Optimal Control Problem for an Impulsive Systems of FunctionalDifferential Equations with a Nonlinear Function under the Sign of a First-Order Differential

Abstract

In this paper the optimal control problems for an impulsive systems of functionaldifferential equations with a nonlinear function under the sign of the first-order differential and
with maxima are investigated. The Initial value problem is reduced to a system of nonlinear
functional-integral equations in a Banach space BD[0, T], Rⁿ. In the fixed values of control
function, by the method of contracting mappings proves the existence and uniqueness of state
function for a nonlinear systems of functional-integral equations with maxima. Then using
functional of quality, we are built Pontryagin’s function and obtain criteria of optimality. Then
we are proved existence and uniqueness of control function.