Computing a basin of attraction to a target region by solving bilinear semi-definite problems

Zhikun She; Bai Xue

doi:10.1007/978-3-642-23568-9_26

Computing a basin of attraction to a target region by solving bilinear semi-definite problems

Zhikun She^*
, Bai Xue

^*Corresponding author for this work

School of Mathematical Sciences

Beihang University

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

7 Scopus citations

Abstract

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.

Original language	English
Title of host publication	Computer Algebra in Scientific Computing - 13th International Workshop, CASC 2011, Proceedings
Pages	333-344
Number of pages	12
DOIs	https://doi.org/10.1007/978-3-642-23568-9_26
State	Published - 2011
Event	13th International Workshop on Computer Algebra in Scientific Computing, CASC 2011 - Kassel, Germany Duration: 5 Sep 2011 → 9 Sep 2011

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	6885 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	13th International Workshop on Computer Algebra in Scientific Computing, CASC 2011
Country/Territory	Germany
City	Kassel
Period	5/09/11 → 9/09/11

Access to Document

10.1007/978-3-642-23568-9_26

Cite this

She, Z., & Xue, B. (2011). Computing a basin of attraction to a target region by solving bilinear semi-definite problems. In Computer Algebra in Scientific Computing - 13th International Workshop, CASC 2011, Proceedings (pp. 333-344). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 6885 LNCS). https://doi.org/10.1007/978-3-642-23568-9_26

She, Zhikun ; Xue, Bai. / Computing a basin of attraction to a target region by solving bilinear semi-definite problems. Computer Algebra in Scientific Computing - 13th International Workshop, CASC 2011, Proceedings. 2011. pp. 333-344 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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abstract = "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.",

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She, Z & Xue, B 2011, Computing a basin of attraction to a target region by solving bilinear semi-definite problems. in Computer Algebra in Scientific Computing - 13th International Workshop, CASC 2011, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 6885 LNCS, pp. 333-344, 13th International Workshop on Computer Algebra in Scientific Computing, CASC 2011, Kassel, Germany, 5/09/11. https://doi.org/10.1007/978-3-642-23568-9_26

Computing a basin of attraction to a target region by solving bilinear semi-definite problems. / She, Zhikun; Xue, Bai.
Computer Algebra in Scientific Computing - 13th International Workshop, CASC 2011, Proceedings. 2011. p. 333-344 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 6885 LNCS).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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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.

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She Z, Xue B. Computing a basin of attraction to a target region by solving bilinear semi-definite problems. In Computer Algebra in Scientific Computing - 13th International Workshop, CASC 2011, Proceedings. 2011. p. 333-344. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-642-23568-9_26

Computing a basin of attraction to a target region by solving bilinear semi-definite problems

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