Necessary conditions for nonsmooth optimal impulse control problem with intermediate constraints

Nonlinear optimal control problems, in which state trajectories are permitted to be discontinuous at a finite number of times, and the jump times are choice variables, are analysed. Problems such as these arise in economics, lazer technique, and robototechnique. Necessary conditions for optimality, in the form of a Maximum Principle, for the impulse optimal control problems with general terminal and intermediate state constraints are presented. The proof of these necessary conditions is based on using the Maximum Principle for optimal multiprocesses.