Kolloquium: Michael Schuster (FAU Erlangen-Nürnberg): Nodal Control and Probabilistic Constrained Optimization using the Example of Gas Networks

Nodal Control and Probabilistic Constrained Optimization using the Example of Gas Networks – Vortragender: Michael Schuster, FAU Erlangen-Nürnberg – Einladender: M. Gugat

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 in e.g., the boundary
data. We first consider a stationary gas transport model with uncertain boundary data on networks. We provide an efficient approach based on kernel density estimation to compute the probability that random boundary data is feasible. In this context feasible means that the pressure corresponding to the random boundary data meets some box constraints at the network junctions. We further provide an extension of this approach to dynamical systems.

Besides we consider an optimal boundary control problem governed by a transport equation with uncertainty in the initial data and/or in the source term. The convex objective function depends on the boundary traces of the transport equation. We provide an integral turnpike property for the dynamic optimal control and the corresponding static optimal control.