An analogue of the Euler equation and necessary conditions for second-order optimality in one two-stage control problem for integro-differential equations of Volterra type
Abstract:
We consider one two-stage (step) optimal control problem, described in two-time intervals by various Volterra-type
integro-differential equations. Under the assumption that the control domain is open, the first and second variations of the
Boltz-type quality functional are calculated. An analogue of the Euler equation (first order necessary optimality condition) has
been received. Using the condition of non-negativity of the second variation of the quality functional along the optimal control,
a number of constructively verifiable necessary conditions for second-order optimality are proved. The case of classically
singular controls is studied.
Keywords:stepwise optimal control problem, integro-differential equation of Volterra type, variation of the functional,
analogue of the Euler equation, optimal control, singular control in the classical sense.
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