Document Type : Research Paper
Authors
Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Chennai, Tamil Nadu, India.
Abstract
This study is concerned with finding the controllability of granular type-2
fuzzy fractional-order dynamical control systems (GrT2FuFDCS) using
Mittag-Leffler matrix function. Some new concepts concerning to granular
interval valued type-2 fuzzy fractional derivative is introduced in
this paper. To arrive at finding the controllability of the type-2 fuzzy
dynamical system, type-2 triangular fuzzy function and type-2 triangular
fuzzy numbers are used to model fractional dynamical control
system. Besides, the controllability Grammian matrix is defined based
on Mittag-Leffler matrix function. Granular fuzzy Laplace transform and
inverse Laplace transform are utilized to derive the solution of the type-
2 triangular fuzzy fractional-order control systems. The derived results
ensure that the controllability of the proposed GrT2FuFDCS for both
linear and non-linear case exists. Finally, numerical examples and their
simulation results are given to illustrate the merit of the obtained results.
Keywords
- Horizontal membership function
- Type-2 triangular fuzzy number
- Type-2 fuzzy granular Laplace transform
- Type-2 fuzzy fractional differential equations, Granular differentiability
- Granular fuzzy fractional derivative
- Type-2 fuzzy fractional granular controllability
Main Subjects
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