Determining over- and under-constrained systems of equations using structural constraint delta

Abstract

Computer aided modeling and simulation of complex physical systems, using components from multiple application domains, such as electrical, mechanical, and hydraulic, have in recent years witnessed a significant growth of interest. In the last decade, equation-based object-oriented (EOO) modeling languages, (e.g. Modelica, gPROMS, and VHDL-AMS) based on acausal modeling using Differential Algebraic Equations (DAEs), have appeared. With such languages, it is possible to model physical systems at a high level of abstraction by using reusable components. A model in an EOO language needs to have the same number of equations as unknowns. A previously unsolved problem concerning this property is the efficient detection of over- or under-constrained models in the case of separately compiled models. This paper describes a novel technique to determine over- and under-constrained systems of equations in models, based on a concept called structural constraint delta. In many cases it is also possible to locate the source of the constraint-problem. Our approach makes use of static type checking and consists of a type inference algorithm. We have implemented it for a subset of the Modelica language, and successfully validated it on several examples.