Dimitri Dzhgarkava

Problem of Optimal Control with One-sided Mixed Restrictions for Controlled Objects Described by Integral Equations With Measure

abstract:
For extremal problems in $B$-spaces, a modified version of the method of joint covering is considered and a necessary condition of criticality is proved. In the space of regular functions with values in a $B$-space, the properties of a bilinear integral with measure are studied; a theorem on the existence of a solution of a nonhomogeneous integral equation with measure is proved; for controlled objects described both by integral equations with measure and by one-sided mixed restrictions, the necessary conditions of optimality are derived from those of criticality.

Mathematics Subject Classification: 42K22.

Key words and phrases: Method of joint covering, differential of a convex set, necessary conditions of criticality, regular functions, integral calculus with measure, integral equation with measure, optimal control, mixed restrictions, the necessary conditions of optimality.