On the relaxation of state-constrained linear control problems via Henig dilating cones

• Autorzy: Kogut P. I. , Leugering G. , Schiel R.
• Języki publikacji: EN

Abstrakty

EN

We discuss a regularization of state-constrained optimal control problems via a Henig relaxation of ordering cones. Considering a state-constrained optimal control problem, the pointwise state constraint is replaced by an inequality condition involving a so-called Henig dilating cone. It is shown that this class of cones provides a reasonable solid approximation of the typically nonsolid ordering cones which correspond to pointwise state constraints. Thereby, constraint qualifications, which are based on the existence of interior points, can be applied to given problems. Moreover, we characterize admissibility and solvability of the original problem by analyzing the associated relaxed problem. We also show that the optimality system for the original problem can be obtained through the limit passage in the corresponding optimality system for the relaxed problem. As an example of our approach, we derive the optimality conditions for a state constrained Neumann boundary optimal control problem and show that in this case the corresponding Lagrange multipliers are more regular than Borel measures.

Słowa kluczowe

EN

optimal control; state constrains; relaxation; Henig dilating cone; optimality conditions

• Wydawca: Systems Research Institute, Polish Academy of Sciences
• Czasopismo: Control and Cybernetics
• Rocznik: 2016
• Tom: Vol. 45, no. 2
• Strony: 131--162
• Opis fizyczny: Bibliogr. 28 poz., rys., tab.

Twórcy

autor

Kogut P. I.

• Department of Differential Equations, Dnipropetrovsk National University, Gagarin av., 72, 49010 Dnipro, Ukraine

autor

Leugering G.

• Department Mathematik Lehrstuhl II Universit¨at Erlangen-Nu¨rnberg Cauerstr. 11 D-91058 Erlangen, Germany

autor

Schiel R.

• Department Mathematik Lehrstuhl II Universit¨at Erlangen-Nu¨rnberg Cauerstr. 11 D-91058 Erlangen, 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).