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Optimal Control Problems with Discounting

Chapter
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Part of the SpringerBriefs in Optimization book series (BRIEFSOPTI)

Abstract

In this chapter we continue our study of the structure of approximate solutions of the discrete-time optimal control problems with a compact metric space of states X and with a singleton turnpike. These problems are described by a nonempty closed set \(\Omega \subset X \times X\) which determines a class of admissible trajectories (programs) and by a bounded upper semicontinuous objective function \(v:X\times X \to R^1\) which determines an optimality criterion. We show the stability of the turnpike phenomenon under small perturbations of the objective function v and the set Ω in the case with discounting. The results of the chapter generalize the results obtained in [54] for the discounting case with a perturbation only on the objective function.

Keywords

Discrete-time Optimal Control Problem Turnpike Phenomenon Admissible Trajectories Optimality Criterion Induction Property 
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Copyright information

© The Author 2014

Authors and Affiliations

  1. 1.Department of MathematicsTechnion- Israel Institute of TechnologyHaifaIsrael

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