Exploiting Invariants in the Numerical Solution of Multipoint Boundary Value Problems for DAE

Authors:
Volker H. Schulz;Hans Georg Bock;Marc C. Steinbach
Affiliations:
-;-;-
Venue:
SIAM Journal on Scientific Computing
Year:
1998

Citing 0
Cited 3

On Efficient Computation of the Optimization Problem Arising in the Inverse Modeling of Non-Stationary Multiphase Multicomponent Flow Through Porous Media

Computational Optimization and Applications
A globally convergent semi-smooth Newton method for control-state constrained DAE optimal control problems

Computational Optimization and Applications
On the numerical treatment of linear-quadratic optimal control problems for general linear time-varying differential-algebraic equations

Journal of Computational and Applied Mathematics

Quantified Score

Hi-index	0.00

Visualization

Abstract

This paper presents a new approach to the numerical solution of boundary value problems for higher-index differential-algebraic equations (DAEs). Invariants known for the original DAE as well as invariants of the reduced index 1 formulation are exploited to stabilize initial value problem (IVP) integration, derivative generation, and nonlinear and linear systems solution of an enhanced multiple shooting method. Extensions to collocation are given. Applications are presented for two important problem classes: parameter estimation in multibody systems given in descriptor form, and singular and state-constrained optimal control problems. In particular, generalizations of the "internal numerical differentiation" technique to DAE with invariants and a new multistage least squares decomposition technique for DAE boundary value problems are developed, which are implemented in the multiple shooting code PARFIT and in the collocation code COLFIT. Further, a method is described which minimizes the number of necessary directional derivatives in the presence of multipoint conditions and invariants. As numerical applications, a parameter identification problem for a slider crank mechanism and a periodic cruise optimal control problem for a motor glider aircraft are treated.