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Implicit Structural Analysis of Multimode DAE Systems

Abstract : The Modelica mathematical modeling language, based on Differential Algebraic Equations (DAE), brings several specific issues that do not exist with modeling languages based on Ordinary Differential Equations. The main problem is the determination of the differentiation index and latent equations. Prior to generating simulation code and calling solvers, the compilation of a Modelica model requires a structural analysis step, which reduces the differentiation index to a level acceptable by numerical solvers. The Modelica language allows hybrid models with multiple modes, mode-dependent dynamics and state-dependent mode switching. These Multimode DAE (mDAE) systems are much harder to deal with. The main difficulties are (i) the combinatorial explosion of the number of modes, and (ii) the correct handling of mode switchings. The focus of this report is on the first issue, namely : How can one perform a structural analysis of an mDAE in all possible modes, without enumerating these modes? A structural analysis algorithmfor mDAE systems is presented, based on an implicit representation of the varying structure of an mDAE. It generalizes J. Pryce’s structural analysis method to the multimode case and uses Binary Decision Diagrams (BDD) to represent the mode-dependent structure of an mDAE. The algorithm determines, as a function of the mode, the set of latent equations, the leading variables and the state vector. This is then used to compute a mode-dependent block-triangular decomposition ofthe system, that can be used to generate simulation code with a mode-dependent scheduling of the blocks of equations.This report is an extended version of the homonym paper, published in the proceedings of the HSCC’20 conference.
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Contributor : Benoît Caillaud <>
Submitted on : Wednesday, February 12, 2020 - 5:20:27 PM
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Benoît Caillaud, Mathias Malandain, Joan Thibault. Implicit Structural Analysis of Multimode DAE Systems. [Research Report] RR-9322, Inria Rennes - Bretagne Atlantique; IRISA, Université de Rennes. 2020. ⟨hal-02476541⟩



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