A numerical algebraic geometry approach to regional stability analysis of polynomial systems
We explore region of attraction (ROA) estimation for polynomial systems via the numerical solution of polynomial equations. Computing an optimal, stable sub-level set of a Lyapunov function is first posed as a polynomial optimization problem. Solutions to this optimization problem are found by solvi...
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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/1721.1/90911 https://orcid.org/0000-0002-8935-7449 https://orcid.org/0000-0002-8712-7092 |
| _version_ | 1811084696361107456 |
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| author | Wampler, Charles Permenter, Frank Noble Tedrake, Russell Louis |
| author2 | Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory |
| author_facet | Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory Wampler, Charles Permenter, Frank Noble Tedrake, Russell Louis |
| author_sort | Wampler, Charles |
| collection | MIT |
| description | We explore region of attraction (ROA) estimation for polynomial systems via the numerical solution of polynomial equations. Computing an optimal, stable sub-level set of a Lyapunov function is first posed as a polynomial optimization problem. Solutions to this optimization problem are found by solving a polynomial system of equations using techniques from numerical algebraic geometry. This system describes KKT points and singular points not satisfying a regularity condition. Though this system has exponentially many solutions, the proposed method trivially parallelizes and is practical for problems of moderate dimension and degree. In suitably generic settings, the method can solve the underlying optimization problem to arbitrary precision, which could make it a useful tool for studying popular semidefinite programming based relaxations used in ROA analysis. |
| first_indexed | 2024-09-23T12:56:10Z |
| format | Article |
| id | mit-1721.1/90911 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T12:56:10Z |
| publishDate | 2014 |
| publisher | Institute of Electrical and Electronics Engineers (IEEE) |
| record_format | dspace |
| spelling | mit-1721.1/909112022-09-28T10:56:34Z A numerical algebraic geometry approach to regional stability analysis of polynomial systems Wampler, Charles Permenter, Frank Noble Tedrake, Russell Louis Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science Permenter, Frank Noble Tedrake, Russell Louis We explore region of attraction (ROA) estimation for polynomial systems via the numerical solution of polynomial equations. Computing an optimal, stable sub-level set of a Lyapunov function is first posed as a polynomial optimization problem. Solutions to this optimization problem are found by solving a polynomial system of equations using techniques from numerical algebraic geometry. This system describes KKT points and singular points not satisfying a regularity condition. Though this system has exponentially many solutions, the proposed method trivially parallelizes and is practical for problems of moderate dimension and degree. In suitably generic settings, the method can solve the underlying optimization problem to arbitrary precision, which could make it a useful tool for studying popular semidefinite programming based relaxations used in ROA analysis. 2014-10-14T14:02:46Z 2014-10-14T14:02:46Z 2013-06 Article http://purl.org/eprint/type/ConferencePaper 978-1-4799-0178-4 978-1-4799-0177-7 978-1-4799-0175-3 0743-1619 http://hdl.handle.net/1721.1/90911 Permenter, Frank, Charles Wampler, and Russ Tedrake. “A Numerical Algebraic Geometry Approach to Regional Stability Analysis of Polynomial Systems.” 2013 American Control Conference (June 2013). https://orcid.org/0000-0002-8935-7449 https://orcid.org/0000-0002-8712-7092 en_US http://dx.doi.org/10.1109/ACC.2013.6580150 Proceedings of the 2013 American Control Conference Creative Commons Attribution-Noncommercial-Share Alike http://creativecommons.org/licenses/by-nc-sa/4.0/ application/pdf Institute of Electrical and Electronics Engineers (IEEE) MIT web domain |
| spellingShingle | Wampler, Charles Permenter, Frank Noble Tedrake, Russell Louis A numerical algebraic geometry approach to regional stability analysis of polynomial systems |
| title | A numerical algebraic geometry approach to regional stability analysis of polynomial systems |
| title_full | A numerical algebraic geometry approach to regional stability analysis of polynomial systems |
| title_fullStr | A numerical algebraic geometry approach to regional stability analysis of polynomial systems |
| title_full_unstemmed | A numerical algebraic geometry approach to regional stability analysis of polynomial systems |
| title_short | A numerical algebraic geometry approach to regional stability analysis of polynomial systems |
| title_sort | numerical algebraic geometry approach to regional stability analysis of polynomial systems |
| url | http://hdl.handle.net/1721.1/90911 https://orcid.org/0000-0002-8935-7449 https://orcid.org/0000-0002-8712-7092 |
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