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Article: Geometric Programming for Optimal Positive Linear Systems
Title | Geometric Programming for Optimal Positive Linear Systems |
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Authors | |
Keywords | Delayed linear systems geometric programming $H^2$ norm $H^infty$ norm Hankel norm |
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, v. 65 n. 11, p. 4648-4663 How to Cite? |
Abstract | This article studies the parameter tuning problem of positive linear systems for optimizing their stability properties. We specifically show that, under certain regularity assumptions on the parameterization, the problem of finding the minimum-cost parameters that achieve a given requirement on a system norm reduces to a geometric program, which, in turn, can be exactly and efficiently solved by convex optimization. The flexibility of geometric programming allows the state, input, and output matrices of the system to simultaneously depend on the parameters to be tuned. The class of system norms under consideration includes the H 2 norm, H ∞ norm, Hankel norm, and Schatten p-norm. Also, the parameter tuning problem for ensuring the robust stability of the system under structural uncertainties is shown to be solved by geometric programming. The proposed optimization framework is further extended to delayed positive linear systems, where it is shown that the parameter tuning problem jointly constrained by the exponential decay rate, the L 1 -gain, and the L ∞ -gain can be solved by convex optimization. The assumption on the system parameterization is stated in terms of posynomial functions, which form a broad class of functions and thus allow us to deal with various interesting positive linear systems arising from, for example, dynamical buffer networks and epidemic spreading processes. We present numerical examples to illustrate the effectiveness of the proposed optimization framework. |
Persistent Identifier | http://hdl.handle.net/10722/303964 |
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 | Ogura, M | - |
dc.contributor.author | Kishida, M | - |
dc.contributor.author | Lam, J | - |
dc.date.accessioned | 2021-09-23T08:53:18Z | - |
dc.date.available | 2021-09-23T08:53:18Z | - |
dc.date.issued | 2020 | - |
dc.identifier.citation | IEEE Transactions on Automatic Control, 2020, v. 65 n. 11, p. 4648-4663 | - |
dc.identifier.issn | 0018-9286 | - |
dc.identifier.uri | http://hdl.handle.net/10722/303964 | - |
dc.description.abstract | This article studies the parameter tuning problem of positive linear systems for optimizing their stability properties. We specifically show that, under certain regularity assumptions on the parameterization, the problem of finding the minimum-cost parameters that achieve a given requirement on a system norm reduces to a geometric program, which, in turn, can be exactly and efficiently solved by convex optimization. The flexibility of geometric programming allows the state, input, and output matrices of the system to simultaneously depend on the parameters to be tuned. The class of system norms under consideration includes the H 2 norm, H ∞ norm, Hankel norm, and Schatten p-norm. Also, the parameter tuning problem for ensuring the robust stability of the system under structural uncertainties is shown to be solved by geometric programming. The proposed optimization framework is further extended to delayed positive linear systems, where it is shown that the parameter tuning problem jointly constrained by the exponential decay rate, the L 1 -gain, and the L ∞ -gain can be solved by convex optimization. The assumption on the system parameterization is stated in terms of posynomial functions, which form a broad class of functions and thus allow us to deal with various interesting positive linear systems arising from, for example, dynamical buffer networks and epidemic spreading processes. We present numerical examples to illustrate the effectiveness of the proposed optimization framework. | - |
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 | Delayed linear systems | - |
dc.subject | geometric programming | - |
dc.subject | $H^2$ norm | - |
dc.subject | $H^infty$ norm | - |
dc.subject | Hankel norm | - |
dc.title | Geometric Programming for Optimal Positive Linear Systems | - |
dc.type | Article | - |
dc.identifier.email | Lam, J: jlam@hku.hk | - |
dc.identifier.authority | Lam, J=rp00133 | - |
dc.description.nature | link_to_subscribed_fulltext | - |
dc.identifier.doi | 10.1109/TAC.2019.2960697 | - |
dc.identifier.scopus | eid_2-s2.0-85095690866 | - |
dc.identifier.hkuros | 325360 | - |
dc.identifier.volume | 65 | - |
dc.identifier.issue | 11 | - |
dc.identifier.spage | 4648 | - |
dc.identifier.epage | 4663 | - |
dc.identifier.isi | WOS:000583711500012 | - |
dc.publisher.place | United States | - |