TY - GEN
T1 - Interval-based solving of hybrid constraint systems
AU - Ishii, Daisuke
AU - Ueda, Kazunori
AU - Hosobe, Hiroshi
AU - Goldsztejn, Alexandre
N1 - Funding Information:
⋆ This research is partially supported by JSPS, Grant-in-Aid for Young Scientists (B) 20700033.
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
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U2 - 10.3182/20090916-3-es-3003.00026
DO - 10.3182/20090916-3-es-3003.00026
M3 - Conference contribution
AN - SCOPUS:79960952956
SN - 9783902661593
T3 - IFAC Proceedings Volumes (IFAC-PapersOnline)
SP - 144
EP - 149
BT - 3rd IFAC Conference on Analysis and Design of Hybrid Systems, ADHS'09 - Proceedings
PB - IFAC Secretariat
ER -