Uniqueness of Completions for Linear Time Varying Differential AlgebraicEquations

摘要

Differentiation of differential algebraic equations is used for many purposes,ranging from index reduction to control techniques such as system inversion. General numerical methods, which can be used when other, more efficient methods, such as implicit Runge-Kutta (IRK) or backward differentiation (BDF) fail, have been proposed based on derivative arrays. Most of these approaches consist of determining all or part of a completion of the original vector field defined by the DAE. In more complex problems these completions would probably be determined numerically. That the differentiated equations do not uniquely determine a completion is known. However, we have shown that the introduced dynamics are essentially arbitrary off the solution manifold if no restrictions are placed on the numerical method computing the completion, and the coefficients do not even have to be smooth if different values of t would lead, for example, to changes in choice of pivots during Gaussian elimination.