Structural Analysis of Multi-Mode DAE Systems

Albert Benveniste 1 Benoît Caillaud 1 Hilding Elmqvist 2 Khalil Ghorbal 1 Martin Otter 3 Marc Pouzet 4
1 HYCOMES - Modélisation hybride & conception par contrats pour les systèmes embarqués multi-physiques
Inria Rennes – Bretagne Atlantique , IRISA_D4 - LANGAGE ET GÉNIE LOGICIEL
4 Parkas - Parallélisme de Kahn Synchrone
DI-ENS - Département d'informatique de l'École normale supérieure, CNRS - Centre National de la Recherche Scientifique, Inria de Paris
Abstract : Differential Algebraic Equation (DAE) systems constitute the mathematical model supporting physical modeling languages such as Modelica, VHDL-AMS, or Simscape. Unlike ODEs, they exhibit subtle issues because of their implicit latent equations and related differentiation index. Multi-mode DAE (mDAE) systems are much harder to deal with, not only because of their mode-dependent dynamics, but essentially because of the events and resets occurring at mode transitions. Unfortunately, the large literature devoted to the numerical analysis of DAEs does not cover the multi-mode case. It typically says nothing about mode changes. This lack of foundations cause numerous difficulties to the existing modeling tools. Some models are well handled, others are not, with no clear boundary between the two classes. In this paper we develop a comprehensive mathematical approach to the structural analysis of mDAE systems which properly extends the usual analysis of DAE systems. We define a constructive semantics based on nonstandard analysis and show how to produce execution schemes in a systematic way.
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Albert Benveniste, Benoît Caillaud, Hilding Elmqvist, Khalil Ghorbal, Martin Otter, et al.. Structural Analysis of Multi-Mode DAE Systems. Proceedings of the 20th International Conference on Hybrid Systems: Computation and Control, 2017, Apr 2017, Pittsburgh, PA, United States. ⟨10.1145/3049797.3049806⟩. ⟨hal-01521918⟩

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