Preprint 02-2020

The Pantelides algorithm for delay differential-algebraic equations

Author(s) : Ines Ahrens , Benjamin Unger

Preprint series of the Institute of Mathematics, Technische Universität Berlin
Preprint 02-2020

MSC 2000

34A09 Implicit equations, differential-algebraic equations

65L80 Methods for differential-algebraic equations

Abstract :
We present a graph-theoretical approach that can detect which equations of a delay differential-algebraic equation (DDAE) need to be differentiated or shifted to construct a solution of the DDAE. Our approach exploits the observation that differentiation and shifting are very similar from a structural point of view, which allows us to generalize the Pantelides algorithm for differential-algebraic equations to the DDAE setting. The primary tool for the extension is the introduction of equivalence classes in the graph of the DDAE, which also allows us to derive a necessary and sufficient criterion for the termination of the new algorithm.

Keywords : delay differential-algebraic equation, structural analysis, Pantelides algorithm