
Journal of Convex Analysis 21 (2014), No. 3, 681701 Copyright Heldermann Verlag 2014 Turnpike Properties of Approximate Solutions of Nonconcave DiscreteTime Optimal Control Problems Alexander J. Zaslavski Dept. of Mathematics, Technion, Israel Institute of Technology, 32000 Haifa, Israel ajzasl@tx.technion.ac.il We study the structure of approximate solutions of an autonomous nonconcave discretetime control system with a compact metric space of states. This control system is described by a bounded upper semicontinuous objective function which determines an optimality criterion. We are interested in turnpike properties of the approximate solutions which are independent of the length of the interval, for all sufficiently large intervals. We show that the turnpike property of approximate solutions on finite intervals follows from the asymptotic turnpike property of approximate solutions of the corresponding infinite horizon optimal control problem. We also show that this asymptotic turnpike property for the corresponding infinite horizon optimal control problem holds for most objective functions in the sense of Baire category. Keywords: Compact metric space, generic property, good program, turnpike property. MSC: 49J99 [ Fulltextpdf (145 KB)] for subscribers only. 