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Journal of Dynamical and Control Systems
Erschienen in: Journal of Dynamical and Control Systems 4/2013

01.10.2013

Necessity of Vanishing Shadow Price in Infinite Horizon Control Problems

verfasst von: Dmitry Khlopin

Erschienen in: Journal of Dynamical and Control Systems | Ausgabe 4/2013

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Abstract

This paper refines the necessary optimality conditions for uniformly overtaking optimal control on infinite horizon in the free end case. This condition is applicable to general non-stationary systems and the optimal objective value is not necessarily finite. In the papers of S.M. Aseev, A.V. Kryazhimskii, V.M. Veliov, K.O. Besov there was suggested a boundary condition for equations of the Pontryagin Maximum Principle. Each optimal process corresponds to a unique solution satisfying the boundary condition. Following A. Seierstad’s idea, in this paper we prove a more general geometric version of that boundary condition. We show that this condition is necessary for uniformly overtaking optimal control on infinite horizon in the free end case. A number of assumptions under which this condition selects a unique Lagrange multiplier is obtained. Some examples are discussed.
Vorheriger Artikel Stochastic Near-Optimal Singular Controls for Jump Diffusions: Necessary and Sufficient Conditions
Nächster Artikel Controllability of the Semilinear Beam Equation

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Metadaten
Titel
Necessity of Vanishing Shadow Price in Infinite Horizon Control Problems
verfasst von
Dmitry Khlopin
Publikationsdatum
01.10.2013
Verlag
Springer US
Erschienen in
Journal of Dynamical and Control Systems / Ausgabe 4/2013
Print ISSN: 1079-2724
Elektronische ISSN: 1573-8698
DOI
https://doi.org/10.1007/s10883-013-9192-5

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