Hamilton-Jacobi conditions for an impulsive control problem

摘要

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