  We study model predictive control for singular differential-algebraic
equations with higher index. This is a novelty when compared to the literature
where only regular differential-algebraic equations with additional assumptions
on the index and/or controllability are considered. By regularization
techniques, we are able to derive an equivalent optimal control problem for an
ordinary differential equation to which well-known model predictive control
techniques can be applied. This allows the construction of terminal constraints
and costs such that the origin is asymptotically stable w.r.t. the resulting
closed-loop system.
