Backward Invariance for Linear Differential Algebraic Equations

Stefano Tognazzi, Mirco Tribastone, Max Tschaikowski, Andrea Vandin

Research output: Chapter in Book/Report/Conference proceedingArticle in proceedingsResearchpeer-review

Abstract

Differential-algebraic equations (DAEs) are a widespread dynamical model that describes continuously evolving quantities defined with differential equations, subject to constraints expressed through algebraic relationships. As such, DAEs arise in many fields ranging from physics, chemistry, and engineering. In this paper we focus on linear DAEs, and develop a theory for their minimization up to an equivalence relation. We present backward invariance, which relates DAE variables that have equal solutions at all time points (thus requiring them to start with equal initial conditions) and extends the line of research on backward-type bisimulations developed for Markov chains and ordinary differential equations. We apply our results to the electrical engineering domain, showing that backward invariance can explain symmetries in certain networks as well as analyze DAEs which could not be originally treated due to their size.
Original languageEnglish
Title of host publicationProceedings of 2018 IEEE Conference on Decision and Control
PublisherIEEE
Publication date2018
Pages3771-3776
ISBN (Print)9781538613948
DOIs
Publication statusPublished - 2018
Event57th IEEE Conference on Decision and Control - Fontainebleau , Miami, United States
Duration: 17 Dec 201819 Dec 2018
https://cdc2018.ieeecss.org/

Conference

Conference57th IEEE Conference on Decision and Control
LocationFontainebleau
CountryUnited States
CityMiami
Period17/12/201819/12/2018
Internet address

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