@article{Bettiol:2016,
author = {Bettiol, P and Khalil, N and Vinter, RB},
journal = {Journal of Convex Analysis},
pages = {291--311},
title = {Normality of Generalized Euler-Lagrange Conditions for State Constrained Optimal Control Problems},
volume = {23},
year = {2016}
}

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TY  - JOUR
AB  - We consider state constrained optimal control problems in which the cost to minimize comprises both integral and end-point terms, establishing normality of the generalized Euler-Lagrange condition. Simple examples illustrate that the validity of the Euler-Lagrange condition (and related necessary conditions), in normal form, depends crucially on the interplay between velocity sets, the left end-point constraint set and the state constraint set. We show that this is actually a common feature for general state constrained optimal control problems, in which the state constraint is represented by closed convex sets and the left end-point constraint is a closed set. In these circumstances classical constraint qualifications involving the state constraints and the velocity sets cannot be used alone to guarantee normality of the necessary conditions. A key feature of this paper is to prove that the additional information involving tangent vectors to the left end-point and the state constraint sets can be used to establish normality.
AU  - Bettiol,P
AU  - Khalil,N
AU  - Vinter,RB
EP  - 311
PY  - 2016///
SN  - 0944-6532
SP  - 291
TI  - Normality of Generalized Euler-Lagrange Conditions for State Constrained Optimal Control Problems
T2  - Journal of Convex Analysis
VL  - 23
ER  - 

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