Abstract
In this chapter we study the turnpike property for the nonconvex optimal control problems described by the differential inclusion $$\dot{x} \in a(x)$$ . We study the infinite horizon problem of maximizing the functional $$\int_{0}^{T} u(x(t))\,dt$$ 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.
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