Journal of Convex Analysis 21 (2014), No. 3, 681--701
Copyright Heldermann Verlag 2014
Turnpike Properties of Approximate Solutions of Nonconcave Discrete-Time Optimal Control Problems
Alexander J. Zaslavski
Dept. of Mathematics, Technion, Israel Institute of Technology, 32000 Haifa, Israel
We study the structure of approximate solutions of an autonomous nonconcave discrete-time 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.
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