A robust regional eigenvalue assignment problem using rank-one control for undamped gyroscopic systems

Considering the advantages of economic benefit and cost reduction by using rank-one control, we investigated the problem of robust regional eigenvalue assignment using rank-one control for undamped gyroscopic systems. Based on the orthogonality relation, we presented a method for solving partial eig...

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Published inAIMS mathematics Vol. 9; no. 7; pp. 19104 - 19124
Main Authors He, Binxin, Liu, Hao
Format Journal Article
LanguageEnglish
Published AIMS Press 01.01.2024
Subjects
rank-one control
regional eigenvalue assignment
robustness
undamped gyroscopic systems
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ISSN2473-6988
2473-6988
DOI10.3934/math.2024931

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Abstract Considering the advantages of economic benefit and cost reduction by using rank-one control, we investigated the problem of robust regional eigenvalue assignment using rank-one control for undamped gyroscopic systems. Based on the orthogonality relation, we presented a method for solving partial eigenvalue assignment problems to reassign partial undesired eigenvalues accurately. Since it is difficult to achieve robust control by assigning desired eigenvalues to precise positions with rank-one control, we assigned eigenvalues within specified regions to provide the necessary freedom. According to the sensitivity analysis theories, we derived the sensitivity of closed-loop eigenvalues to parameter perturbations to measure robustness and proposed a numerical algorithm for solving robust regional eigenvalue assignment problems so that the closed-loop eigenvalues were insensitive to parameter perturbations. Numerical experiments demonstrated the effectiveness of our method.
AbstractList Considering the advantages of economic benefit and cost reduction by using rank-one control, we investigated the problem of robust regional eigenvalue assignment using rank-one control for undamped gyroscopic systems. Based on the orthogonality relation, we presented a method for solving partial eigenvalue assignment problems to reassign partial undesired eigenvalues accurately. Since it is difficult to achieve robust control by assigning desired eigenvalues to precise positions with rank-one control, we assigned eigenvalues within specified regions to provide the necessary freedom. According to the sensitivity analysis theories, we derived the sensitivity of closed-loop eigenvalues to parameter perturbations to measure robustness and proposed a numerical algorithm for solving robust regional eigenvalue assignment problems so that the closed-loop eigenvalues were insensitive to parameter perturbations. Numerical experiments demonstrated the effectiveness of our method.
Author Liu, Hao
He, Binxin
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Cites_doi 10.1016/j.ymssp.2021.108728
10.1007/s00707-018-2118-2
10.1016/j.jsv.2009.02.020
10.1016/j.ymssp.2021.108348
10.1016/j.laa.2010.07.014
10.1137/1031049
10.1137/S0036144500381988
10.1016/j.jsv.2016.08.002
10.1006/mssp.2001.1444
10.1016/j.ymssp.2019.106396
10.1016/j.ymssp.2022.108974
10.1115/1.1311792
10.1016/S0024-3795(96)00036-5
10.1016/j.jprocont.2020.08.004
10.1016/j.ymssp.2019.106404
10.1016/j.ymssp.2013.06.008
10.1016/j.ymssp.2021.108250
10.2514/1.24349
10.1016/j.apor.2020.102460
10.1007/s11012-020-01289-w
10.1016/j.ymssp.2010.04.005
10.1088/1742-6596/744/1/012008
10.1016/j.ymssp.2022.108976
10.1016/j.amc.2016.02.012
10.1016/j.ymssp.2016.12.011
10.1007/s10509-018-3400-4
10.1115/1.4002340
10.1016/j.apnum.2020.08.018
10.4208/eajam.040718.091218
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  doi: 10.1016/j.ymssp.2021.108728
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  doi: 10.1007/s00707-018-2118-2
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  doi: 10.1016/j.jsv.2009.02.020
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  doi: 10.1016/j.ymssp.2021.108348
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  doi: 10.1016/j.laa.2010.07.014
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  doi: 10.1137/1031049
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  doi: 10.1016/j.ymssp.2022.108974
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  doi: 10.1115/1.1311792
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  doi: 10.1016/S0024-3795(96)00036-5
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  doi: 10.1016/j.ymssp.2021.108250
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  doi: 10.2514/1.24349
– ident: key-10.3934/math.2024931-5
  doi: 10.1016/j.apor.2020.102460
– ident: key-10.3934/math.2024931-8
  doi: 10.1007/s11012-020-01289-w
– ident: key-10.3934/math.2024931-28
  doi: 10.1016/j.ymssp.2010.04.005
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  doi: 10.1088/1742-6596/744/1/012008
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  doi: 10.1016/j.ymssp.2022.108976
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  doi: 10.1016/j.amc.2016.02.012
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  doi: 10.1016/j.ymssp.2016.12.011
– ident: key-10.3934/math.2024931-15
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  doi: 10.1007/s10509-018-3400-4
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  doi: 10.1115/1.4002340
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  doi: 10.1016/j.apnum.2020.08.018
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  doi: 10.4208/eajam.040718.091218
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SubjectTerms rank-one control
regional eigenvalue assignment
robustness
undamped gyroscopic systems
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Title A robust regional eigenvalue assignment problem using rank-one control for undamped gyroscopic systems
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