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Article: A Bernstein Polynomial Approach to Estimating Reachable Set of Periodic Piecewise Polynomial Systems
Title | A Bernstein Polynomial Approach to Estimating Reachable Set of Periodic Piecewise Polynomial Systems |
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Authors | |
Keywords | Bernstein polynomial periodic piecewise polynomial systems reachable set estimation time-varying systems |
Issue Date | 2020 |
Publisher | Institute of Electrical and Electronics Engineers. The Journal's web site is located at http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=9 |
Citation | IEEE Transactions on Automatic Control, 2020, Epub 2020-11-20 How to Cite? |
Abstract | In this paper, a Bernstein polynomial approach is first applied to the estimation of reachable set for a class of periodic piecewise polynomial systems (PPPSs), whose subsystems are time-varying and can be expanded to Bernstein polynomial forms. A lemma on the negativity/positivity for a class of Bernstein polynomial matrix functions is presented, which can provide a feasible set larger than that by the existing method. Based on the integration of the presented lemma and the theory of matrix polynomials, two tractable sufficient conditions are developed. For comparison of conservatism, the reachable set estimation is achieved through optimizing the ellipsoidal bounding region. Four sets of constraints with different conservatism are derived and compared. The effectiveness and superiority of the Bernstein polynomial approach in reachable set estimation are demonstrated via an illustrative example. The results show that the proposed approach enables lower conservatism in reachable set estimation, providing an intuitive route to tackle time-varying parameter products with high powers. |
Persistent Identifier | http://hdl.handle.net/10722/299724 |
ISSN | 2023 Impact Factor: 6.2 2023 SCImago Journal Rankings: 4.501 |
ISI Accession Number ID |
DC Field | Value | Language |
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dc.contributor.author | Xie, X | - |
dc.contributor.author | Fan, C | - |
dc.contributor.author | Kwok, KW | - |
dc.contributor.author | Lam, J | - |
dc.date.accessioned | 2021-05-26T03:28:11Z | - |
dc.date.available | 2021-05-26T03:28:11Z | - |
dc.date.issued | 2020 | - |
dc.identifier.citation | IEEE Transactions on Automatic Control, 2020, Epub 2020-11-20 | - |
dc.identifier.issn | 0018-9286 | - |
dc.identifier.uri | http://hdl.handle.net/10722/299724 | - |
dc.description.abstract | In this paper, a Bernstein polynomial approach is first applied to the estimation of reachable set for a class of periodic piecewise polynomial systems (PPPSs), whose subsystems are time-varying and can be expanded to Bernstein polynomial forms. A lemma on the negativity/positivity for a class of Bernstein polynomial matrix functions is presented, which can provide a feasible set larger than that by the existing method. Based on the integration of the presented lemma and the theory of matrix polynomials, two tractable sufficient conditions are developed. For comparison of conservatism, the reachable set estimation is achieved through optimizing the ellipsoidal bounding region. Four sets of constraints with different conservatism are derived and compared. The effectiveness and superiority of the Bernstein polynomial approach in reachable set estimation are demonstrated via an illustrative example. The results show that the proposed approach enables lower conservatism in reachable set estimation, providing an intuitive route to tackle time-varying parameter products with high powers. | - |
dc.language | eng | - |
dc.publisher | Institute of Electrical and Electronics Engineers. The Journal's web site is located at http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=9 | - |
dc.relation.ispartof | IEEE Transactions on Automatic Control | - |
dc.rights | IEEE Transactions on Automatic Control. Copyright © Institute of Electrical and Electronics Engineers. | - |
dc.rights | ©20xx IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works. | - |
dc.subject | Bernstein polynomial | - |
dc.subject | periodic piecewise polynomial systems | - |
dc.subject | reachable set estimation | - |
dc.subject | time-varying systems | - |
dc.title | A Bernstein Polynomial Approach to Estimating Reachable Set of Periodic Piecewise Polynomial Systems | - |
dc.type | Article | - |
dc.identifier.email | Xie, X: xcxie@connect.hku.hk | - |
dc.identifier.email | Fan, C: fanccra@hku.hk | - |
dc.identifier.email | Kwok, KW: kwokkw@hku.hk | - |
dc.identifier.email | Lam, J: jlam@hku.hk | - |
dc.identifier.authority | Kwok, KW=rp01924 | - |
dc.identifier.authority | Lam, J=rp00133 | - |
dc.description.nature | link_to_subscribed_fulltext | - |
dc.identifier.doi | 10.1109/TAC.2020.3037041 | - |
dc.identifier.scopus | eid_2-s2.0-85098747598 | - |
dc.identifier.hkuros | 322566 | - |
dc.identifier.volume | Epub 2020-11-20 | - |
dc.identifier.isi | WOS:000698859900030 | - |
dc.publisher.place | United States | - |