EXPLOITING INVARIANTS IN THE NUMERICAL-SOLUTION OF MULTIPOINT BOUNDARY-VALUE-PROBLEMS FOR DAES

This paper presents a new approach to the numerical solution of bounda ry value problems for higher-index differential-algebraic equations (D AEs). Invariants known for the original DAE as well as invariants of t he reduced index 1 formulation are exploited to stabilize initial valu e problem (IVP) integration, derivative generation, and nonlinear and linear systems solution of an enhanced multiple shooting method. Exten sions to collocation are given. Applications are presented for two imp ortant problem classes: parameter estimation in multibody systems give n in descriptor form, and singular and state-constrained optimal contr ol problems. In particular, generalizations of the ''internal numerica l differentiation'' technique to DAE with invariants and a new multist age least squares decomposition technique for DAE boundary value probl ems are developed, which are implemented in the multiple shooting code PARFIT and in the collocation code COLFIT. Further, a method is descr ibed which minimizes the number of necessary directional derivatives i n the presence of multipoint conditions and invariants. As numerical a pplications, a parameter identification problem for a slider crank mec hanism and a periodic cruise optimal control problem for a motor glide r aircraft are treated.