nonlinearity of the PV module, an artificial neural network (ANN) loop has been used to consistently generate an optimal reference voltage. Using FO control, an incommensurate FO backstepping controller (FO-BSC) has been ultimately integrated for tracking the maximum power point in the presence of tremendously atmospheric conditions and load changes. In this

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Robust Adaptive Interval Type-2 Fuzzy Synchronization for a Class of Fractional Order Chaotic Systems

Cited by 9 publications

References 48 publications

Novel Hybrid Interval Type-2 Fuzzy Adaptive Backstepping Control for a Class of Uncertain Discrete-Time Nonlinear Systems

Novel Hybrid Interval Type-2 Fuzzy Adaptive Backstepping Control for a Class of Uncertain Discrete-Time Nonlinear Systems

An Improved Robust Fractionalized PID Controller for a Class of Fractional-Order Systems with Measurement Noise

Design of neural network fractional‐order backstepping controller for MPPT of PV systems using fractional‐order boost converter

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