Aktuelles

Title: Probabilistic Contsrained Optimization with ODEs and PDEs 

Abstract:

Uncertainty often plays an important role in gas transport and probabilistic constraints are an excellent modeling tool to obtain controls and other quantities that are robust against perturbations. To efficiently evaluate the probabilistic constraint, we present an approach based on kernel density estimation, such that the probabilistic constrained optimization problem can be considered as classical nonllinear problem, allowing us to apply classical nonlinear optimization theory.
As an application, we consider and analyze the steady state and the transient gas flow in pipeline networks. We introduce the modelling based on the isothermal Euler equations including random boundary data, leading to optimal control problems with probabilistic constraints.

Schuster_Seoul2025

Michael Schuster gave a talk at SIGOPT – International Conference on Optimization, 04.-06. March 2025 in Siegen.
Title: The Location Problem for Compressor Stations in Pipeline Networks

In the operation of pipeline networks, compressors play a crucial role in ensuring the network’s functionality for various scenarios. In this contribution we address the important question of finding the optimal location of the compressors. That results in non-convex mixed integer stochastic optimization problems with probabilistic constraints.
Using a steady state model for the gas flow in pipeline networks including compressor control and uncertain loads given by certain probability distributions, the problem of finding the optimal location for the control on the network, s.t. the control cost is minimal and the gas pressure stays within given bounds, is considered.
In the deterministic setting, explicit bounds for the pipe length and the inlet pressure, s.t. a unique optimal compressor location with minimal control cost exists, are presented. In the probabilistic setting, an existence result for the optimal compressor location is presented and the uniqueness of the solution is discussed depending on the probability distribution.
Further the problem of finding the optimal compressor locations on networks including the number of compressor stations as variable is considered. Results for the existence of optimal locations on a graph in both, the deterministic and the probabilistic setting, are presented. The paper concludes with an illustrative example on a diamond graph demonstrating that the minimal number of compressor stations is not necessarily equal to the optimal number.

slides_Schuster_sigopt25

Martin Gugat and Jan Giesselmann gave presentations at the „Mathematics and Decision Conference „,  which was held at  UM6P University,  Benguerir, Morocco, within the minisymposium on „Control and Applications“ which was organised by Abeladim Elakri, Lahcen Maniar and Enrique Zuazua. They presented research on „Data assimilation for gas flows via observers using distributed measurements“ (Jan Giesselmann) and „Synchronization of observer systems for the flow in gas networks“ (Martin Gugat).