### 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 language | English |
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Title of host publication | IFAC Proceedings Volumes (IFAC-PapersOnline) |

Pages | 144-149 |

Number of pages | 6 |

Volume | 3 |

Edition | PART 1 |

Publication status | Published - 2009 |

Event | 3rd IFAC Conference on Analysis and Design of Hybrid Systems, ADHS'09 - Zaragoza Duration: 2009 Sep 16 → 2009 Sep 18 |

### Other

Other | 3rd IFAC Conference on Analysis and Design of Hybrid Systems, ADHS'09 |
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City | Zaragoza |

Period | 09/9/16 → 09/9/18 |

### Fingerprint

### Keywords

- Constraint programming
- Hybrid systems
- Interval arithmetic

### ASJC Scopus subject areas

- Control and Systems Engineering

### Cite this

*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.

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

*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.

}

TY - GEN

T1 - Interval-based solving of hybrid constraint systems

AU - Ishii, Daisuke

AU - Ueda, Kazunori

AU - Hosobe, Hiroshi

AU - Goldsztejn, Alexandre

PY - 2009

Y1 - 2009

N2 - 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.

AB - 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.

KW - Constraint programming

KW - Hybrid systems

KW - Interval arithmetic

UR - http://www.scopus.com/inward/record.url?scp=79960952956&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=79960952956&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:79960952956

SN - 9783902661593

VL - 3

SP - 144

EP - 149

BT - IFAC Proceedings Volumes (IFAC-PapersOnline)

ER -