Turnpike Properties of Discrete-Time Problems

Alexander J. Zaslavski
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Alexander J. Zaslavski: Technion - Israel Institute of Technology

Chapter Chapter 2 in Turnpike Phenomenon and Infinite Horizon Optimal Control, 2014, pp 23-145 from Springer

Abstract: Abstract In this chapter we study the structure of approximate solutions of an autonomous discrete-time control system with a compact metric space of states X. This control system is described by a bounded upper semicontinuous function v : X × X → R 1 $$v: X \times X \rightarrow R^{1}$$ which determines an optimality criterion and by a nonempty closed set Ω ⊂ X × X which determines a class of admissible trajectories (programs). We are interested in turnpike properties of the approximate solutions which are independent of the length of the interval, for all sufficiently large intervals. When X is a compact convex subset of a finite-dimensional Euclidean space, the set Ω is convex, and the function v is strictly concave we obtain a full description of the structure of approximate solutions.

Keywords: Turnpike Property (TP); Discrete-time Control Systems; Semicontinuous Function; Turnpike Phenomenon; Turnpike Results (search for similar items in EconPapers)
Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:spr:spochp:978-3-319-08828-0_2

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DOI: 10.1007/978-3-319-08828-0_2

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