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Necessary optimality conditions of first and second order for systems with boundary conditions. (English) Zbl 1209.49023
Summary: We consider an optimal control problem wherein the state of a system is determined from a controlled system of ordinary differential equations with two-point boundary conditions. Admissible controls are chosen from a class of bounded and measurable functions. The validity of the Pontryagin maximum principle is proved for the investigated class of problems. The increment formula of the second-order functional is calculated. On the basis of needle-shaped control variations we obtain necessary optimality conditions for singular controls in the sense of the Pontryagin maximum principle.
MSC:
49K15Optimal control problems with ODE (optimality conditions)