A search algorithm for the compact uncertainty region of system elements with interval and affine constraint properties
This study proposes a search algorithm for the compact uncertainty region of system elements with affine constraints and interval information. While existing studies have considered only the interval information of uncertainty, the proposed algorithm reflects both the interval and affine constraints...
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| Published in | Applied mathematics and computation Vol. 477; p. 128823 |
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| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
Elsevier Inc
15.09.2024
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| Online Access | Get full text |
| ISSN | 0096-3003 |
| DOI | 10.1016/j.amc.2024.128823 |
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| Abstract | This study proposes a search algorithm for the compact uncertainty region of system elements with affine constraints and interval information. While existing studies have considered only the interval information of uncertainty, the proposed algorithm reflects both the interval and affine constraints of uncertain elements to reduce conservatism due to uncertainties. First, the affine constraints of uncertainty are plotted in an N-dimensional space, where N is the number of elements that should be considered. Due to the properties of the affine constraints, the affine constraints are expressed as an (N-1) dimensional structure. The interval information is then expressed as an N-dimensional structure. The algorithm iteratively checks the edges of the N-dimensional structure between two geometrical structures to determine the intersection region. The algorithm then collects the vertices of the convex polytope that overlap the two structures. To show the effectiveness of proposed algorithm, this study proposes a consensus criterion for a multi-agent time-delayed system with uncertain switching topologies as an application of a system with uncertainties in system elements.
•We clarify the motivation and contribution of this paper.•We update figures in Example 1.•We add the Example 2 to better show the efficiency of proposed algorithm.•To help us understand, we added Remarks 1, 8. |
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| AbstractList | This study proposes a search algorithm for the compact uncertainty region of system elements with affine constraints and interval information. While existing studies have considered only the interval information of uncertainty, the proposed algorithm reflects both the interval and affine constraints of uncertain elements to reduce conservatism due to uncertainties. First, the affine constraints of uncertainty are plotted in an N-dimensional space, where N is the number of elements that should be considered. Due to the properties of the affine constraints, the affine constraints are expressed as an (N-1) dimensional structure. The interval information is then expressed as an N-dimensional structure. The algorithm iteratively checks the edges of the N-dimensional structure between two geometrical structures to determine the intersection region. The algorithm then collects the vertices of the convex polytope that overlap the two structures. To show the effectiveness of proposed algorithm, this study proposes a consensus criterion for a multi-agent time-delayed system with uncertain switching topologies as an application of a system with uncertainties in system elements.
•We clarify the motivation and contribution of this paper.•We update figures in Example 1.•We add the Example 2 to better show the efficiency of proposed algorithm.•To help us understand, we added Remarks 1, 8. |
| ArticleNumber | 128823 |
| Author | Park, PooGyeon Park, Chan-eun Sub Lee, Ho |
| Author_xml | – sequence: 1 givenname: Ho surname: Sub Lee fullname: Sub Lee, Ho email: hosub@postech.ac.kr organization: Department of Electrical Engineering, POSTECH, Pohang, Republic of Korea – sequence: 2 givenname: Chan-eun surname: Park fullname: Park, Chan-eun email: chaneun@knu.ac.kr organization: School of Electronics Engineering, Kyungpuk National University, Daegu, Republic of Korea – sequence: 3 givenname: PooGyeon surname: Park fullname: Park, PooGyeon email: ppg@postech.ac.kr organization: Department of Electrical Engineering, POSTECH, Pohang, Republic of Korea |
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| Cites_doi | 10.1016/j.automatica.2019.108515 10.1016/j.automatica.2008.11.005 10.1016/j.automatica.2022.110357 10.1016/j.nahs.2023.101336 10.1007/s12555-021-0415-3 10.1109/TCYB.2020.2981158 10.1016/j.jfranklin.2015.01.004 10.1016/j.ins.2023.03.070 10.1109/TAC.2022.3226703 10.1109/TCYB.2022.3181820 10.1109/TCYB.2022.3217197 10.1109/TIE.2015.2504043 10.1109/TCYB.2022.3141599 10.1109/TAC.2009.2017963 10.1109/TSMC.2022.3170573 10.1109/TNSE.2019.2911713 10.1016/j.amc.2022.126968 10.1002/rnc.5986 |
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| Keywords | Linear matrix inequality Switching topology Uncertainty of system elements Multi-agent systems Uncertain transition rate |
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| SubjectTerms | Linear matrix inequality Multi-agent systems Switching topology Uncertain transition rate Uncertainty of system elements |
| Title | A search algorithm for the compact uncertainty region of system elements with interval and affine constraint properties |
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