Nondegenerate Necessary Conditions for Optimal Impulsive Control Problems with State Constraints

A free time impulsive control problem with state constraints and equality and inequality constraints on the trajectory endpoints is considered in this article. After presenting an appropriate solution concept, necessary conditions of optimality in the form a Maximum Principle are stated. An essential feature of these conditions is that they do not degenerate, i.e., they remain informative even for abnormal control processes. These conditions are derived by using a penalty function method.