Solving variable-order fractional differential algebraic equations via generalized fuzzy hyperbolic model with application in electric circuit modeling

Mortezaee, Marziyeh; Ghovatmand, M.; Nazemi, Alireza

doi:10.1007/s00500-020-04969-7

Cited by 4 publications

(2 citation statements)

References 54 publications

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“…Existence of this merit in fuzzy systems, is due to the possibility of linguistic interpretation in the form of rules. The success of fuzzy systems is evident from its applicability and relevance in numerous research areas such as solving complex nonlinear system identification and control problems as well as approximating the solution of a class of partial differential equations, variable‐order fractional differential algebraic equations and optimal control problems (see References 21‐34). One of the reasons for this success is the ability of fuzzy systems to approximate any nonlinear system (see References 35‐39).…”

Section: Introductionmentioning

confidence: 99%

An application of a fuzzy system for solving time delay fractional optimal control problems with Atangana–Baleanu derivative

Mortezaee

Ghovatmand

Nazemi

2022

Optim Control Appl Methods

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In this article, a new approach based on fuzzy systems is used for solving time delay fractional order optimal control problems. The fractional derivatives are considered in the Atangana–Baleanu sense that is a new derivative with the nonsingular and nonlocal kernel. By means of the calculus of variations and the formula for fractional integration by parts, the necessary optimality conditions associated to the time delay problem is derived. In order to solve the obtained optimality system, the solution of the system is first approximated by fuzzy solutions with adjustable parameters. The optimality system is then reduced to an unconstrained optimization problem by using appropriate error function. A learning algorithm is also presented to achieve the parameters of these fuzzy solutions. The efficiency and accuracy of the proposed approach are assessed through some illustrative examples of the time delay fractional optimal control problems.

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Section: Introductionmentioning

confidence: 99%

An application of a fuzzy system for solving time delay fractional optimal control problems with Atangana–Baleanu derivative

Mortezaee

Ghovatmand

Nazemi

2022

Optim Control Appl Methods

Self Cite

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“…In recent years, some numerical methods have been proposed for solving FDAEs. Researchers investigated the numerical solutions of FDAEs by using various methods [15][16][17][18][19][20][21][22]. However, most of the methods cannot be used directly for solving the FDAEs modelled for mechanical systems or established with an engineering background.…”

Section: Introductionmentioning

confidence: 99%

A Numerical Method for a System of Fractional Differential-Algebraic Equations Based on Sliding Mode Control

et al. 2020

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Fractional calculus is widely used in engineering fields. In complex mechanical systems, multi-body dynamics can be modelled by fractional differential-algebraic equations when considering the fractional constitutive relations of some materials. In recent years, there have been a few works about the numerical method of the fractional differential-algebraic equations. However, most of the methods cannot be directly applied in the equations of dynamic systems. This paper presents a numerical algorithm of fractional differential-algebraic equations based on the theory of sliding mode control and the fractional calculus definition of Grünwald–Letnikov. The algebraic equation is considered as the sliding mode surface. The validity of the present method is verified by comparing with an example with exact solutions. The accuracy and efficiency of the present method are studied. It is found that the present method has very high accuracy and low time consumption. The effect of violation corrections on the accuracy is investigated for different time steps.

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An Application of Generalized Fuzzy Hyperbolic Model for Solving Fractional Optimal Control Problems with Caputo–Fabrizio Derivative

Mortezaee

Ghovatmand

Nazemi

2020

Neural Process Lett

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Solving variable-order fractional differential algebraic equations via generalized fuzzy hyperbolic model with application in electric circuit modeling

Cited by 4 publications

References 54 publications

An application of a fuzzy system for solving time delay fractional optimal control problems with Atangana–Baleanu derivative

An application of a fuzzy system for solving time delay fractional optimal control problems with Atangana–Baleanu derivative

A Numerical Method for a System of Fractional Differential-Algebraic Equations Based on Sliding Mode Control

An Application of Generalized Fuzzy Hyperbolic Model for Solving Fractional Optimal Control Problems with Caputo–Fabrizio Derivative

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