Research on the Reliability of a Two-Robot Security System with Early Warning Function
In this paper, the mathematical model of a kind of two-robot security system with an early warning function is studied. By using strongly continuous operator semigroup theory and Volterra integral equation theory, the properties of the semigroup of the system operator, the existence and uniqueness o...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2023-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2023/3214866 |
| _version_ | 1797807275594743808 |
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| author | Yuhong Cui Youde Tao Zongyang Li |
| author_facet | Yuhong Cui Youde Tao Zongyang Li |
| author_sort | Yuhong Cui |
| collection | DOAJ |
| description | In this paper, the mathematical model of a kind of two-robot security system with an early warning function is studied. By using strongly continuous operator semigroup theory and Volterra integral equation theory, the properties of the semigroup of the system operator, the existence and uniqueness of nonnegative solution, and the well-posedness of solution are discussed, respectively. Under the assumption that the failure rate and repair rate of the system are constants, the equations of the robot system are transformed into an ordinary differential equation group, and then the instantaneous reliability and stable-state reliability of the system are obtained. The reliability and zero-state controllability of the system are proved. Finally, the numerical solution of the system model is obtained by using MATLAB mathematical software, and the corresponding numerical simulation diagram is given. The results show that the conclusions of numerical calculation and numerical simulation are in accordance with the results of reliability theory, thereby the reliability of the robot safety system is verified. |
| first_indexed | 2024-03-13T06:20:08Z |
| format | Article |
| id | doaj.art-e0650c1c24f44c2793424c9cb81a1490 |
| institution | Directory Open Access Journal |
| issn | 2314-4785 |
| language | English |
| last_indexed | 2024-03-13T06:20:08Z |
| publishDate | 2023-01-01 |
| publisher | Hindawi Limited |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj.art-e0650c1c24f44c2793424c9cb81a14902023-06-10T00:00:04ZengHindawi LimitedJournal of Mathematics2314-47852023-01-01202310.1155/2023/3214866Research on the Reliability of a Two-Robot Security System with Early Warning FunctionYuhong Cui0Youde Tao1Zongyang Li2College of Mathematics and StatisticsCollege of Mathematics and StatisticsCollege of Mathematics and StatisticsIn this paper, the mathematical model of a kind of two-robot security system with an early warning function is studied. By using strongly continuous operator semigroup theory and Volterra integral equation theory, the properties of the semigroup of the system operator, the existence and uniqueness of nonnegative solution, and the well-posedness of solution are discussed, respectively. Under the assumption that the failure rate and repair rate of the system are constants, the equations of the robot system are transformed into an ordinary differential equation group, and then the instantaneous reliability and stable-state reliability of the system are obtained. The reliability and zero-state controllability of the system are proved. Finally, the numerical solution of the system model is obtained by using MATLAB mathematical software, and the corresponding numerical simulation diagram is given. The results show that the conclusions of numerical calculation and numerical simulation are in accordance with the results of reliability theory, thereby the reliability of the robot safety system is verified.http://dx.doi.org/10.1155/2023/3214866 |
| spellingShingle | Yuhong Cui Youde Tao Zongyang Li Research on the Reliability of a Two-Robot Security System with Early Warning Function Journal of Mathematics |
| title | Research on the Reliability of a Two-Robot Security System with Early Warning Function |
| title_full | Research on the Reliability of a Two-Robot Security System with Early Warning Function |
| title_fullStr | Research on the Reliability of a Two-Robot Security System with Early Warning Function |
| title_full_unstemmed | Research on the Reliability of a Two-Robot Security System with Early Warning Function |
| title_short | Research on the Reliability of a Two-Robot Security System with Early Warning Function |
| title_sort | research on the reliability of a two robot security system with early warning function |
| url | http://dx.doi.org/10.1155/2023/3214866 |
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