Regularization of Higher-Index Differential-Algebraic Equations with Rank-Deficient Constraints

In this paper we present several regularizations for higher-index differential-algebraic equations with rank-deficient or singular constraints. These types of problems arise, for example, in the solution of constrained mechanical systems, when a mechanism's trajectory passes through or near a kinematic singularity. We derive a class of regularizations for these problems which is based on minimization of the norm of the constraints. The new regularizations are analogous to trust-region methods of numerical optimization. We give convergence results for the regularizations and present some numerical experiments which illustrate their effectiveness.

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