Optimal Control Problems with Discounting
In this chapter we continue our study of the structure of approximate solutions of the discrete-time optimal control problems with a compact metric space of states X and with a singleton turnpike. These problems are described by a nonempty closed set \(\Omega \subset X \times X\) which determines a class of admissible trajectories (programs) and by a bounded upper semicontinuous objective function \(v:X\times X \to R^1\) which determines an optimality criterion. We show the stability of the turnpike phenomenon under small perturbations of the objective function v and the set Ω in the case with discounting. The results of the chapter generalize the results obtained in  for the discounting case with a perturbation only on the objective function.