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Abstract

The project focuses on control theory in order to study hybrid dynamical systems composed from the model hierarchy of gas networks up to the level of nonlinear iso-thermal euler-equations on pipelines and their interaction with discrete network components such as on/off-flaps, -valves and -compressors. The main line of research concerns mathematical foundations and shall answer questions for example regarding regularity and sensitivity of solutions for hyperbolic PDEs interacting with discrete events. The main challenges are the formulation of suitable solution concepts and their mathematical abstraction including the ability to topologize the instances and to find representations of sensitivities for events using adjoint-based methods. In case of state dependend switching, zeno effects are to be considered. Besides contributions to the above theoretical foundations, we expect by our study novel, locally convergent numerical methods by embedding the developed sensitivity formulas into derivative based optimization algorithms in order to efficently solve mixed-integer optimal control problems on the level of PDE-gas-dynamics. 

 

A poster to A03(phase1) can be found here.