A Nash equilibrium approach for multiobjective optimal control problems with elliptic partial differential equations

• Autorzy: Dreves A.
• Języki publikacji: EN

Abstrakty

EN

We consider the generalized Nash equilibrium as a solution concept for multiobjective optimal control problems governed by elliptic partial differential equations with constraints not only for the control but also for the state variables. In the first part, we present a constructive proof of the existence of a generalized Nash equilibrium via an approximating sequence of suitable finite dimensional discretizations. In the second part, we propose a variant of a potential reduction algorithm for the numerical solution of these discretized problems. In contrast to the existing numerical approaches ours does not require the computation of the control–to–state mapping. Instead we introduce different state variables and guarantee that they become equal at a solution. We prove sufficient conditions for the convergence of our algorithm to a solution. Furthermore, some numerical results showing the applicability are provided.

Słowa kluczowe

EN

multiobjective optimization; generalized Nash equilibrium; optimal control problem; elliptic partial differential equation; finite elements; interior point method

• Wydawca: Systems Research Institute, Polish Academy of Sciences
• Czasopismo: Control and Cybernetics
• Rocznik: 2016
• Tom: Vol. 45, no. 4
• Strony: 457--482
• Opis fizyczny: Bibliogr. 23 poz., rys.

Twórcy

autor

Dreves A.

• Universit¨at der Bundeswehr Mu¨nchen, Department of Aerospace Engineering, Werner-Heisenberg Weg 39, 85577 Neubiberg, Germany

Bibliografia

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Uwagi

PL

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę (zadania 2017).