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

Department of Aeronautics and Astronautics

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

18 Citations (Scopus)

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
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

Publication series

Name	43rd Annual Allerton Conference on Communication, Control and Computing 2005
Volume	2

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

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 (pp. 640-649). (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.

Wang, Ta Chung ; Lall, Sanjay ; West, Matthew. / Polynomial level-set methods for nonlinear dynamical systems analysis. 43rd Annual Allerton Conference on Communication, Control and Computing 2005. University of Illinois at Urbana-Champaign, Coordinated Science Laboratory and Department of Computer and Electrical Engineering, 2005. pp. 640-649 (43rd Annual Allerton Conference on Communication, Control and Computing 2005).

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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 = "Wang, {Ta Chung} and Sanjay Lall and Matthew West",

year = "2005",

language = "English",

series = "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",

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

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

}

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

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

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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.

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M3 - Conference contribution

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T3 - 43rd Annual Allerton Conference on Communication, Control and Computing 2005

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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

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Y2 - 28 September 2005 through 30 September 2005

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Wang TC, Lall S, West M. Polynomial level-set methods for nonlinear dynamical systems analysis. In 43rd Annual Allerton Conference on Communication, Control and Computing 2005. University of Illinois at Urbana-Champaign, Coordinated Science Laboratory and Department of Computer and Electrical Engineering. 2005. p. 640-649. (43rd Annual Allerton Conference on Communication, Control and Computing 2005).

Polynomial level-set methods for nonlinear dynamical systems analysis

Abstract

Publication series

Other

All Science Journal Classification (ASJC) codes

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