Optimality Conditions for Discrete-Time Optimal Control on Infinite Horizon

Aseev SM, Krastanov MI, & Veliov VM (2016). Optimality Conditions for Discrete-Time Optimal Control on Infinite Horizon. Reseach Unit ORCOS, Vienna University of Technology , Vienna, Austria.

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Abstract

The paper presents first order necessary optimality conditions of Pontrygin's type for a general class of discrete-time optimal control problems on infinite horizon. The main novelty is that the adjoint function, for which the (local) maximum condition in the Pontryagin principle holds, is explicitly defined for any given optimal state-control process. This is done based on ideas from previous papers of the first and the last authors concerning continuous-time problems. In addition, the obtained (local) maximum principle is in a normal form, and the optimality has the general meaning of weakly overtaking optimality (hence unbounded processes are allowed), which is important for many economic applications. Two examples are given, which demonstrate the applicability of the obtained results in cases where the known necessary optimality conditions fail to identify the optimal solutions.

Item Type: Other
Additional Information: SWM/ORCOS Research Report 2016-09
Uncontrolled Keywords: discrete-time control systems, optimality conditions, Pontryagin maximum principle, transversality conditions.
Research Programs: Advanced Systems Analysis (ASA)
Depositing User: Romeo Molina
Date Deposited: 09 Nov 2016 14:25
Last Modified: 09 Nov 2016 14:26
URI: http://pure.iiasa.ac.at/13925

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