Low-Complexity Polytopic Invariant Sets for Linear Systems Subject to Norm-Bounded Uncertainty
We propose a novel algorithm to compute low-complexity polytopic robust control invariant (RCI) sets, along with the corresponding state-feedback gain, for linear discrete-time systems subject to norm-bounded uncertainty, additive disturbances and state/input constraints. Using a slack variable appr...
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| Published in | IEEE transactions on automatic control Vol. 60; no. 5; pp. 1416 - 1421 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
IEEE
01.05.2015
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| Abstract | We propose a novel algorithm to compute low-complexity polytopic robust control invariant (RCI) sets, along with the corresponding state-feedback gain, for linear discrete-time systems subject to norm-bounded uncertainty, additive disturbances and state/input constraints. Using a slack variable approach, we propose new results to transform the original nonlinear problem into a convex/LMI problem whilst introducing only minor conservatism in the formulation. Through numerical examples, we illustrate that the proposed algorithm can yield improved maximal/minimal volume RCI set approximations in comparison with the schemes given in the literature. |
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| AbstractList | We propose a novel algorithm to compute low-complexity polytopic robust control invariant (RCI) sets, along with the corresponding state-feedback gain, for linear discrete-time systems subject to norm-bounded uncertainty, additive disturbances and state/input constraints. Using a slack variable approach, we propose new results to transform the original nonlinear problem into a convex/LMI problem whilst introducing only minor conservatism in the formulation. Through numerical examples, we illustrate that the proposed algorithm can yield improved maximal/minimal volume RCI set approximations in comparison with the schemes given in the literature. |
| Author | Tahir, Furqan Jaimoukha, Imad M. |
| Author_xml | – sequence: 1 givenname: Furqan surname: Tahir fullname: Tahir, Furqan email: ftahir49@hotmail.com organization: Perceptive Eng. Ltd., Daresbury, UK – sequence: 2 givenname: Imad M. surname: Jaimoukha fullname: Jaimoukha, Imad M. email: i.jaimouka@imperial.ac.uk organization: Dept. of Electr. & Electron. Eng., Imperial Coll. London, London, UK |
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| Cites_doi | 10.1007/978-0-8176-4606-6 10.1016/S0005-1098(03)00128-6 10.1016/j.automatica.2006.11.006 10.1137/S003614450444614X 10.1016/j.automatica.2013.06.015 10.1007/BF00941398 10.1109/TAC.2005.843854 10.1016/j.jprocont.2012.08.003 10.1080/00207171003692662 10.1109/9.935072 10.1109/9.975496 10.1007/s10107-005-0692-2 10.1023/A:1021727806358 10.1016/S0005-1098(99)00113-2 10.1137/S1052623496305717 10.1080/00207178808906132 |
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| SubjectTerms | Additives Approximation algorithms Approximation methods Linear matrix inequalities Optimization Silicon Uncertainty |
| Title | Low-Complexity Polytopic Invariant Sets for Linear Systems Subject to Norm-Bounded Uncertainty |
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