Abstract

Often in dynamic optimal control problems with a long time horizon, in a large neighburhood of the middle of the time interval the optimal control and the optimal state are very close to the solution of a static control problem that is derived from the dynamic optimal control problems by omitting the information about the initial state and possibly a desired terminal state.

This can be shown in different situations, for example under exact controllability assumptions or with the assumption of nodal profile exact controllability, as studied by Tatsien Li and his group. In this situation, we obtain the turnpike property with interior decay, that has been discussed in the paper Mathematics of Control, Signals, and Systems volume 33, pages 237–258 (2021).