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Article

C0-Semigroups Approach to the Reliability Model Based on Robot-Safety System

by
Ehmet Kasim
*,† and
Aihemaitijiang Yumaier
College of Mathematics and Systems Science, Xinjiang University, Urumqi 830046, China
*
Author to whom correspondence should be addressed.
These authors contributed equally to this work.
Submission received: 8 May 2024 / Revised: 6 June 2024 / Accepted: 13 June 2024 / Published: 24 June 2024
(This article belongs to the Special Issue Infinite Dynamical System and Differential Equations)

Abstract

This paper considers a system with one robot and n safety units (one of which works while the others remain on standby), which is described by an integro-deferential equation. The system can fail in the following three ways: fails with an incident, fails safely and fails due to the malfunction of the robot. Using the C0semigroups theory of linear operators, we first show that the system has a unique non-negative, time-dependent solution. Then, we obtain the exponential convergence of the time-dependent solution to its steady-state solution. In addition, we study the asymptotic behavior of some time-dependent reliability indices and present a numerical example demonstrating the effects of different parameters on the system.
Keywords: robot-safety system; C0-semigroups; well-posedness; exponential stability; reliability indices robot-safety system; C0-semigroups; well-posedness; exponential stability; reliability indices

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MDPI and ACS Style

Kasim, E.; Yumaier, A. C0-Semigroups Approach to the Reliability Model Based on Robot-Safety System. Axioms 2024, 13, 423. https://0-doi-org.brum.beds.ac.uk/10.3390/axioms13070423

AMA Style

Kasim E, Yumaier A. C0-Semigroups Approach to the Reliability Model Based on Robot-Safety System. Axioms. 2024; 13(7):423. https://0-doi-org.brum.beds.ac.uk/10.3390/axioms13070423

Chicago/Turabian Style

Kasim, Ehmet, and Aihemaitijiang Yumaier. 2024. "C0-Semigroups Approach to the Reliability Model Based on Robot-Safety System" Axioms 13, no. 7: 423. https://0-doi-org.brum.beds.ac.uk/10.3390/axioms13070423

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