  The paper extends an impulsive control-theoretical framework towards dynamic
systems in the space of measures. We consider a transport equation describing
the time-evolution of a conservative "mass" (probability measure), which
represents an infinite ensemble of interacting particles. The driving vector
field contains nonlocal terms and it is affine in the control variable. The
control is assumed to be common for all the agents, i.e., it is a function of
time variable only. The main feature of the addressed model is the admittance
of "shock" impacts, i.e. controls, whose influence on each agent can be
arbitrary close to Dirac-type distributions. We construct an impulsive
relaxation of this system and of the corresponding optimal control problem. For
the latter we establish a necessary optimality condition in the form of
Pontryagin's Maximum Principle.
