Projection onto the Set of Rank-Constrained Structured Matrices for Reduced-Order Controller Design
In this paper, we propose an efficient numerical computation method of reduced-order controller design for linear time-invariant systems. The design problem is described by linear matrix inequalities (LMIs) with a rank constraint on a structured matrix, due to which the problem is non-convex. Instea...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-09-01
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| Series: | Algorithms |
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| Online Access: | https://www.mdpi.com/1999-4893/15/9/322 |
| _version_ | 1797492013487095808 |
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| author | Masaaki Nagahara Yu Iwai Noboru Sebe |
| author_facet | Masaaki Nagahara Yu Iwai Noboru Sebe |
| author_sort | Masaaki Nagahara |
| collection | DOAJ |
| description | In this paper, we propose an efficient numerical computation method of reduced-order controller design for linear time-invariant systems. The design problem is described by linear matrix inequalities (LMIs) with a rank constraint on a structured matrix, due to which the problem is non-convex. Instead of the heuristic method that approximates the matrix rank by the nuclear norm, we propose a numerical projection onto the rank-constrained set based on the alternating direction method of multipliers (ADMM). Then the controller is obtained by alternating projection between the rank-constrained set and the LMI set. We show the effectiveness of the proposed method compared with existing heuristic methods, by using 95 benchmark models from the COMPL<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mrow></mrow><mi>e</mi></msub></semantics></math></inline-formula>ib library. |
| first_indexed | 2024-03-10T00:57:29Z |
| format | Article |
| id | doaj.art-3032165ddb774ff99b1da04e9ffb8679 |
| institution | Directory Open Access Journal |
| issn | 1999-4893 |
| language | English |
| last_indexed | 2024-03-10T00:57:29Z |
| publishDate | 2022-09-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Algorithms |
| spelling | doaj.art-3032165ddb774ff99b1da04e9ffb86792023-11-23T14:40:23ZengMDPI AGAlgorithms1999-48932022-09-0115932210.3390/a15090322Projection onto the Set of Rank-Constrained Structured Matrices for Reduced-Order Controller DesignMasaaki Nagahara0Yu Iwai1Noboru Sebe2Institute of Environmental Science and Technology, The University of Kitakyushu, Fukuoka 808-0135, JapanFaculty of Environmental Engineering, The University of Kitakyushu, Fukuoka 808-0135, JapanFaculty of Computer Science and Systems Engineering, Kyushu Institute of Technology, Fukuoka 820-8502, JapanIn this paper, we propose an efficient numerical computation method of reduced-order controller design for linear time-invariant systems. The design problem is described by linear matrix inequalities (LMIs) with a rank constraint on a structured matrix, due to which the problem is non-convex. Instead of the heuristic method that approximates the matrix rank by the nuclear norm, we propose a numerical projection onto the rank-constrained set based on the alternating direction method of multipliers (ADMM). Then the controller is obtained by alternating projection between the rank-constrained set and the LMI set. We show the effectiveness of the proposed method compared with existing heuristic methods, by using 95 benchmark models from the COMPL<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mrow></mrow><mi>e</mi></msub></semantics></math></inline-formula>ib library.https://www.mdpi.com/1999-4893/15/9/322reduced-order controlrank constraintlinear matrix inequalityalternating projectionconvex optimization |
| spellingShingle | Masaaki Nagahara Yu Iwai Noboru Sebe Projection onto the Set of Rank-Constrained Structured Matrices for Reduced-Order Controller Design Algorithms reduced-order control rank constraint linear matrix inequality alternating projection convex optimization |
| title | Projection onto the Set of Rank-Constrained Structured Matrices for Reduced-Order Controller Design |
| title_full | Projection onto the Set of Rank-Constrained Structured Matrices for Reduced-Order Controller Design |
| title_fullStr | Projection onto the Set of Rank-Constrained Structured Matrices for Reduced-Order Controller Design |
| title_full_unstemmed | Projection onto the Set of Rank-Constrained Structured Matrices for Reduced-Order Controller Design |
| title_short | Projection onto the Set of Rank-Constrained Structured Matrices for Reduced-Order Controller Design |
| title_sort | projection onto the set of rank constrained structured matrices for reduced order controller design |
| topic | reduced-order control rank constraint linear matrix inequality alternating projection convex optimization |
| url | https://www.mdpi.com/1999-4893/15/9/322 |
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