Turnpike Conditions in Infinite Dimensional Optimal Control by Alexander J. Zaslavski

Author:Alexander J. Zaslavski
Language: eng
Format: epub, pdf
ISBN: 9783030201784
Publisher: Springer International Publishing

In the sequel we use the following result which easily follows the definitions.

Proposition 5.24

Let f have (P1) and . There exists an (f)-good pair (x, u) ∈ X(0, ∞) satisfying x(0) = z if and only if .

LSC property implies the following result.

Proposition 5.25

Let f have LSC property, T 2 > T 2 ≥ 0, and L > 0. Then 1. There exists (x, u) ∈ X(T 1, T 2) such that

2. If T 2 − T 1 ≥ 2L, , , then there exists (x, u) ∈ X(T 1, T 2) such that x(T i) = z i , i = 1, 2 and

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