International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 33-36, Pages 1855-1879
doi:10.1155/S0161171204308033

Maximum principle and its extension for bounded control problems with boundary conditions

Abstract

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.