Polynomial level-set method for polynomial system reachable set estimation

Ta-Chung Wang, Sanjay Lall, Matthew West

Research output: Contribution to journalArticle

11 Citations (Scopus)

Abstract

In this paper, we present a polynomial level-set method for advecting a semi-algebraic set for polynomial systems. This method uses the sub-level representation of sets. The problem of flowing these sets under the advection map of a dynamical system is converted to a semi-definite program, which is then used to compute the coefficients of the polynomials. The method presented in this paper does not require either the sets being positively invariant or star-shaped. Hence, the proposed algorithm can describe the behavior of system states both inside and outside the domain of attraction and can also be used to describe more complex shapes of sets. We further address the related problems of constraining the degree of the polynomials. Various numerical examples are presented to show the effectiveness of advection approach.

Original languageEnglish
Article number6517253
Pages (from-to)2508-2521
Number of pages14
JournalIEEE Transactions on Automatic Control
Volume58
Issue number10
DOIs
Publication statusPublished - 2013 Oct 7

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Set theory
Polynomials
Advection
Stars
Dynamical systems

All Science Journal Classification (ASJC) codes

  • Control and Systems Engineering
  • Computer Science Applications
  • Electrical and Electronic Engineering

Cite this

Wang, Ta-Chung ; Lall, Sanjay ; West, Matthew. / Polynomial level-set method for polynomial system reachable set estimation. In: IEEE Transactions on Automatic Control. 2013 ; Vol. 58, No. 10. pp. 2508-2521.
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Polynomial level-set method for polynomial system reachable set estimation. / Wang, Ta-Chung; Lall, Sanjay; West, Matthew.

In: IEEE Transactions on Automatic Control, Vol. 58, No. 10, 6517253, 07.10.2013, p. 2508-2521.

Research output: Contribution to journalArticle

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