Necessary conditions of optimality for vector-valued impulsive control problems with state constraints

A vector-valued impulsive control problem is considered whose dynamics, defined by a differential inclusion, have to satisfy state constraints and are such that the vector fields associated 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 conditions are obtained by taking a limit of those for an appropriate sequence of auxiliary “standard” optimal control problems approximating the original one. An example to illustrate the nature of the new optimality conditions is provided.