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Conference Paper: On the complexity of SOS programming: formulas for general cases and exact reductions
| Title | On the complexity of SOS programming: formulas for general cases and exact reductions |
|---|---|
| Authors | |
| Issue Date | 2017 |
| Publisher | The Society of Instrument and Control Engineers (SICE). |
| Citation | Proceedings of the 2017 SICE International Symposium on Control Systems (ISCS 2017), Okayama, Japan, 6-9 March 2017 How to Cite? |
| Abstract | The minimization of a linear cost function subject to the condition that some matrix polynomials depending linearly on the decision variables are sums of squares of matrix polynomials (SOS) is known as SOS programming. This paper proposes an analysis of the complexity of SOS programming, in particular of the number of linear matrix inequality (LMI) scalar variables required for establishing whether a matrix polynomial is SOS. This number is analyzed in the general case and in the case of some exact reductions achievable for some classes of matrix polynomials. An analytical formula is proposed in each case in order to provide this number as a function of the number of polynomial variables, degree and size of the matrix polynomials. Some tables reporting this number are also provided as reference for the reader. An application in robust stability analysis of polytopic systems is presented to show the usefulness of the proposed results. |
| Description | Session: Robust Control - no. 6 |
| Persistent Identifier | http://hdl.handle.net/10722/242355 |
| ISBN |
| DC Field | Value | Language |
|---|---|---|
| dc.contributor.author | Chesi, G | - |
| dc.date.accessioned | 2017-07-24T01:38:40Z | - |
| dc.date.available | 2017-07-24T01:38:40Z | - |
| dc.date.issued | 2017 | - |
| dc.identifier.citation | Proceedings of the 2017 SICE International Symposium on Control Systems (ISCS 2017), Okayama, Japan, 6-9 March 2017 | - |
| dc.identifier.isbn | 978-4-907764-54-8 | - |
| dc.identifier.uri | http://hdl.handle.net/10722/242355 | - |
| dc.description | Session: Robust Control - no. 6 | - |
| dc.description.abstract | The minimization of a linear cost function subject to the condition that some matrix polynomials depending linearly on the decision variables are sums of squares of matrix polynomials (SOS) is known as SOS programming. This paper proposes an analysis of the complexity of SOS programming, in particular of the number of linear matrix inequality (LMI) scalar variables required for establishing whether a matrix polynomial is SOS. This number is analyzed in the general case and in the case of some exact reductions achievable for some classes of matrix polynomials. An analytical formula is proposed in each case in order to provide this number as a function of the number of polynomial variables, degree and size of the matrix polynomials. Some tables reporting this number are also provided as reference for the reader. An application in robust stability analysis of polytopic systems is presented to show the usefulness of the proposed results. | - |
| dc.language | eng | - |
| dc.publisher | The Society of Instrument and Control Engineers (SICE). | - |
| dc.relation.ispartof | SICE International Symposium on Control Systems | - |
| dc.title | On the complexity of SOS programming: formulas for general cases and exact reductions | - |
| dc.type | Conference_Paper | - |
| dc.identifier.email | Chesi, G: chesi@eee.hku.hk | - |
| dc.identifier.authority | Chesi, G=rp00100 | - |
| dc.identifier.hkuros | 273432 | - |
| dc.publisher.place | Japan | - |