Necessary conditions of optimality for vector-valued impulsive control problems

A vector-valued impulsive control problem is considered whose dynamics, def ined by a differential inclusion, are such that the vector fields associate d with the singular term do not satisfy the so-called Frobenius condition. A concept of robust solution based on a new reparametrization procedure is adopted in order to derive necessary conditions of optimality. These condit ions are obtained by taking a limit of those for an appropriate sequence of auxiliary "standard" optimal control problems approximating the original o ne. An example to illustrate the nature of the new optimality conditions is provided. (C) 2000 Elsevier Science B.V. All rights reserved.