Polynomial level-set methods for nonlinear dynamical systems analysis

Ta-Chung Wang; Sanjay Lall; Matthew West

Polynomial level-set methods for nonlinear dynamical systems analysis

Ta-Chung Wang, Sanjay Lall, Matthew West

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

Abstract

In this paper, we present a method for computing the domain of attraction for non-linear dynamical systems. We propose a level-set method where sets are represented as sublevel sets of polynomials. The problem of flowing these sets under the advection map of a dynamical system is converted to a semidefinite program, which we use to compute the coeficients of the polynomials. We further address the related problems of constraining the degree of the polynomials and the connectedness of the associated sets.

Original language	English
Title of host publication	43rd Annual Allerton Conference on Communication, Control and Computing 2005
Publisher	University of Illinois at Urbana-Champaign, Coordinated Science Laboratory and Department of Computer and Electrical Engineering
Pages	640-649
Number of pages	10
Volume	2
ISBN (Electronic)	9781604234916
Publication status	Published - 2005
Event	43rd Annual Allerton Conference on Communication, Control and Computing 2005 - Monticello, United States Duration: 2005 Sept 28 → 2005 Sept 30

Other

Other	43rd Annual Allerton Conference on Communication, Control and Computing 2005
Country/Territory	United States
City	Monticello
Period	05-09-28 → 05-09-30

All Science Journal Classification (ASJC) codes

Computer Networks and Communications
Computer Science Applications

Cite this

@inproceedings{22450f6c4e38414ea99c00a85803c690,

title = "Polynomial level-set methods for nonlinear dynamical systems analysis",

abstract = "In this paper, we present a method for computing the domain of attraction for non-linear dynamical systems. We propose a level-set method where sets are represented as sublevel sets of polynomials. The problem of flowing these sets under the advection map of a dynamical system is converted to a semidefinite program, which we use to compute the coeficients of the polynomials. We further address the related problems of constraining the degree of the polynomials and the connectedness of the associated sets.",

author = "Ta-Chung Wang and Sanjay Lall and Matthew West",

year = "2005",

language = "English",

volume = "2",

pages = "640--649",

booktitle = "43rd Annual Allerton Conference on Communication, Control and Computing 2005",

publisher = "University of Illinois at Urbana-Champaign, Coordinated Science Laboratory and Department of Computer and Electrical Engineering",

note = "43rd Annual Allerton Conference on Communication, Control and Computing 2005 ; Conference date: 28-09-2005 Through 30-09-2005",

}

Wang, T-C, Lall, S & West, M 2005, Polynomial level-set methods for nonlinear dynamical systems analysis. in 43rd Annual Allerton Conference on Communication, Control and Computing 2005. vol. 2, University of Illinois at Urbana-Champaign, Coordinated Science Laboratory and Department of Computer and Electrical Engineering, pp. 640-649, 43rd Annual Allerton Conference on Communication, Control and Computing 2005, Monticello, United States, 05-09-28.

Polynomial level-set methods for nonlinear dynamical systems analysis. / Wang, Ta-Chung; Lall, Sanjay; West, Matthew.

43rd Annual Allerton Conference on Communication, Control and Computing 2005. Vol. 2 University of Illinois at Urbana-Champaign, Coordinated Science Laboratory and Department of Computer and Electrical Engineering, 2005. p. 640-649.

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

TY - GEN

T1 - Polynomial level-set methods for nonlinear dynamical systems analysis

AU - Wang, Ta-Chung

AU - Lall, Sanjay

AU - West, Matthew

PY - 2005

Y1 - 2005

N2 - In this paper, we present a method for computing the domain of attraction for non-linear dynamical systems. We propose a level-set method where sets are represented as sublevel sets of polynomials. The problem of flowing these sets under the advection map of a dynamical system is converted to a semidefinite program, which we use to compute the coeficients of the polynomials. We further address the related problems of constraining the degree of the polynomials and the connectedness of the associated sets.

AB - In this paper, we present a method for computing the domain of attraction for non-linear dynamical systems. We propose a level-set method where sets are represented as sublevel sets of polynomials. The problem of flowing these sets under the advection map of a dynamical system is converted to a semidefinite program, which we use to compute the coeficients of the polynomials. We further address the related problems of constraining the degree of the polynomials and the connectedness of the associated sets.

UR - http://www.scopus.com/inward/record.url?scp=84962076535&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84962076535&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:84962076535

VL - 2

SP - 640

EP - 649

BT - 43rd Annual Allerton Conference on Communication, Control and Computing 2005

PB - University of Illinois at Urbana-Champaign, Coordinated Science Laboratory and Department of Computer and Electrical Engineering

T2 - 43rd Annual Allerton Conference on Communication, Control and Computing 2005

Y2 - 28 September 2005 through 30 September 2005

ER -

Polynomial level-set methods for nonlinear dynamical systems analysis

Abstract

Other

All Science Journal Classification (ASJC) codes

Other files and links

Fingerprint

Cite this