# Erratum to: Averaging and Linear Programming in Some Singularly Perturbed Problems of Optimal Control

Erratum to: Averaging and Linear Programming in Some Singularly Perturbed Problems of Optimal... Appl Math Optim (2015) 71:277–278 DOI 10.1007/s00245-014-9265-1 ERRATUM Erratum to: Averaging and Linear Programming in Some Singularly Perturbed Problems of Optimal Control Vladimir Gaitsgory · Sergey Rossomakhine Published online: 12 August 2014 © Springer Science+Business Media New York 2014 Erratum to: Appl Math Optim DOI 10.1007/s00245-014-9257-1 The proof of Theorem 3.14 is based on several lemmas, one of which is Lemma 5.3. The argument used in the proof of the latter is based on the fact that, for any (u ¯, y ¯) ∈ clθ , where def ∗ ∗ ∗ θ ={(u, y) : (u, y) = (u (τ ), y (τ )) for some τ ∈[0, ∞)} t t t ∗ ∗ ((u (τ ), y (τ )) being the admissible pair of the associated system introduced in t t Assumption 3.11(iii)), μ (t )( B (u ¯, y ¯)) > 0 ∀ r > 0, (1.1) def ∗ ∗ ∗ where μ (t ) is the occupational measure generated by (u (τ ), y (τ )) and B (u ¯, y ¯) = t t {(u, y) :||u −¯ u|| + || y −¯ y|| < r } (see (5.55)). The online version of the original http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Mathematics and Optimization Springer Journals

# Erratum to: Averaging and Linear Programming in Some Singularly Perturbed Problems of Optimal Control

, Volume 71 (2) – Apr 1, 2015
2 pages

/lp/springer_journal/erratum-to-averaging-and-linear-programming-in-some-singularly-8wczFH4LUa
Publisher
Springer US
Subject
Mathematics; Calculus of Variations and Optimal Control; Optimization; Systems Theory, Control; Theoretical, Mathematical and Computational Physics; Mathematical Methods in Physics; Numerical and Computational Physics
ISSN
0095-4616
eISSN
1432-0606
D.O.I.
10.1007/s00245-014-9265-1
Publisher site
See Article on Publisher Site

### Abstract

Appl Math Optim (2015) 71:277–278 DOI 10.1007/s00245-014-9265-1 ERRATUM Erratum to: Averaging and Linear Programming in Some Singularly Perturbed Problems of Optimal Control Vladimir Gaitsgory · Sergey Rossomakhine Published online: 12 August 2014 © Springer Science+Business Media New York 2014 Erratum to: Appl Math Optim DOI 10.1007/s00245-014-9257-1 The proof of Theorem 3.14 is based on several lemmas, one of which is Lemma 5.3. The argument used in the proof of the latter is based on the fact that, for any (u ¯, y ¯) ∈ clθ , where def ∗ ∗ ∗ θ ={(u, y) : (u, y) = (u (τ ), y (τ )) for some τ ∈[0, ∞)} t t t ∗ ∗ ((u (τ ), y (τ )) being the admissible pair of the associated system introduced in t t Assumption 3.11(iii)), μ (t )( B (u ¯, y ¯)) > 0 ∀ r > 0, (1.1) def ∗ ∗ ∗ where μ (t ) is the occupational measure generated by (u (τ ), y (τ )) and B (u ¯, y ¯) = t t {(u, y) :||u −¯ u|| + || y −¯ y|| < r } (see (5.55)). The online version of the original

### Journal

Applied Mathematics and OptimizationSpringer Journals

Published: Apr 1, 2015

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