Optimal Control Problems Arising in Forest Management by Alexander J. Zaslavski

Author:Alexander J. Zaslavski
Language: eng
Format: epub, pdf
ISBN: 9783030235871
Publisher: Springer International Publishing

and

(Here we assume that supremum over an empty set is −∞.) It is easy to see that the following result holds.

Proposition 3.11

Let , T 1 < T 2 be integers, u t, t = T 1, …, T 2 − 1 be bounded and upper semicontinuous functions and let be finite. Then there exists a program such that

Theorem 3.12

Let 𝜖 be a positive number. Then there exist an integer τ > 0 and a positive number γ such that for each natural number T > 2τ, each sequence of bounded functions u t : Ω → R 1 , t = 0, …, T − 1 satisfying ∥u t − u∥≤ γ, t = 0, 1, …, T − 1 and each program which satisfies

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