Tracking Control of a Class of Fuzzy Dynamical Systems Under the Concept of Granular Differentiability
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 fu...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Tsinghua University Press
2023-06-01
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| Series: | Fuzzy Information and Engineering |
| Subjects: | |
| Online Access: | https://www.sciopen.com/article/10.26599/FIE.2023.9270007 |
| _version_ | 1797741984942653440 |
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| author | Seyed Mohammad Mehdi Abbasi Aliakbar Jalali |
| author_facet | Seyed Mohammad Mehdi Abbasi Aliakbar Jalali |
| author_sort | Seyed Mohammad Mehdi Abbasi |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-12T14:34:31Z |
| format | Article |
| id | doaj.art-a8de560d1016451d99ba8a64cc85da13 |
| institution | Directory Open Access Journal |
| issn | 1616-8658 1616-8666 |
| language | English |
| last_indexed | 2024-03-12T14:34:31Z |
| publishDate | 2023-06-01 |
| publisher | Tsinghua University Press |
| record_format | Article |
| series | Fuzzy Information and Engineering |
| spelling | doaj.art-a8de560d1016451d99ba8a64cc85da132023-08-17T10:22:45ZengTsinghua University PressFuzzy Information and Engineering1616-86581616-86662023-06-0115218320110.26599/FIE.2023.9270007Tracking Control of a Class of Fuzzy Dynamical Systems Under the Concept of Granular DifferentiabilitySeyed Mohammad Mehdi Abbasi0Aliakbar Jalali1Department of Electrical Engineering, Iran University of Science and Technology, Tehran 15614, IranDepartment of Electrical Engineering, Iran University of Science and Technology, Tehran 15614, IranIn 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.https://www.sciopen.com/article/10.26599/FIE.2023.9270007horizontal membership functionfuzzy controlfuzzy linear systemgranular arithmeticgranular derivative |
| spellingShingle | Seyed Mohammad Mehdi Abbasi Aliakbar Jalali Tracking Control of a Class of Fuzzy Dynamical Systems Under the Concept of Granular Differentiability Fuzzy Information and Engineering horizontal membership function fuzzy control fuzzy linear system granular arithmetic granular derivative |
| title | Tracking Control of a Class of Fuzzy Dynamical Systems Under the Concept of Granular Differentiability |
| title_full | Tracking Control of a Class of Fuzzy Dynamical Systems Under the Concept of Granular Differentiability |
| title_fullStr | Tracking Control of a Class of Fuzzy Dynamical Systems Under the Concept of Granular Differentiability |
| title_full_unstemmed | Tracking Control of a Class of Fuzzy Dynamical Systems Under the Concept of Granular Differentiability |
| title_short | Tracking Control of a Class of Fuzzy Dynamical Systems Under the Concept of Granular Differentiability |
| title_sort | tracking control of a class of fuzzy dynamical systems under the concept of granular differentiability |
| topic | horizontal membership function fuzzy control fuzzy linear system granular arithmetic granular derivative |
| url | https://www.sciopen.com/article/10.26599/FIE.2023.9270007 |
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