On constraint qualifications for nondegenerate necessary      conditions of optimality applied to optimal control problems

Sofia O. Lopes; Fernando A. C. C. Fontes; Maria do Rosário de Pinho

doi:10.3934/dcds.2011.29.559

Article Contents

2011, Volume 29, Issue 2: 559-575. Doi: 10.3934/dcds.2011.29.559

This issue Previous Article Regularity of optimal transport and cut locus: From nonsmooth analysis to geometry to smooth analysis Next Article Euler-Lagrange equations for composition functionals in calculus of variations on time scales

On constraint qualifications for nondegenerate necessary conditions of optimality applied to optimal control problems

1.
CMAT e Departamento de Matemática e Aplicações, Universidade do Minho, 4800-058 Guimarães
2.
ISR-Porto, Faculdade de Engenharia, Universidade do Porto, 4200-465 Porto

Received: August 31, 2009

Revised: March 31, 2010

Published: May 2011

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Abstract

We address necessary conditions of optimality (NCO), in the form of a maximum principle, for optimal control problems with state constraints. In particular, we are interested in the NCO that are strengthened to avoid the degeneracy phenomenon that occurs when the trajectory hits the boundary of the state constraint. In the literature on this subject, we can distinguish two types of constraint qualifications (CQ) under which the strengthened NCO can be applied: CQ involving the optimal control and CQ not involving it. Each one of these types of CQ has its own merits. The CQs involving the optimal control are not so easy to verify, but, are typically applicable to problems with less regularity on the data. In this article, we provide conditions under which the type of CQ involving the optimal control can be reduced to the other type. In this way, we also provide nondegenerate NCO that are valid under a different set of hypotheses.

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Mathematics Subject Classification: 49K15, 49K30.

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