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Fuzzy Information and Engineering 2023, 15(2): 183-201 https://doi.org/10.26599/FIE.2023.9270007
Article | Open Access | Issue | Published: 30 June 2023

Tracking Control of a Class of Fuzzy Dynamical Systems Under the Concept of Granular Differentiability

Show Author's Information Seyed Mohammad Mehdi Abbasi1( ),  Aliakbar Jalali1
Department of Electrical Engineering, Iran University of Science and Technology, Tehran 15614, Iran
Keywords:
fuzzy control, horizontal membership function, fuzzy linear system, granular arithmetic, granular derivative
Cite this article:
Abbasi SMM, Jalali A. Tracking Control of a Class of Fuzzy Dynamical Systems Under the Concept of Granular Differentiability. Fuzzy Information and Engineering, 2023, 15(2): 183-201. https://doi.org/10.26599/FIE.2023.9270007
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Abstract Full text About this article

In this work, the tracking control of a class of uncertain linear dynamical systems is investigated. The uncertainty is considered to be represented as fuzzy numbers, and hence, these uncertain dynamical systems are referred to as fuzzy linear dynamical systems, which are presented in the form of fuzzy differential equations (FDEs). The solution of an FDE is found using an approach called relative-distance-measure fuzzy interval arithmetic and under the granular differentiability concept. The control objective is to provide a control law such that the output of the system tracks a desired reference input in the presence of uncertainties. To this end, a theorem is proposed, which suggests that the control law should take the form of a feedback of fuzzy states with fuzzy gains and a fuzzy pre-compensator. However, since the fuzzy states of the system may not always be measurable, a fuzzy observer is designed for the estimation of such fuzzy states. It is also clearly shown that the generalized Hukuhara differentiability concept is unable for solving the problem examined in this study. Finally, the efficiency of the approach is examined for a plane landing control problem.


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About this article

Tracking Control of a Class of Fuzzy Dynamical Systems Under the Concept of Granular Differentiability

Show Author's information Seyed Mohammad Mehdi Abbasi1( ), Aliakbar Jalali1
Department of Electrical Engineering, Iran University of Science and Technology, Tehran 15614, Iran

Abstract

In this work, the tracking control of a class of uncertain linear dynamical systems is investigated. The uncertainty is considered to be represented as fuzzy numbers, and hence, these uncertain dynamical systems are referred to as fuzzy linear dynamical systems, which are presented in the form of fuzzy differential equations (FDEs). The solution of an FDE is found using an approach called relative-distance-measure fuzzy interval arithmetic and under the granular differentiability concept. The control objective is to provide a control law such that the output of the system tracks a desired reference input in the presence of uncertainties. To this end, a theorem is proposed, which suggests that the control law should take the form of a feedback of fuzzy states with fuzzy gains and a fuzzy pre-compensator. However, since the fuzzy states of the system may not always be measurable, a fuzzy observer is designed for the estimation of such fuzzy states. It is also clearly shown that the generalized Hukuhara differentiability concept is unable for solving the problem examined in this study. Finally, the efficiency of the approach is examined for a plane landing control problem.

Keywords: fuzzy control, horizontal membership function, fuzzy linear system, granular arithmetic, granular derivative

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Received: 20 February 2023
Accepted: 26 March 2023
Published: 30 June 2023
Issue date: June 2023

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© The Author(s) 2023. Published by Tsinghua University Press.

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This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).

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