A new approach for solving a class of fuzzy optimal control systems under generalized Hukuhara differentiability

Najariyan, Marzieh; Farahi, Mohammad Hadi

doi:10.1016/j.jfranklin.2015.01.006

Cited by 46 publications

(18 citation statements)

References 15 publications

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“…With successful applications in medicine (John and Innocent 2005;Garibaldi et al 2012;Mazandarani and Kamyad 2011;Najariyan et al 2011), control theory (Najariyan and Farahi 2015), food science (Zolfaghari et al 2014), mathematics (Najariyan and Mazandarani 2015), computing with words (Mendel 2016), decision making (Wang et al 2016;Das et al 2016), fuzzy logic is well known as an effective tool for dealing with uncertainty in modeling processes. Generalization of concepts and achievements already obtained in the field of mathematics using fuzzy logic have recently captured much attention.…”

Section: Introductionmentioning

confidence: 99%

Type-2 fuzzy linear systems

2017

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Section: Introductionmentioning

confidence: 99%

Type-2 fuzzy linear systems

2017

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“…The main features of our optimality conditions were summarized and highlighted with three illustrative examples. Two of the examples give interesting insights to the results of [26,28].…”

Section: Example 3 (Example 3 Of Najariyan and Farahimentioning

confidence: 86%

“…Here we show that fuzzy minimizers for [28, Example 3] do not exist. [28]). Consider the following problem:…”

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confidence: 99%

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A necessary condition of Pontryagin type for fuzzy fractional optimal control problems

Fard¹,

Soolaki²,

Torres³

2018

Discrete &Amp; Continuous Dynamical Systems - S

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We prove necessary optimality conditions of Pontryagin type for a class of fuzzy fractional optimal control problems with the fuzzy fractional derivative described in the Caputo sense. The new results are illustrated by computing the extremals of three fuzzy optimal control systems, which improve recent results of Najariyan and Farahi.2010 Mathematics Subject Classification. Primary: 26A33, 93C42; Secondary: 49K05. 1 2 O. S. FARD, J. SOOLAKI AND D. F. M. TORRESnonlinear systems are proposed based on the framework of the Takagi-Sugeno (T-S) fuzzy model originated from fuzzy identification [38]. Moreover, for most of the T-S modelled nonlinear systems, fuzzy control design is carried out by the aid of the parallel distributed compensation (PDC) approach [42]. However, it is still possible to enumerate all works that establish necessary optimality conditions for the fuzzy calculus of variations or fuzzy optimal control: see [8,10,11,12,26,27,36,37].In [26,27], Najariyan and Farahi obtain necessary optimality conditions of Pontryagin type for a very special case of fuzzy optimal control problems, using α-cuts and presentation of numbers in a more compact form by moving to the field of complex numbers. The authors of [26,27] study the following fuzzy optimal control problem subject to a time-invariant linear control system:

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“…The common attempts to cope with the modeling and control of time-variant systems have been focused on development of adaptive models, such as Adaptive fuzzy systems [10][11][12][13][14] and adaptive neural networks [15,16]. However, in many real-world industrial systems, the adaptive model, or the ability to adapt, cannot cover the whole operating conditions of the system.…”

Section: Introductionmentioning

confidence: 99%