Unmaximized inclusion necessary conditions for nonconvex constrained optimal control problems
ISR and DEEC,
Faculdade de Engenharia da Universidade do Porto,
Rua Dr. Roberto Frias,
4200-465 Porto, Portugal;
2 Officina Mathematica, Universidade do Minho, 4800-058 Guimarães, Portugal; email@example.com
Revised: 19 November 2004
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.
Mathematics Subject Classification: 49K15
Key words: Optimal control / state constraints / nonsmooth analysis / Euler-Lagrange inclusion.
© EDP Sciences, SMAI, 2005