@article{GugatHanteJin2020, author = {Gugat, Martin and Hante, Falk and Jin, Li}, title = {Closed loop control of gas flow in a pipe: Stability for a transient model}, series = {at - Automatisierungstechnik}, journal = {at - Automatisierungstechnik}, year = {2020}, abstract = {This contribution focuses on the analysis and control of friction-dominated flow of gas in pipes. The pressure in the gas flow is governed by a partial differential equation that is a doubly nonlinear parabolic equation of p-Laplace type, where p=2/3. Such equations exhibit positive solutions, finite speed of propagation and satisfy a maximum principle. The pressure is fixed on one end (upstream), and the flow is specified on the other end (downstream). These boundary conditions determine a unique steady equilibrium flow. We present a boundary feedback flow control scheme, that ensures local exponential stability of the equilibrium in an L2-sense. The analysis is done both for the pde system and an ode system that is obtained by a suitable spatial semi-discretization. The proofs are based upon suitably chosen Lyapunov functions.}, language = {en} } @article{HanteLeugeringMartinetal.2016, author = {Hante, Falk and Leugering, G{\"u}nter and Martin, Alexander and Schewe, Lars and Schmidt, Martin}, title = {Challenges in optimal control problems for gas and fluid flow in networks of pipes and canals: From modeling to industrial applications}, pages = {40}, year = {2016}, abstract = {We consider optimal control problems for the flow of gas or fresh water in pipe networks as well as drainage or sewer systems in open canals. The equations of motion are taken to be represented by the nonlinear isothermal Euler gas equations, the water hammer equations, or the St.~Venant equations for flow. We formulate model hierarchies and derive an abstract model for such network flow problems including pipes, junctions, and controllable elements such as valves, weirs, pumps, as well as compressors. We use the abstract model to give an overview of the known results and challenges concerning equilibria, well-posedness, controllability, and optimal control. A major challenge concerning the optimization is to deal with switching on-off states that are inherent to controllable devices in such applications combined with continuous simulation and optimization of the gas flow. We formulate the corresponding mixed-integer nonlinear optimal control problems and outline a decomposition approach as a solution technique.}, language = {en} } @article{GugatHante2017, author = {Gugat, Martin and Hante, Falk}, title = {Lipschitz Continuity of the Value Function in Mixed-Integer Optimal Control Problems}, series = {Mathematics of Control, Signals, and Systems}, volume = {29}, journal = {Mathematics of Control, Signals, and Systems}, number = {1}, doi = {10.1007/s00498-016-0183-4}, year = {2017}, language = {en} } @article{HanteSchmidt2017, author = {Hante, Falk and Schmidt, Martin}, title = {Complementarity-Based Nonlinear Programming Techniques for Optimal Mixing in Gas Networks}, series = {EURO Journal on Computational Optimization}, journal = {EURO Journal on Computational Optimization}, number = {7(3)}, pages = {299 -- 323}, year = {2017}, abstract = {We consider nonlinear and nonsmooth mixing aspects in gas transport optimization problems. As mixed-integer reformulations of pooling-type mixing models already render small-size instances computationally intractable, we investigate the applicability of smooth nonlinear programming techniques for equivalent complementarity-based reformulations. Based on recent results for remodeling piecewise affine constraints using an inverse parametric quadratic programming approach, we show that classical stationarity concepts are meaningful for the resulting complementarity-based reformulation of the mixing equations. Further, we investigate in a numerical study the performance of this reformulation compared to a more compact complementarity-based one that does not feature such beneficial regularity properties. All computations are performed on publicly available data of real-world size problem instances from steady-state gas transport.}, language = {en} } @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{HanteMommerPotschka, author = {Hante, Falk and Mommer, Mario and Potschka, Andreas}, title = {Newton-Picard preconditioners for time-periodic, parabolic optimal control problems}, series = {SIAM Journal on Numerical Analysis}, volume = {53}, journal = {SIAM Journal on Numerical Analysis}, number = {5}, doi = {10.1137/140967969}, pages = {2206 -- 2225}, language = {en} } @article{DomschkeGrossHilleretal.2015, author = {Domschke, Pia and Groß, Martin and Hiller, Benjamin and Hante, Falk and Schewe, Lars and Schmidt, Martin}, title = {Mathematische Modellierung, Simulation und Optimierung von Gastransportnetzwerken}, series = {gwf-gas/erdgas}, volume = {11}, journal = {gwf-gas/erdgas}, pages = {880 -- 885}, year = {2015}, language = {de} } @inproceedings{Hante, author = {Hante, Falk}, title = {On the relaxation gap for PDE mixed-integer optimal control problems}, series = {Proceedings in Applied Mathematics and Mechanics}, volume = {16}, booktitle = {Proceedings in Applied Mathematics and Mechanics}, doi = {10.1002/pamm.201610380}, pages = {783 -- 784}, 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{GugatLeugeringHante2015, author = {Gugat, Martin and Leugering, G{\"u}nter and Hante, Falk}, title = {Stationary States in Gas Networks}, series = {Networks and Heterogeneous Media}, volume = {10}, journal = {Networks and Heterogeneous Media}, number = {2}, editor = {Piccoli, Benedetto}, doi = {doi:10.3934/nhm.2015.10.295}, pages = {295 -- 320}, year = {2015}, abstract = {Pipeline networks for gas transportation often contain circles. For such networks it is more difficult to determine the stationary states than for networks without circles. We present a method that allows to compute the stationary states for subsonic pipe flow governed by the isothermal Euler equations for certain pipeline networks that contain circles. We also show that suitably chosen boundary data determine the stationary states uniquely. The construction is based upon novel explicit representations of the stationary states on single pipes for the cases with zero slope and with nonzero slope. In the case with zero slope, the state can be represented using the Lambert-W function.}, language = {en} }