Necessary Conditions of Optimality for Vector-Valued Impulsive Control Problems Fernando Lobo Pereira a,1 Geraldo Nunes Silva b,2 a Instituto de Sistemas e Robotica Fac. de Eng. da Universidade do Porto R. Bragas, 4099 Porto Codex, Portugal e-mail: flp@fe.up.pt b Dept. Computer Science and Statistics Universidade Estadual Paulista C. P. 136, S. J. Rio Preto-SP, Brasil e-mail: gsilva@dcce.ibilce.unesp.br Abstract 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 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 approxi- mating the original one. An example to illustrate the nature of the new optimality conditions is provided. Key words: Vector-valued Impulsive Control; Differential Inclusions; Necessary Conditions of Optimality 1 Introduction In this paper, we address impulsive control problems for which the control measure is vector valued and the hypotheses on the data allow measurable time dependence and a time varying control constraint set. More specifically, 1 Supported by Praxis XXI program of FCT and ICCIT of Portugal 2 Supported by CNPq and FAPESP of Brazil Preprint submitted to Elsevier Preprint 20 July 2004