Explicit Solutions for Root Optimization of a Polynomial Family With One Affine Constraint
Given a family of real or complex monic polynomials of fixed degree with one affine constraint on their coefficients, consider the problem of minimizing the root radius (largest modulus of the roots) or root abscissa (largest real part of the roots). We give constructive methods for efficiently comp...
| Main Authors: | , , , |
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| Other Authors: | |
| Format: | Article |
| Language: | en_US |
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Institute of Electrical and Electronics Engineers (IEEE)
2014
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| Online Access: | http://hdl.handle.net/1721.1/90396 https://orcid.org/0000-0001-9088-0205 |
| _version_ | 1826199218276007936 |
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| author | Blondel, Vincent D. Gurbuzbalaban, Mert Megretski, Alexandre Overton, Michael L. |
| author2 | Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science |
| author_facet | Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science Blondel, Vincent D. Gurbuzbalaban, Mert Megretski, Alexandre Overton, Michael L. |
| author_sort | Blondel, Vincent D. |
| collection | MIT |
| description | Given a family of real or complex monic polynomials of fixed degree with one affine constraint on their coefficients, consider the problem of minimizing the root radius (largest modulus of the roots) or root abscissa (largest real part of the roots). We give constructive methods for efficiently computing the globally optimal value as well as an optimal polynomial when the optimal value is attained and an approximation when it is not. An optimal polynomial can always be chosen to have at most two distinct roots in the real case and just one distinct root in the complex case. Examples are presented illustrating the results, including several fixed-order controller optimal design problems. |
| first_indexed | 2024-09-23T11:16:37Z |
| format | Article |
| id | mit-1721.1/90396 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T11:16:37Z |
| publishDate | 2014 |
| publisher | Institute of Electrical and Electronics Engineers (IEEE) |
| record_format | dspace |
| spelling | mit-1721.1/903962022-09-27T18:20:59Z Explicit Solutions for Root Optimization of a Polynomial Family With One Affine Constraint Blondel, Vincent D. Gurbuzbalaban, Mert Megretski, Alexandre Overton, Michael L. Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science Megretski, Alexandre Given a family of real or complex monic polynomials of fixed degree with one affine constraint on their coefficients, consider the problem of minimizing the root radius (largest modulus of the roots) or root abscissa (largest real part of the roots). We give constructive methods for efficiently computing the globally optimal value as well as an optimal polynomial when the optimal value is attained and an approximation when it is not. An optimal polynomial can always be chosen to have at most two distinct roots in the real case and just one distinct root in the complex case. Examples are presented illustrating the results, including several fixed-order controller optimal design problems. 2014-09-26T15:28:04Z 2014-09-26T15:28:04Z 2012-11 2011-12 Article http://purl.org/eprint/type/JournalArticle 0018-9286 1558-2523 http://hdl.handle.net/1721.1/90396 Blondel, V. D., M. Gurbuzbalaban, A. Megretski, and M. L. Overton. “Explicit Solutions for Root Optimization of a Polynomial Family With One Affine Constraint.” IEEE Trans. Automat. Contr. 57, no. 12 (December 2012): 3078–3089. https://orcid.org/0000-0001-9088-0205 en_US http://dx.doi.org/10.1109/tac.2012.2202069 IEEE Transactions on Automatic Control Creative Commons Attribution-Noncommercial-Share Alike http://creativecommons.org/licenses/by-nc-sa/4.0/ application/pdf Institute of Electrical and Electronics Engineers (IEEE) Other univ. web domain |
| spellingShingle | Blondel, Vincent D. Gurbuzbalaban, Mert Megretski, Alexandre Overton, Michael L. Explicit Solutions for Root Optimization of a Polynomial Family With One Affine Constraint |
| title | Explicit Solutions for Root Optimization of a Polynomial Family With One Affine Constraint |
| title_full | Explicit Solutions for Root Optimization of a Polynomial Family With One Affine Constraint |
| title_fullStr | Explicit Solutions for Root Optimization of a Polynomial Family With One Affine Constraint |
| title_full_unstemmed | Explicit Solutions for Root Optimization of a Polynomial Family With One Affine Constraint |
| title_short | Explicit Solutions for Root Optimization of a Polynomial Family With One Affine Constraint |
| title_sort | explicit solutions for root optimization of a polynomial family with one affine constraint |
| url | http://hdl.handle.net/1721.1/90396 https://orcid.org/0000-0001-9088-0205 |
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