Consistent Approximations to Impulsive Optimal Control Problems
  We analyse the theory of consistent approximations given by Polak and we use it in an impulsive optimal control problem. We reparametrize the original system and build consistent approximations for this new reparametrized problem. So, we prove that if a sequence of solution of the consistent approximations is converging, it will converge to a solution of the reparametrized problem, and, finally, we show that from a solution of the reparametrized problem we can find a solution of the original one. 
Daniella Porto, Geraldo Nunes Silva and Helo\'isa Helena Marino Silva
math.OC