Interval-based solving of hybrid constraint systems

Daisuke Ishii, Kazunori Ueda, Hiroshi Hosobe, Alexandre Goldsztejn

    Research output: Chapter in Book/Report/Conference proceedingConference contribution

    4 Citations (Scopus)

    Abstract

    An approach to reliable modeling, simulation and verification of hybrid systems is interval arithmetic, which guarantees that a set of intervals narrower than specified size encloses the solution. Interval-based computation of hybrid systems is often difficult, especially when the systems are described by nonlinear ordinary differential equations (ODEs) and nonlinear algebraic equations. We formulate the problem of detecting a discrete change in hybrid systems as a hybrid constraint system (HCS), consisting of a flow constraint on trajectories (i.e. continuous functions over time) and a guard constraint on states causing discrete changes. We also propose a technique for solving HCSs by coordinating (i) interval-based solving of nonlinear ODEs, and (ii) a constraint programming technique for reducing interval enclosures of solutions. The proposed technique reliably solves HCSs with nonlinear constraints. Our technique employs the interval Newton method to accelerate the reduction of interval enclosures, while guaranteeing that the enclosure contains a solution.

    Original languageEnglish
    Title of host publicationIFAC Proceedings Volumes (IFAC-PapersOnline)
    Pages144-149
    Number of pages6
    Volume3
    EditionPART 1
    Publication statusPublished - 2009
    Event3rd IFAC Conference on Analysis and Design of Hybrid Systems, ADHS'09 - Zaragoza
    Duration: 2009 Sep 162009 Sep 18

    Other

    Other3rd IFAC Conference on Analysis and Design of Hybrid Systems, ADHS'09
    CityZaragoza
    Period09/9/1609/9/18

    Fingerprint

    Enclosures
    Hybrid systems
    Ordinary differential equations
    Newton-Raphson method
    Nonlinear equations
    Trajectories
    Computer simulation

    Keywords

    • Constraint programming
    • Hybrid systems
    • Interval arithmetic

    ASJC Scopus subject areas

    • Control and Systems Engineering

    Cite this

    Ishii, D., Ueda, K., Hosobe, H., & Goldsztejn, A. (2009). Interval-based solving of hybrid constraint systems. In IFAC Proceedings Volumes (IFAC-PapersOnline) (PART 1 ed., Vol. 3, pp. 144-149)

    Interval-based solving of hybrid constraint systems. / Ishii, Daisuke; Ueda, Kazunori; Hosobe, Hiroshi; Goldsztejn, Alexandre.

    IFAC Proceedings Volumes (IFAC-PapersOnline). Vol. 3 PART 1. ed. 2009. p. 144-149.

    Research output: Chapter in Book/Report/Conference proceedingConference contribution

    Ishii, D, Ueda, K, Hosobe, H & Goldsztejn, A 2009, Interval-based solving of hybrid constraint systems. in IFAC Proceedings Volumes (IFAC-PapersOnline). PART 1 edn, vol. 3, pp. 144-149, 3rd IFAC Conference on Analysis and Design of Hybrid Systems, ADHS'09, Zaragoza, 09/9/16.
    Ishii D, Ueda K, Hosobe H, Goldsztejn A. Interval-based solving of hybrid constraint systems. In IFAC Proceedings Volumes (IFAC-PapersOnline). PART 1 ed. Vol. 3. 2009. p. 144-149
    Ishii, Daisuke ; Ueda, Kazunori ; Hosobe, Hiroshi ; Goldsztejn, Alexandre. / Interval-based solving of hybrid constraint systems. IFAC Proceedings Volumes (IFAC-PapersOnline). Vol. 3 PART 1. ed. 2009. pp. 144-149
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