Hamilton-Jacobi Conditions for an Impulsive Control Problem

Abstract

A vector-valued impulsive control problem is considered whose dynamics,defined by a differential inclusion, are such that the vector fields associated withthe singular term do not satisfy the so called Frobenius condition. A concept ofproper solution based on a reparametrization procedure is adopted which enables thederivation of optimality conditions of the Hamilton-Jacobi type. These conditions areobtained by taking a limit of those for an appropriate sequence of auxiliary standardoptimal control problems approximating the original one.