State Constraints in Impulsive Control Problems: Gamkrelidze-Like Conditions of Optimality
An impulsive control problem with state constraints is considered. A Pontryagin maximum principle in the framework of R.V. Gamkrelidze is derived, being its proof based on a certain penalization technique and on the application of Ekelands variational principle. This approach is distinct from the more usual ones in Impulsive Control theory based on a reduction to a conventional control problem and exhibits the advantage of allowing to address problems with dynamics which are merely measurable in the time variable. Controllability assumptions to ensure the non-degeneracy of the conditions are provided in the impulsive control context. An example demonstrating the significance of the conditions is given.
state constraints impulsive control maximum principle 49n25