Nonoverlapping domain decomposition for optimal control problems governed by semilinear models for gas flow in networks

• Autorzy: Leugering G. , Martin A. , Schmidt M. , Sirvent M.
• Języki publikacji: EN

Abstrakty

EN

We consider optimal control problems for gas flow in pipeline networks. The equations of motion are taken to be represented by a first-order system of hyperbolic semilinear equations derived from the fully nonlinear isothermal Euler gas equations. We formulate an optimal control problem on a network and introduce a tailored time discretization thereof. In order to further reduce the complexity, we consider an instantaneous control strategy. The main part of the paper is concerned with a nonoverlapping domain decomposition of the optimal control problem on the graph into local problems on smaller sub-graphs—ultimately on single edges. We prove convergence of the domain decomposition method on networks and study the wellposedness of the corresponding time-discrete optimal control problems. The point of the paper is that we establish virtual control problems on the decomposed subgraphs such that the corresponding optimality systems are in fact equal to the systems obtained via the domain decomposition of the entire optimality system.

Słowa kluczowe

EN

optimal control; gas networks; Euler equation; semilinear PDE; nonoverlapping domain decomposition

• Wydawca: Systems Research Institute, Polish Academy of Sciences
• Czasopismo: Control and Cybernetics
• Rocznik: 2017
• Tom: Vol. 46, no. 3
• Strony: 191--225
• Opis fizyczny: Bibliogr. 28 poz., rys.

Twórcy

autor

Leugering G.

• Friedrich-Alexander-Universit¨at Erlangen-Nu¨rnberg (FAU), Lehrstuhl Angewandte Mathematik (Lehrstuhl II), Cauerstr. 11, 91058 Erlangen, Germany

autor

Martin A.

• Friedrich-Alexander-Universit¨at Erlangen-Nrnberg (FAU), Discrete Optimization, Cauerstr. 11, 91058 Erlangen, Germany

autor

Schmidt M.

• Friedrich-Alexander-Universit¨at Erlangen-Nrnberg (FAU), Discrete Optimization, Cauerstr. 11, 91058 Erlangen, Germany

autor

Sirvent M.

• Friedrich-Alexander-Universit¨at Erlangen-Nrnberg (FAU), Discrete Optimization, Cauerstr. 11, 91058 Erlangen, Germany

Bibliografia

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Uwagi

PL

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2018).