Hybrid systems of differential-algebraic equations – Analysis and numerical solution

We consider hybrid systems of differential-algebraic equations and present a general framework for general nonlinear over- and underdetermined hybrid systems that allows the analysis of existence and uniqueness and the application of index reduction methods for hybrid differential-algebraic systems. A particular difficulty in the numerical simulation of hybrid systems is (numerical) chattering, i.e., fast oscillations between modes of operations. A regularization technique using sliding modes allows us to regularize the system behavior in the case of chattering. Further, we show how chattering behavior during the numerical solution can be prevented using sliding mode simulation. The advantage of the sliding mode simulation is illustrated by numerical examples.