On the solvability of control synthesis problems for nonlinear oscillatory optimization processes described by integro-differential equations

The solvability of synthesis problems for distributed and boundary controls in minimizing problems for piecewise linear functionals for oscillatory processes described by partial integro-differential equations with Fredholm integral operators are examined. For the Bellman functional, a specific integro-differential equation is obtained. An algorithm for constructing a solution of the control synthesis problem of distributed and boundary controls is described. A procedure for determining controls as functions (functionals) of the state of the controlled process is constructed.