There is an increasing number of applications whose trajectories are better modeled by discontinuous or impulsive trajectories. Thus, we explore optimality conditions for impulsive control system expressed in terms of an Hamilton-Jacobi-Bellman equation. We use a measure driven differential inclusion to model the impulsive behavior since it provides a formal framework in which the control space is complete. Additionally, we use the impulsive Euler solution and invariance results to derive feedback optimal control synthesis.