STRUCTURAL-ANALYSIS OF DIFFERENTIAL-ALGEBRAIC EQUATION SYSTEMS - THEORY AND APPLICATIONS

The choice of a feasible numerical method for the solution of a Differential-Algebraic Equation (DAE) model of general type F(z, z, u) = 0 requires knowledge about its solvability, index, number and type of dynamic degrees of freedom as well as the set of equations to be satisfied by consistent initial conditions. Furthermore, a set of design quantities has to be specified. Important properties of DAEs are concisely defined and related among each other. A new structural algorithm which determines structural properties of DAEs is developed and compared to another conceptually different structural algorithm proposed earlier by Pantelides [(1988) SIAM J. Sci. Stat. Comput. 9, 213-231]. Both algorithms were implemented as structural analysis tools to provide a fast a priori characterization of general DAEs F(z, z, u) = 0 prior to any numerical solution. Some examples illustrate how the information obtained can be used to address various significant issues in process modelling, simulation, and in the evaluation of control configurations for nonlinear systems.