MIP-based instantaneous control of mixed-integer PDE-constrained gas transport problems

• Published in: Computational optimization and applications Vol. 70; no. 1; pp. 267 - 294
• Main Authors: Gugat, Martin, Leugering, Günter, Martin, Alexander, Schmidt, Martin, Sirvent, Mathias, Wintergerst, David
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.05.2018; Springer Nature B.V
• Subjects: Computational fluid dynamics; Convex and Discrete Geometry; Euler-Lagrange equation; Gas transport; Management Science; Mathematics; Mathematics and Statistics; Nonlinear control; Nonlinear equations; Operations Research; Operations Research/Decision Theory; Optimization; Ordinary differential equations; Partial differential equations; Solvers; Stability; Statistics; Switching theory; Transportation networks; Well posed problems; 76B75; Mixed-integer optimal control; 49J20; 90C35; Mixed-integer linear optimization; 90C11; Instantaneous control; Partial differential equations on graphs; Gas networks; 49J15
• ISSN: 0926-6003; 1573-2894
• DOI: 10.1007/s10589-017-9970-1

We study the transient optimization of gas transport networks including both discrete controls due to switching of controllable elements and nonlinear fluid dynamics described by the system of isothermal Euler equations, which are partial differential equations in time and 1-dimensional space. This...