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Aseev, S., Krastanov, M., & Veliov, V. (2016). Optimality Conditions for Discrete-Time Optimal Control on Infinite Horizon (No. 2016–09). http://hdl.handle.net/20.500.12708/39088
E105-04 - Forschungsbereich Variationsrechnung, Dynamische Systeme und Operations Research
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Report No.:
2016-09
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Date (published):
2016
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Number of Pages:
17
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Keywords:
discrete-time control systems; optimality conditions; Pontryagin maximum principle; transversality conditions
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Abstract:
The paper presents rst order necessary optimality conditions of Pontrygin's type for a general class of discrete-time optimal control problems on in nite horizon. The main novelty is that the adjoint function, for which the (local) maximum condition in the Pontryagin principle holds, is explicitly de ned for any given optimal state-control process. This is done based on ideas from previous papers ...
The paper presents rst order necessary optimality conditions of Pontrygin's type for a general class of discrete-time optimal control problems on in nite horizon. The main novelty is that the adjoint function, for which the (local) maximum condition in the Pontryagin principle holds, is explicitly de ned for any given optimal state-control process. This is done based on ideas from previous papers of the rst and the last authors concerning continuous-time problems. In addition, the obtained (local) max-
imum 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.
