Necessary optimality conditions for impulsive control problems

In this article, we present first and second order necessary conditions of optimality for impulsive control problems recently obtained by the authors. Two kind of results are discussed: first order necessary conditions of optimality for the free time optimal control problem with state and control constraints and second order necessary conditions for fixed time optimal control problems with state endpoint and control constraints. The main feature of these conditions is their nondegeneracy. A discussion of these results in the context of the state-of-the-art providing a historical perspective and insight for future perspectives is also included. Copyright © IFAC GENERALIZED SOLUTIONS IN CONTROL PROBLEMS. 2004.