Minimal Time Impulse Control for a Class of Homogeneous Evolution Equations

In this paper, we deal with a minimal time control problem for a class of homogeneous evolution equations with impulse controls. We provide a systematical method to study the existence, uniqueness and bang-bang property of optimal controls for the problem. Moreover, we also establish the continuous dependence of the optimal control by the continuity of the minimal time function of this problem with respect to the parameters.