# The Pantelides algorithm for delay differential-algebraic equations

## TL;DR

This paper extends the Pantelides algorithm to delay differential-algebraic equations using a graph-theoretical approach, enabling structural detection of equations needing differentiation or shifting for solution construction.

## Contribution

It introduces a generalized algorithm for DDAEs based on graph equivalence classes, providing a necessary and sufficient criterion for algorithm termination.

## Key findings

- The extended algorithm effectively identifies equations requiring differentiation or shifting.
- The approach offers a structural criterion for algorithm termination.
- It generalizes the Pantelides algorithm to DDAEs using graph theory.

## 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.

---
Source: https://tomesphere.com/paper/1908.01514