Towards Integrating Hybrid DAEs with a High-Index DAE Solver

Nedialko S. Nedialkov (1) , Nacim Ramdani (2)

1 McMaster University - Department of Computing and Software
2 COPRIN - Constraints solving, optimization and robust interval analysis

J.D. Pryce and N.S. Nedialkov have developed a Taylor series method and a C++ package, DaeTs, for solving numerically an initial-value problem differential-algebraic equation (DAE) that can be of high index, high order, nonlinear, and fully implicit. Numerical results have shown this method to be efficient and very accurate, and particularly suitable for problems that are of too high an index for present DAE solvers. However, DaeTs cannot be applied to systems of DAEs that change at points it time, also called hybrid or multi-mode DAEs. This paper presents methods for extending Daets with the capability to integrate hybrid DAEs. Methods for event location and consistent initializations are given. Daets is applied to simulate a model of a parallel robot: a hybrid system of index-3 DAEs with closed-loop control.

Mots clés: high-index differential-algebraic equations; hybrid systems; structural analysis; consistent initialization

Domaines: Robotique [cs.RO]; Systèmes dynamiques [math.DS]

Nedialko S. Nedialkov, Nacim Ramdani. Towards Integrating Hybrid DAEs with a High-Index DAE Solver. [Research Report] RR-6834, INRIA. 2009, pp.16. ⟨inria-00360999⟩