German Title: Numerische Lösung von Optimalsteuerungsproblemen mit impliziten Unstetigkeiten mit Anwendungen in der Verfahrenstechnik

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Abstract

In the thesis on hand we treat optimal control problems for implicitly discontinuous dynamical processes. We give a general model formulation which includes implicitly given state dependent discontinuities in the right hand sides of the DAE system. The formulation is adapted to real-world applications from chemical and biotechnological engineering. The resulting problems are large scale constrained problems of optimal control with implicitly given discontinuities of a priori unknown chronology and number. Our solution approach builds on the direct multiple shooting approach which allows the combination of appropriate DAE solvers with modern simultaneous optimization strategies. To solve the underlying optimization problem we apply SQP methods. We explain our strategy to provide sensitivity information at the presence of implicitly given discontinuities for large scale models. Efficient techniques for the derivative generation of the right hand sides particularly adapted to structural sparsity pattern changes of the adjacent Jacobians are presented. We formulate an algorithm to treat the optimization problem which depends on the chronology and number of discontinuities occuring in a digraph given by the successive trajectories of the SQP steps. We explain our modeling of a complex rack-in process of a distillation column and present the models of two biotechnological processes. Each of the models is equipped with characteristical implicit state dependent discontinuities of a priori unknown chronology. In numerical experiments we show the efficient applicability of our algorithms to the presented chemical process and to the two biotechnological applications. We apply our approach to optimal feedback control of a biotechnological application with implicit discontinuities.