In this chapter we study the turnpike property for the nonconvex optimal control problems described by the differential inclusion . We study the infinite horizon problem of maximizing the functional as T grows to infinity. The purpose of this chapter is to avoid the convexity conditions usually assumed in turnpike theory. A turnpike theorem is proved in which the main conditions are imposed on the mapping a and the function u. It is shown that these conditions may hold for mappings a with nonconvex images and for nonconcave functions u.
This article considers the application of the notion of statistical convergence in turnpike theory. The first results have been obtained recently [, , ]. We briefly discuss the importance of this conjunction, present some results obtained and, finally, we formulate a challenge problem for future investigations.