Interval-based solving of hybrid constraint systems

Daisuke Ishii*, Kazunori Ueda, Hiroshi Hosobe, Alexandre Goldsztejn

*Corresponding author for this work

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

5 Citations (Scopus)


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 publication3rd IFAC Conference on Analysis and Design of Hybrid Systems, ADHS'09 - Proceedings
PublisherIFAC Secretariat
Number of pages6
EditionPART 1
ISBN (Print)9783902661593
Publication statusPublished - 2009

Publication series

NameIFAC Proceedings Volumes (IFAC-PapersOnline)
NumberPART 1
ISSN (Print)1474-6670


  • Constraint programming
  • Hybrid systems
  • Interval arithmetic

ASJC Scopus subject areas

  • Control and Systems Engineering


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