Research Papers

Some Kinds of the Controllable Problems for Fuzzy Control Dynamic Systems

[+] Author and Article Information
N. D. Phu

Division of Computational
Mathematics and Engineering,
Institute for Computational Science and
Faculty of Mathematics and Statistics,
Ton Duc Thang University,
Ho Chi Minh City 700000, Vietnam
e-mail: nguyendinhphu@tdt.edu.vn

P. V. Tri

Faculty of Foundation Sciences,
Telecommunications University,
Khanh Hoa Province, Vietnam
e-mail: phanvantri82@gmail.com

A. Ahmadian

Institute for Mathematical Research,
University Putra Malaysia,
43400 UPM,
Selangor, Malaysia
e-mail: ahmadian.hosseini@gmail.com

S. Salahshour

Young Researchers and
Elite Club Mobarakeh Branch,
Islamic Azad University,
Mobarakeh, Iran
e-mail: soheilsalahshour@yahoo.com

D. Baleanu

Department of Mathematics,
Cankaya University,
Balgat 06530, Ankara, Turkey;
Institute of Space Sciences,
Magurele-Bucharest 077125, Romania
e-mail: dumitru@cankaya.edu.tr

1Corresponding author.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT,AND CONTROL. Manuscript received May 22, 2017; final manuscript received February 17, 2018; published online April 9, 2018. Assoc. Editor: Ryozo Nagamune.

J. Dyn. Sys., Meas., Control 140(9), 091008 (Apr 09, 2018) (10 pages) Paper No: DS-17-1264; doi: 10.1115/1.4039484 History: Received May 22, 2017; Revised February 17, 2018

In this work, we have discussed the fuzzy solutions for fuzzy controllable problem, fuzzy feedback problem, and fuzzy global controllable (GC) problems. We use the method of successive approximations under the generalized Lipschitz condition for the local existence and furthermore, we have described the contraction principle under suitable conditions for global existence and uniqueness of fuzzy solutions. We have too the GC results for fuzzy systems. Some examples and computer simulation illustrating our approach are also given for these controllable problems.

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Grahic Jump Location
Fig. 1

(FHg1) solution of Example 4.1 when a=1,b=0.2

Grahic Jump Location
Fig. 2

(FHg2) solution of Example 4.1 when a=1,b=0.2

Grahic Jump Location
Fig. 3

(FHg1) solution of Example 4.1 when a=−1,b=0.2

Grahic Jump Location
Fig. 4

(FHg2) solution of Example 4.1 when a=−1,b=0.2

Grahic Jump Location
Fig. 5

(FHg1) solution of Example 4.2 when b=1,α=0.5

Grahic Jump Location
Fig. 6

(FHg2) solution of Example 4.2 when b=1,α=0.5



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