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 |
|---|---|
| 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 |
|---|---|
| City | Zaragoza |
| Period | 09/9/16 → 09/9/18 |
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Keywords
- Constraint programming
- Hybrid systems
- Interval arithmetic
ASJC Scopus subject areas
- Control and Systems Engineering
Cite this
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 proceeding › Conference contribution
}
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 -