TRR 154

SFB Transregio 154

Mathematical Modelling, Simulation and Optimization Using the Example of Gas Networks

Homepage SFB Transregio 154

Prof. Dr. Enrique Zuazua and Prof. Dr. Martin Gugat are members of the SFB Transregio.

C03: Nodal control and the turnpike phenomenon
(2018-2021)

Turnpike results provide connections between the solutions of transient and the corresponding stationary optimal control problems that are often used as models in the control of gas transport networks. In this way turnpike results give a theoretical foundation for the approximation of transient optimal controls by the solutions of stationary optimal control problems that have a simpler structure. Turnpike studies can also be considered as investigations of the structure of the transient optimal controls. In the best case the stationary optimal controls approximate the transient optimal controls exponentially fast.

Prof. Dr. Martin Gugat (Erlangen), Prof. Dr. Rüdiger Schultz (Duisburg), Michael Schuster (Erlangen)

C05: Observer-based data assimilation for time dependent flows on gas networks (2018-2021)

This project studies data assimilation methods for models of compressible flows in gas networks. The basic idea of data assimilation is to include measurement data into simulations during runtime in order to make their results more precise and more reliable. This can be achieved by augmenting the original model equations with control terms at nodes and on pipes that steer the solutions towards the measured data. This gives rise to a new system called “observer”. This project is going to explore how much data is needed so that convergence of the observer towards the solution of the original system can be guaranteed, how fast this convergence is and how measurement errors affect the solution.

Prof. Dr. Jan Giesselmann (Darmstadt),Prof. Dr. Martin Gugat (Erlangen)

C08: Random Batch Methods for Optimal Control of Network Dynamics (2018-2021)

This Subproject, led by Falk Hante (Humboldt-Universität zu Berlin) and Enrique Zuazua (FAU Erlangen-Nürnberg) focuses on hyperbolic and parabolic dynamics on networks and random batch methods for control. The aim is to restrict the overall network dynamics to subgraphs as a random batch for the computation of a stochastic gradient descent direction. We aim to develop a convergence theory and develop control methodologies of gas networks employing techniques of model predictive control. This approach can then readily be extended to incorporate uncertainties in the model by adapting concepts from the theory of simultaneous control of parameter-dependent systems.

Prof. Dr. Falk Hante (Berlin),Prof. Dr. Enrique Zuazau (Erlangen), Lukas Wolff

Team Uncertainty (2018-2021)

We analyze the (stationary and transient) gas transport with uncertain boundary data. This leads to optimization problems with probabilistic constraints. Our main methods to work with probabilistic constrained optimization problems are the spheric-radial decomposition and kernel-density estimation.
Arbeitsgruppe Jens Lang (Homepage)

Prof. Dr. Martin Gugat (Erlangen), Michael Schuster (Erlangen), Prof. Jens Lang (Darmstadt), Elisa Strauch

Finished Projects

Feasibility: Robust Nodal controllability (2014-2017)

We study optimal control problems with hyperbolic pdes and boundary data with stochastic influence. Nodal controls means that the control acts at a finite number of points in the network.
We develop an analytical framework for the systems dynamics, risk-neutral and risk-averse objective functions and and prove the existence of optimal controls. We also derive necessary optimality conditions. To treat the stochastic influence, the analysis of the optimal value function is necessary.

Prof. Dr. Martin Gugat (Erlangen), Prof. Dr. Rüdiger Schultz (Duisburg)
Friedrich-Alexander-Universität Erlangen-Nürnberg