Turnpike Phenomenon and Infinite Horizon Optimal Control by Alexander J. Zaslavski

Author:Alexander J. Zaslavski
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

Let z ∈ R n and there exists an (f)-good function v: [0, ∞) → R n such that v(0) = z. Denote by a unique (f)-overtaking optimal function satisfying Y (f, z)(0) = z which exists by Theorem 3.19.

In this chapter we prove the following theorem obtained in [61] which describes the structure of approximate solutions of variational problems in the regions containing the left end point.

Theorem 3.20.

Let M,ε > 0 be real numbers and let L 0 ≥ 1 be an integer. Then there exist a positive number δ and an integer such that for each number T ≥ L 1 , each point z ∈ X M , and each a.c. function v: [0,T] → R n which satisfies

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