Necessity of Vanishing Shadow Price in Infinite Horizon Control Problems

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• 作者：Dmitry Khlopin
• 关键词：Optimal control ; Infinite horizon problem ; Transversality condition for infinity ; Necessary conditions ; Uniformly overtaking optimal control ; Shadow price ; Unique Lagrange multiplier ; 49K15 ; 49J45 ; 37N40 ; 91B62
• 刊名：Journal of Dynamical and Control Systems
• 出版年：2013
• 出版时间：October 2013
• 年：2013
• 卷：19
• 期：4
• 页码：519-552
• 全文大小：587KB
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• 作者单位：Dmitry Khlopin (1) (2)
  
  1. Krasovskii Institute of Mathematics and Mechanics, Ural Branch, Russian Academy of Sciences, 16, S. Kovalevskaja St., 620990, Yekaterinburg, Russia
  2. Department of Applied Mathematics, Institute of Mathematics and Computer Science, Ural Federal University, 4, Turgeneva St., 620083, Yekaterinburg, Russia
  
• ISSN：1573-8698

文摘

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.