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Turnpike Properties of Discrete-Time Problems

In: Turnpike Phenomenon and Infinite Horizon Optimal Control

Author

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  • Alexander J. Zaslavski

    (Technion - Israel Institute of Technology)

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.

Suggested Citation

  • Alexander J. Zaslavski, 2014. "Turnpike Properties of Discrete-Time Problems," Springer Optimization and Its Applications, in: Turnpike Phenomenon and Infinite Horizon Optimal Control, edition 127, chapter 0, pages 23-145, Springer.
    • Handle: RePEc:spr:spochp:978-3-319-08828-0_2
    DOI: 10.1007/978-3-319-08828-0_2
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