Numerical solution of hybrid systems of differential-algebraic equations

We present a mathematical framework for general over- and under-determined 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.