Solvability of optimization problem for the oscillation processes with optimal vector controls

Abstract

The optimal control problem is investigated for oscillation processes, described by integro-differential equations with Fredholm operator when  functions of external and boundary sources nonlinearly dependent on components of optimal vector controls. Optimality conditions are found having specific properties in the case of vector controls. A sufficient condition is established for unique solvability of the nonlinear optimization problems and its complete solution is constructed in the form of optimal control, an optimal process, and a minimum value of the functional.