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In this paper the turnpike property is established for a non-convex optimalcontrol problem in discrete time. The functional is defined by the notion ofthe ideal convergence and can be considered as an analogue of the terminalfunctional defined over infinite time horizon. The turnpike property statesthat every optimal solution converges to some unique optimal stationary pointin the sense of ideal convergence if the ideal is invariant under translations.This kind of convergence generalizes, for example, statistical convergence andconvergence with respect to logarithmic density zero sets.

Invariant ideals and its applications to the turnpike theory