@inproceedings{RuefflerHante, author = {R{\"u}ffler, Fabian and Hante, Falk}, title = {Optimality Conditions for Switching Operator Differential Equations}, abstract = {We consider optimal switching of hybrid abstract evolution equations. The framework includes switching semilinear partial differential equations of parabolic or hyperbolic type, discontinuous state resets, switching costs and allows switching of the principle parts of the equations. We present adjoint-based formulae for the gradient of the cost functional with respect to position and number of switching time points that lead to first order necessary conditions. Moreover, we discuss an alternate-direction approach for implementing descent methods. As an application we consider optimal open/close-switching of valves and on/off-switching control of compressors in a gas network modelled by a graph with simplified euler equations on edges and suitable coupling conditions at nodes.}, language = {en} } @article{RuefflerHante2016, author = {R{\"u}ffler, Fabian and Hante, Falk}, title = {Optimal Switching for Hybrid Semilinear Evolutions}, series = {Nonlinear Analysis: Hybrid Systems}, volume = {22}, journal = {Nonlinear Analysis: Hybrid Systems}, doi = {10.1016/j.nahs.2016.05.001}, pages = {215 -- 227}, year = {2016}, language = {en} } @article{RuefflerMehrmannHante2018, author = {R{\"u}ffler, Fabian and Mehrmann, Volker and Hante, Falk}, title = {Optimal Model Switching for Gas Flow in Pipe Networks}, year = {2018}, abstract = {We consider model adaptivity for gas flow in pipeline networks. For each instant in time and for each pipe in the network a model for the gas flow is to be selected from a hierarchy of models in order to maximize a performance index that balances model accuracy and computational cost for a simulation of the entire network. This combinatorial problem involving partial differential equations is posed as an optimal switching control problem for abstract semilinear evolutions. We provide a theoretical and numerical framework for solving this problem using a two stage gradient descent approach based on switching time and mode insertion gradients. A numerical study demonstrates the practicability of the approach.}, language = {en} }