Vasilieva, Olga Maximum principle and its extension for bounded control problems with boundary conditions. (English) Zbl 1079.49020 Int. J. Math. Math. Sci. 2004, No. 33-36, 1855-1879 (2004). Summary: This note is focused on a bounded control problem with boundary conditions. The control domain need not be convex. A first-order necessary condition for optimality is obtained in the customary form of the maximum principle, and a second-order necessary condition for optimality of singular controls is derived on the basis of the second-order increment formula using the method of increments along with the linearization approach. Cited in 4 Documents MSC: 49K15 Optimality conditions for problems involving ordinary differential equations 34B15 Nonlinear boundary value problems for ordinary differential equations 34H05 Control problems involving ordinary differential equations Keywords:optimal control; maximum principle; nonlinear boundary value problem; needle-shaped variation PDFBibTeX XMLCite \textit{O. Vasilieva}, Int. J. Math. Math. Sci. 2004, No. 33--36, 1855--1879 (2004; Zbl 1079.49020) Full Text: DOI EuDML