On problems of dynamic optimal nodal control for gas networks

Martin Gugat (1) , Jan Sokolowski (2, 3, 4)

1 FAU - Friedrich-Alexander Universität Erlangen-Nürnberg = University of Erlangen-Nuremberg
2 IECL - Institut Élie Cartan de Lorraine
3 UFPB - Universidade Federal da Paraiba / Federal University of Paraiba
4 Systems Research Institute

We consider a dynamic optimal control problem for gaspipeline systems. The flow is governed by a quasilinear hyperbolicmodel. Since in the operation of the gas networks regular solutionswithout shocks are desirable, we impose appropriate state and controlconstraint in order to guarantee that a classical solution is generated.Due to aW2,∞-regularization term in the objective function, we canshow the existence of an optimal control. Moreover, we give conditionsthat guarantee that the control becomes constant a the end of the con-trol time interval if the weight of the regularization term is sufficientlylarge

Mots clés: optimal nodal control; gas network; turnpike property; quasi-linear hyperbolic problem; dynamic control; static control

Domaines: Mathématiques [math]

Martin Gugat, Jan Sokolowski. On problems of dynamic optimal nodal control for gas networks. 2021. ⟨hal-03120667⟩