Instantaneous optimal control of friction dominated flow in a gas-network

Günter Leugering (1) , Gisèle Mophou (2)

1 Department Mathematik [Erlangen]
2 LAMIA - Laboratoire de Mathématiques Informatique et Applications [UR1_1]

We consider optimal control problems for the flow of gas in a pipe network. The equations of motions are taken to be represented by a nonlinear model derived from asemi-linear approximation of the fully nonlinear isothermal Euler gas equations. We formulate an optimal control problem on a given network and introduce a time discretization thereof. We then study the well-posedness of the corresponding time-discrete optimal control problem. In order to further reduce the complexity, we consider an instantaneous control strategy. This involves a p-Laplace-type problem on the graph with p = 3 2. We prove well-posedness, existence of optimal controls and derive a first order optimality condition. Mathematics Subject Classification (2010). 35J70,49J20,49J45,93C73.

Mots clés: Optimal control; gas networks; p-Laplace problem on a graph; optimality system

Domaines: Mathématiques [math]; Equations aux dérivées partielles [math.AP]

Günter Leugering, Gisèle Mophou. Instantaneous optimal control of friction dominated flow in a gas-network. DFG-AIMS Workshop on Shape Optimization, Homogenization and Control., Mar 2017, Mbour, Senegal. ⟨hal-02548134⟩