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Maximum principle and its extension for bounded control problems with boundary conditions. (English) Zbl 1079.49020
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.
MSC:
49K15Optimal control problems with ODE (optimality conditions)
34B15Nonlinear boundary value problems for ODE
34H05ODE in connection with control problems