A differentiation-based approach to dynamic simulation and optimization with high-index differential-algebraic equations

Reliable methods for solving simulation and dynamic optimization problems must be able to handle the high-index DAEs that arise naturally in these problems. This paper details a modified and automated version of the method of dummy derivatives for solving high-index DAEs that has been implemented within the ABACUSS large-scale equation based modeling environment. To implement our algorithm, we have developed a method for ''dummy variable pivoting'' into a standard DAE solver. Our approach requires a hybrid symbolic and numeric strategy in which we apply computational differentiation to the high-index system, and then employ a numerical integrator to solve the resulting index-1 system. We have modified the dummy derivative method for solving high-index DAEs in several ways to reduce the computational cost required to select and pivot the dummy derivative set. This work demonstrates the feasibility and desirability of using a hybrid numerical and symbolic strategy for the solution of certain classes of simulation and dynamic optimization problems.