TY - GEN
T1 - Using SOS for optimal semialgebraic representation of sets
T2 - 2019 American Control Conference, ACC 2019
AU - Jones, Morgan
AU - Peet, Matthew M.
N1 - Funding Information:
This work was supported by the National Science Foundation under grants No. 1538374 and 1739990.
Publisher Copyright:
© 2019 American Automatic Control Council.
PY - 2019/7
Y1 - 2019/7
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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U2 - 10.23919/acc.2019.8814848
DO - 10.23919/acc.2019.8814848
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.
Y2 - 10 July 2019 through 12 July 2019
ER -