Differential Equivalence for Linear Differential Algebraic Equations

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2022
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Tribastone, Mirco
Tschaikowski, Max
Vandin, Andrea
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Zusammenfassung

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 article, we focus on linear DAEs, and develop a theory for their minimization up to an equivalence relation. We present differential equivalence, 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 bisimulations developed for Markov chains and ordinary differential equations. We apply our results to the electrical engineering domain, showing that differential equivalence can explain invariances in certain networks as well as analyze DAEs, which could not be originally treated due to their size.

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Differential-algebraic systems, linear systems, modeling, model/controller reduction
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ISO 690TOGNAZZI, Stefano, Mirco TRIBASTONE, Max TSCHAIKOWSKI, Andrea VANDIN, 2022. Differential Equivalence for Linear Differential Algebraic Equations. In: IEEE Transactions on Automatic Control. Institute of Electrical and Electronics Engineers (IEEE). 2022, 67(7), pp. 3484-3493. ISSN 0018-9286. eISSN 1558-2523. Available under: doi: 10.1109/TAC.2021.3108530
BibTex
@article{Tognazzi2022Diffe-58073,
  year={2022},
  doi={10.1109/TAC.2021.3108530},
  title={Differential Equivalence for Linear Differential Algebraic Equations},
  number={7},
  volume={67},
  issn={0018-9286},
  journal={IEEE Transactions on Automatic Control},
  pages={3484--3493},
  author={Tognazzi, Stefano and Tribastone, Mirco and Tschaikowski, Max and Vandin, Andrea}
}
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