Abstract
In this paper we show that Sum-of-Squares optimization can be used to find optimal semialgebraic representations of sets. These sets may be explicitly defined, as in the case of discrete points or unions of sets; or implicitly defined, as in the case of attractors of nonlinear systems. We define optimality in the sense of minimum volume, while satisfying constraints that can include set containment, convexity, or Lyapunov stability conditions. Our admittedly heuristic approach to volume minimization is based on the use of a determinant-like objective function. We provide numerical examples for the Lorenz attractor and the Van der Pol limit cycle.
| Original language | English (US) |
|---|---|
| Title of host publication | 2019 American Control Conference, ACC 2019 |
| Publisher | Institute of Electrical and Electronics Engineers Inc. |
| Pages | 2084-2091 |
| Number of pages | 8 |
| ISBN (Electronic) | 9781538679265 |
| State | Published - Jul 1 2019 |
| Event | 2019 American Control Conference, ACC 2019 - Philadelphia, United States Duration: Jul 10 2019 → Jul 12 2019 |
Publication series
| Name | Proceedings of the American Control Conference |
|---|---|
| Volume | 2019-July |
| ISSN (Print) | 0743-1619 |
Conference
| Conference | 2019 American Control Conference, ACC 2019 |
|---|---|
| Country | United States |
| City | Philadelphia |
| Period | 7/10/19 → 7/12/19 |
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ASJC Scopus subject areas
- Electrical and Electronic Engineering
Cite this
Using SOS for optimal semialgebraic representation of sets : Finding minimal representations of limit cycles, chaotic attractors and unions. / Jones, Morgan; Peet, Matthew.
2019 American Control Conference, ACC 2019. Institute of Electrical and Electronics Engineers Inc., 2019. p. 2084-2091 8814848 (Proceedings of the American Control Conference; Vol. 2019-July).Research output: Chapter in Book/Report/Conference proceeding › Conference contribution
}
TY - GEN
T1 - Using SOS for optimal semialgebraic representation of sets
T2 - Finding minimal representations of limit cycles, chaotic attractors and unions
AU - Jones, Morgan
AU - Peet, Matthew
PY - 2019/7/1
Y1 - 2019/7/1
N2 - In this paper we show that Sum-of-Squares optimization can be used to find optimal semialgebraic representations of sets. These sets may be explicitly defined, as in the case of discrete points or unions of sets; or implicitly defined, as in the case of attractors of nonlinear systems. We define optimality in the sense of minimum volume, while satisfying constraints that can include set containment, convexity, or Lyapunov stability conditions. Our admittedly heuristic approach to volume minimization is based on the use of a determinant-like objective function. We provide numerical examples for the Lorenz attractor and the Van der Pol limit cycle.
AB - In this paper we show that Sum-of-Squares optimization can be used to find optimal semialgebraic representations of sets. These sets may be explicitly defined, as in the case of discrete points or unions of sets; or implicitly defined, as in the case of attractors of nonlinear systems. We define optimality in the sense of minimum volume, while satisfying constraints that can include set containment, convexity, or Lyapunov stability conditions. Our admittedly heuristic approach to volume minimization is based on the use of a determinant-like objective function. We provide numerical examples for the Lorenz attractor and the Van der Pol limit cycle.
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M3 - Conference contribution
AN - SCOPUS:85072299272
T3 - Proceedings of the American Control Conference
SP - 2084
EP - 2091
BT - 2019 American Control Conference, ACC 2019
PB - Institute of Electrical and Electronics Engineers Inc.
ER -