Existence of Solutions for the Continuous Algebraic Riccati Equation via Polynomial Optimization
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866916368970940416 |
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| author | Zhang, Juan Zhao, Wenjie |
| author_facet | Zhang, Juan Zhao, Wenjie |
| contents | This paper studies the solution existence of the continuous-time algebraic Riccati equation (CARE). We formulate the CARE as two constrained polynomial optimization problems, and then use Lasserre's hierarchy of semi-definite relaxations to solve them. Compared to the existing work, our approaches can obtain the exact positive semi-definite solution of the CARE when the coefficient matrices are symmetric. Moreover, our methods can detect the nonexistence of the positive semi-definite solution for the CARE. Numerical examples show that our approaches are effective compared to the existing methods. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_13780 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Existence of Solutions for the Continuous Algebraic Riccati Equation via Polynomial Optimization Zhang, Juan Zhao, Wenjie Optimization and Control This paper studies the solution existence of the continuous-time algebraic Riccati equation (CARE). We formulate the CARE as two constrained polynomial optimization problems, and then use Lasserre's hierarchy of semi-definite relaxations to solve them. Compared to the existing work, our approaches can obtain the exact positive semi-definite solution of the CARE when the coefficient matrices are symmetric. Moreover, our methods can detect the nonexistence of the positive semi-definite solution for the CARE. Numerical examples show that our approaches are effective compared to the existing methods. |
| title | Existence of Solutions for the Continuous Algebraic Riccati Equation via Polynomial Optimization |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2408.13780 |