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 \(v: X \times X \rightarrow R^{1}\) 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.
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