Providing a basin of attraction to a target region by computation of Lyapunov-like functions

Stefan Ratschan; Zhikun She

doi:10.1109/ICCCYB.2006.305705

Providing a basin of attraction to a target region by computation of Lyapunov-like functions

Stefan Ratschan^*
, Zhikun She

^*Corresponding author for this work

Czech Academy of Sciences
Max Planck Institute for Informatics

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

13 Scopus citations

Abstract

In this paper, we present a method for computing a basin of attraction to a target region for non-linear ordinary differential equations. This basin of attraction is ensured by a Lyapunov-like polynomial function that we compute using an interval based branch-and-relax algorithm. This algorithm relaxes the necessary conditions on the coefficients of the Lyapunov-like function to a system of linear interval inequalities that can then be solved exactly, and iteratively reduces the relaxation error by recursively decomposing the state space into hyper-rectangles. Tests on an implementation are promising.

Original language	English
Title of host publication	2006 IEEE International Conference on Computational Cybernetics, ICCC
DOIs	https://doi.org/10.1109/ICCCYB.2006.305705
State	Published - 2006
Externally published	Yes
Event	2006 IEEE International Conference on Computational Cybernetics, ICCC - Tallinn, Estonia Duration: 20 Aug 2006 → 22 Aug 2006

Publication series

Name	2006 IEEE International Conference on Computational Cybernetics, ICCC

Conference

Conference	2006 IEEE International Conference on Computational Cybernetics, ICCC
Country/Territory	Estonia
City	Tallinn
Period	20/08/06 → 22/08/06

Access to Document

10.1109/ICCCYB.2006.305705

Cite this

@inproceedings{fc7d6c3345ea4fc5a05650ae7e2c8132,

title = "Providing a basin of attraction to a target region by computation of Lyapunov-like functions",

abstract = "In this paper, we present a method for computing a basin of attraction to a target region for non-linear ordinary differential equations. This basin of attraction is ensured by a Lyapunov-like polynomial function that we compute using an interval based branch-and-relax algorithm. This algorithm relaxes the necessary conditions on the coefficients of the Lyapunov-like function to a system of linear interval inequalities that can then be solved exactly, and iteratively reduces the relaxation error by recursively decomposing the state space into hyper-rectangles. Tests on an implementation are promising.",

author = "Stefan Ratschan and Zhikun She",

year = "2006",

doi = "10.1109/ICCCYB.2006.305705",

language = "英语",

isbn = "1424400716",

series = "2006 IEEE International Conference on Computational Cybernetics, ICCC",

booktitle = "2006 IEEE International Conference on Computational Cybernetics, ICCC",

note = "2006 IEEE International Conference on Computational Cybernetics, ICCC ; Conference date: 20-08-2006 Through 22-08-2006",

}

Ratschan, S & She, Z 2006, Providing a basin of attraction to a target region by computation of Lyapunov-like functions. in 2006 IEEE International Conference on Computational Cybernetics, ICCC., 4097666, 2006 IEEE International Conference on Computational Cybernetics, ICCC, 2006 IEEE International Conference on Computational Cybernetics, ICCC, Tallinn, Estonia, 20/08/06. https://doi.org/10.1109/ICCCYB.2006.305705

Providing a basin of attraction to a target region by computation of Lyapunov-like functions. / Ratschan, Stefan; She, Zhikun.
2006 IEEE International Conference on Computational Cybernetics, ICCC. 2006. 4097666 (2006 IEEE International Conference on Computational Cybernetics, ICCC).

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

TY - GEN

T1 - Providing a basin of attraction to a target region by computation of Lyapunov-like functions

AU - Ratschan, Stefan

AU - She, Zhikun

PY - 2006

Y1 - 2006

N2 - In this paper, we present a method for computing a basin of attraction to a target region for non-linear ordinary differential equations. This basin of attraction is ensured by a Lyapunov-like polynomial function that we compute using an interval based branch-and-relax algorithm. This algorithm relaxes the necessary conditions on the coefficients of the Lyapunov-like function to a system of linear interval inequalities that can then be solved exactly, and iteratively reduces the relaxation error by recursively decomposing the state space into hyper-rectangles. Tests on an implementation are promising.

AB - In this paper, we present a method for computing a basin of attraction to a target region for non-linear ordinary differential equations. This basin of attraction is ensured by a Lyapunov-like polynomial function that we compute using an interval based branch-and-relax algorithm. This algorithm relaxes the necessary conditions on the coefficients of the Lyapunov-like function to a system of linear interval inequalities that can then be solved exactly, and iteratively reduces the relaxation error by recursively decomposing the state space into hyper-rectangles. Tests on an implementation are promising.

UR - https://www.scopus.com/pages/publications/50249132522

U2 - 10.1109/ICCCYB.2006.305705

DO - 10.1109/ICCCYB.2006.305705

M3 - 会议稿件

AN - SCOPUS:50249132522

SN - 1424400716

SN - 9781424400713

T3 - 2006 IEEE International Conference on Computational Cybernetics, ICCC

BT - 2006 IEEE International Conference on Computational Cybernetics, ICCC

T2 - 2006 IEEE International Conference on Computational Cybernetics, ICCC

Y2 - 20 August 2006 through 22 August 2006

ER -

Providing a basin of attraction to a target region by computation of Lyapunov-like functions

Abstract

Publication series

Conference

Access to Document

Other files and links

Fingerprint

Cite this