Analysis of over- and underdetermined nonlinear differential-algebraic systems with application to nonlinear control problems

We study over- and underdetermined systems of nonlinear differential-algebraic equations. Such equations arise in many applications in circuit and multibody system simulation, in particular when automatic model generation is used, or in the analysis and solution of control problems in the behavior framework. We give a general (local) existence and uniqueness theory and apply the results to analyze when nonlinear implicit control problems can be made regular by state or output feedback. The theoretical analysis also leads immediately to numerical methods for the simulation as well as the construction of regularizing feedbacks.