A Modified GMRES Method for Solving a Symmetric Solution to Lyapunov Equation for Multi-Agent Systems
We consider solving a large-scale Lyapunov equation for a multi-agent system. As is well known, the Lyapunov equation can be solved by equivalently rewriting it as a system of linear equations. The difficulties in solving this system are memory requirement and computational complexity due to the lar...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Taylor & Francis Group
2019-11-01
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| Series: | SICE Journal of Control, Measurement, and System Integration |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.9746/jcmsi.12.223 |
| _version_ | 1797661000269299712 |
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| author | Asuka Ohashi Kiyotsugu Takaba |
| author_facet | Asuka Ohashi Kiyotsugu Takaba |
| author_sort | Asuka Ohashi |
| collection | DOAJ |
| description | We consider solving a large-scale Lyapunov equation for a multi-agent system. As is well known, the Lyapunov equation can be solved by equivalently rewriting it as a system of linear equations. The difficulties in solving this system are memory requirement and computational complexity due to the large-scale coefficient matrix involving a number of Kronecker products. This paper presents a modified GMRES method for solving the aforementioned system of linear equations taking account of its tensor structure and the symmetry of the unknown matrix in the Lyapunov equation. Through numerical experiments, the improvement in memory requirement and computational time by the present algorithms is verified in comparison with the previous GMRES-based methods. |
| first_indexed | 2024-03-11T18:39:04Z |
| format | Article |
| id | doaj.art-b038db023935473facf192095e8a8b57 |
| institution | Directory Open Access Journal |
| issn | 1884-9970 |
| language | English |
| last_indexed | 2024-03-11T18:39:04Z |
| publishDate | 2019-11-01 |
| publisher | Taylor & Francis Group |
| record_format | Article |
| series | SICE Journal of Control, Measurement, and System Integration |
| spelling | doaj.art-b038db023935473facf192095e8a8b572023-10-12T13:43:55ZengTaylor & Francis GroupSICE Journal of Control, Measurement, and System Integration1884-99702019-11-0112622322710.9746/jcmsi.12.22312103274A Modified GMRES Method for Solving a Symmetric Solution to Lyapunov Equation for Multi-Agent SystemsAsuka Ohashi0Kiyotsugu Takaba1College of Science and Engineering, Ritsumeikan UniversityCollege of Science and Engineering, Ritsumeikan UniversityWe consider solving a large-scale Lyapunov equation for a multi-agent system. As is well known, the Lyapunov equation can be solved by equivalently rewriting it as a system of linear equations. The difficulties in solving this system are memory requirement and computational complexity due to the large-scale coefficient matrix involving a number of Kronecker products. This paper presents a modified GMRES method for solving the aforementioned system of linear equations taking account of its tensor structure and the symmetry of the unknown matrix in the Lyapunov equation. Through numerical experiments, the improvement in memory requirement and computational time by the present algorithms is verified in comparison with the previous GMRES-based methods.http://dx.doi.org/10.9746/jcmsi.12.223lyapunov equationsymmetric solutionmulti-agent systemtensorn-mode product |
| spellingShingle | Asuka Ohashi Kiyotsugu Takaba A Modified GMRES Method for Solving a Symmetric Solution to Lyapunov Equation for Multi-Agent Systems SICE Journal of Control, Measurement, and System Integration lyapunov equation symmetric solution multi-agent system tensor n-mode product |
| title | A Modified GMRES Method for Solving a Symmetric Solution to Lyapunov Equation for Multi-Agent Systems |
| title_full | A Modified GMRES Method for Solving a Symmetric Solution to Lyapunov Equation for Multi-Agent Systems |
| title_fullStr | A Modified GMRES Method for Solving a Symmetric Solution to Lyapunov Equation for Multi-Agent Systems |
| title_full_unstemmed | A Modified GMRES Method for Solving a Symmetric Solution to Lyapunov Equation for Multi-Agent Systems |
| title_short | A Modified GMRES Method for Solving a Symmetric Solution to Lyapunov Equation for Multi-Agent Systems |
| title_sort | modified gmres method for solving a symmetric solution to lyapunov equation for multi agent systems |
| topic | lyapunov equation symmetric solution multi-agent system tensor n-mode product |
| url | http://dx.doi.org/10.9746/jcmsi.12.223 |
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