Strategies for numerical integration of discontinuous DAE models

In this work, it is presented a novel strategy to solve discontinuous DAEs of floating index type. The switching between DAE models of different indexes and the reinitialization of the system are performed automatically by the code. The direct integration of the high index DAE model is aided by the software. The equation actually fed to the numerical integrator is a weighted sum of the different model equations. The weights are either 0 or 1 inside integration intervals, depending oil whether the corresponding equation is active or not during the time interval in consideration. Across model discontinuities, the numerical values of the weights are taken from 0 to 1 (or vice-versa) via a smooth regularization function, which is a continuous representation of a step function. Several functions are Suitable to perform such task, and the authors suggest a family of functions which are simple and differentiable up to the order needed. As an example, the optimal control of a fedbatch fermentation (production of ethanol by S. cerevisiae) is presented.