The Generalized Solutions of Nonlinear Optimization Problems with Impulse Control

Abstract

The optimal control problem described by a nonlinear ordinary differential equation is considered with unbounded controls. The aim of this paper is to provide a representation of generalized (discontinuous) solutions in terms of differential equations with a measure. By using the method of discontinuous time change the problem with nonlinear dependence on the unbounded controls can be reduced to the simpler one with bounded controls. These results are applied to solving the problem of generalized (discontinuous) solution representation in the dynamic system with impulse-type controls.