Control of System Dynamics in Gas and Water Networks

• Antragsteller: Professor Dr. Martin Gugat; Professor Dr. Michael Herty
• Fachliche Zuordnung: Mathematik
• Förderung: Förderung von 2009 bis 2013
• Projektkennung: Deutsche Forschungsgemeinschaft (DFG) - Projektnummer 133412466

We study the dynamics and control of gas and water transportation networks. The gas and water net providers have three main problems: Under minimal cost they should (1.) satisfy the consumer’s demands (for example gas pressure, amount of gas) (2.) avoid shock waves in order to prevent system damage (for example pipe breaks) and (3.) provide a gas mixture (water resp.) of a certain quality.The system is controlled at certain points in the network by compressors/valves (underflow gates resp.). The net providers have to decide when to switch on/switch off certain compressor stations and close or open the valves.The aims of this projects are the study of controllability to a given demand; the derivation of feedback laws to stabilize the dynamics in order to prevent shocks; to prove the existence of cost optimal controls for an optimal mixture problem for multi-phase gas or water flows; the development of adapted numerical simulation and optimization shemes that preserve the hyperbolic structure of the system; the study of the switching problems motivated by the 0-1 decision problems of the net providers in the operation of the compressors/valves.

• DFG-Verfahren: Schwerpunktprogramme
• Teilprojekt zu: SPP 1253: Optimierung mit partiellen Differentialgleichungen
• Beteiligte Person: Professor Dr. Günter Leugering