Maximum principle for nonsmooth optimal impulse problems

摘要

A class of optimal control problems with discontinuous trajectories and vector-valued impulse controls is considered. The nonsmooth differential system, which define the dynamic of considered problems, is linear in the control's vector measure and doesn't satisfy the so-called well-possedness condition of Frobenius type. Necessary conditions for optimality, in the form a Maximum Principle, for impulse optimal control problem with general terminal and intermediate state constraints are presented. This is assumed that the examined measure is discontinuous at a finite number of times and has no the continuous singular component. The approach of investigation based on a reinterpretation of the impulse optimal control problem as a specific optimal multiprocesses problem.