REGULARIZATION OF HIGHER-INDEX DIFFERENTIAL-ALGEBRAIC EQUATIONS WITH RANK-DEFICIENT CONSTRAINTS

In this paper we present several regularizations for higher-index diff erential-algebraic equations with rank-deficient or singular constrain ts. These types of problems arise, for example, in the solution of con strained mechanical systems, when a mechanism's trajectory passes thro ugh or near a kinematic singularity. We derive a class of regularizati ons for these problems which is based on minimization of the norm of t he 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 illustra te their effectiveness.