TY - GEN
T1 - Computing a basin of attraction to a target region by solving bilinear semi-definite problems
AU - She, Zhikun
AU - Xue, Bai
PY - 2011
Y1 - 2011
N2 - In this paper, we present a sum of squares programming based method for computing a basin of attraction to a target region as large as possible by iteratively searching for Lyapunov-like functions. We start with the basic mathematical notions and show how attraction to a target region can be ensured by Lyapunov-like functions. Then, we present an initial framework for getting an increasing sequence of basins of attraction by iteratively computing Lyapunov-like functions. This framework can be realized by solving bilinear semi-definite problems based on sums of squares decomposition. We implement our algorithm and test it on some interesting examples. The computation results show the usefulness of our method.
AB - In this paper, we present a sum of squares programming based method for computing a basin of attraction to a target region as large as possible by iteratively searching for Lyapunov-like functions. We start with the basic mathematical notions and show how attraction to a target region can be ensured by Lyapunov-like functions. Then, we present an initial framework for getting an increasing sequence of basins of attraction by iteratively computing Lyapunov-like functions. This framework can be realized by solving bilinear semi-definite problems based on sums of squares decomposition. We implement our algorithm and test it on some interesting examples. The computation results show the usefulness of our method.
UR - https://www.scopus.com/pages/publications/80052820658
U2 - 10.1007/978-3-642-23568-9_26
DO - 10.1007/978-3-642-23568-9_26
M3 - 会议稿件
AN - SCOPUS:80052820658
SN - 9783642235672
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 333
EP - 344
BT - Computer Algebra in Scientific Computing - 13th International Workshop, CASC 2011, Proceedings
T2 - 13th International Workshop on Computer Algebra in Scientific Computing, CASC 2011
Y2 - 5 September 2011 through 9 September 2011
ER -