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Unmaximized inclusion necessary conditions for nonconvexconstrained optimal control problems

Published online by Cambridge University Press:  15 September 2005

Maria do Rosário de Pinho ,
Maria Margarida Ferreira  and
Fernando Fontes
Maria do Rosário de Pinho
Affiliation:
ISR and DEEC, Faculdade de Engenharia da Universidade do Porto, Rua Dr. Roberto Frias, 4200-465 Porto, Portugal; mrpinho@fe.up.pt; mmf@fe.up.pt
Maria Margarida Ferreira
Affiliation:
ISR and DEEC, Faculdade de Engenharia da Universidade do Porto, Rua Dr. Roberto Frias, 4200-465 Porto, Portugal; mrpinho@fe.up.pt; mmf@fe.up.pt
Fernando Fontes
Affiliation:
Officina Mathematica, Universidade do Minho, 4800-058 Guimarães, Portugal; ffontes@mct.uminho.pt
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Abstract

Necessary conditions of optimality in the form of Unmaximized Inclusions (UI) are derived for optimal control problems with state constraints. The conditions presented here generalize earlier optimality conditions to problems that may be nonconvex. The derivation of UI-type conditions in the absence of the convexity assumption is of particular importance when deriving necessary conditions for constrained problems. We illustrate this feature by establishing, as an application, optimality conditions for problems that in addition to state constraints incorporate mixed state-control constraints.

Keywords

Optimal controlstate constraintsnonsmooth analysisEuler-Lagrange inclusion.
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 11 , Issue 4 , October 2005 , pp. 614 - 632
Copyright
© EDP Sciences, SMAI, 2005

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