On geometric control and numeric integration of DAEs

Authors:	da Silva Paulo Sergio Pereira, University of São Paulo, Brazil Delaleau Emmanuel, Ecole nationale d'ingenieurs de Brest, France de Souza Iderval Silva, University of São Paulo, Brazil
Topic:	2.3 Non-Linear Control Systems
Session:	Nonlinear Stability and Structural Analysis
Keywords:	DAEs, numerical integration, geometric control

Abstract

Two methods of numerical integration of DAE's using mixedsymbolic/numerical computations are studied in this paper. The firstmethod, not new in the literature, is directly obtained by adecoupling and stabilizing control law. Numerical experiments showsthat this first method may be numerically unstable for high indexsystems. The main problem of the first method is that thestabilization of the constraint manifold is the stabilization of achain of integrators, and this may generate the numerical problemsfound in the experiments. The second method assures a directconvergence to the constraint manifold, and the numerical experimentsshow very good results.