Section: New Results

Structural Analysis of Multi-Mode DAEs

Differential Algebraic Equation (DAE) systems constitute the mathematical model supporting physical modeling languages such as Modelica or Simscape. Unlike Ordinary Differential Equations, or 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 do 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 [11], 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. This work has been accepted for presentation at the HSCC 2017 conference  [19] in April 2017.