We develop a mixed-integer optimal control model with partial differential equation (PDE) constraints for gas transport networks, designed for controlling extreme state transitions, such as flow reversals. Our model shows how to combine binary compressor controls with PDE flow models. We model the flow of gas using a variant of the Euler equations, which we dis- cretize using a finite volume scheme, which obeys conservation of mass and average impulse independent of the direction of flow. The resulting large-scale mixed-integer nonlinear opti- mization problem is difficult to solve by using standard branch-and-bound solvers, and we propose a new tree-search strategy that allow us to solve realistic instances. We compare the performance of several solution schemes on twelve test instances, showing that our custom tree-search strategy greatly outperforms a generic strategy in most instances.
Hahn, Mirko, Leyffer, Sven and Zavala, Victor. "Mixed-Integer PDE-Constrained Optimal Control of Gas Networks", Argonne National Laboratory, Preprint ANL/MCS-P7095-0817