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This article investigates the properness, or well-posedness, of impulsive extension of a conventional optimal control problem. This includes both well-posedness of the solution to impulsive control systems arising as result of an impulsive extension of ordinary differential systems, and existence theorems. Well-posedness in the classic Cauchy sense is proved. Approximation lemmas that guarantee sensitivity to small perturbations in control variables are obtained. Filippov type existence theorems are established. A model example is provided to show the relevance of the impulsive controls problems which are under study.