International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 35, Pages 1855-1879
Maximum principle and its extension for bounded control problems with boundary conditions
Department of Mathematics, University of Valle, Cali, Colombia
Received 5 August 2003
Copyright © 2004 Olga Vasilieva. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
This note is focused on a bounded control problem
with boundary conditions. The control domain need not be convex.
First-order necessary condition for optimality is obtained in the
customary form of the maximum principle, and second-order
necessary condition for optimality of singular controls is
derived on the basis of second-order increment formula using the
method of increments along with linearization approach.