Abstract. We present a mathematical framework for general over-and underdetermined hybrid (switched) systems of differential-algebraic equations (HDAEs). We give a systematic formulation of HDAEs and discuss existence and uniqueness of solutions, the treatment of the switch points and how to perform consistent initialization at switch points.We show how numerical solution methods for DAEs can be adapted for HDAEs and present a numerical results for these methods for the real world example of simulating an automatic gearbox.

Mechatronic shifting simulation of automated transmissions in commercial vehicles is used for optimization and development in today's truck engineering departments at Daimler. Within the ITEA2 project Modelisar in cooperation with ITI GmbH and SIM-PACK AG this application served as a usecase for proof of concept of the newly developed Functional Mock-Up interfaces (FMI). Utilizing these standardized interfaces models from different tools are coupled to build up the overall system for the mechatronic shifting simulation. The coupling via FMI for Model Exchange was achieved for control modules from MATLAB/Simulink into the SimulationX powertrain model and secondly from the 1D-multiphysics powertrain in SimulationX into multibody vehicle in SIMPACK. Furthermore FMI for Co-Simulation was investigated in a pure SimulationX framework for the powertrain model. Very promising results can be observed as for modeling as for simulation processes. The FMI technology has clearly shown its capability to be applied in the productive simulation process.