Set Oriented Numerics and Applications

Oliver Junge^*

Over the last couple of years, a discretization based on sets has proven to be a useful approach for the robust numerical treatment of several problem classes. Originally developed within the context of nonlinear dynamics, in the meantime this concept has also been successfully applied in order to solve optimal control and multiobjective optimization problems. This talk gives an introduction to the basic ideas of the set oriented paradigm and presents three specific methods within the context of their applications: An approach for the identification of energy efficient trajectories for spacecraft, a rigorous numerical method for the identification of chaos in infinite-dimensional dynamical systems as well as the construction of globally optimal controllers for quantized and hybrid control systems.

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Plenary Lecture