  This paper addresses novel applications to practical modeling of the newly
developed theory of necessary optimality conditions in controlled
sweeping/Moreau processes with free time and pointwise control and state
constraints. Problems of this type appear, in particular, in dynamical models
dealing with unmanned surface vehicles (USVs) and nanoparticles. We formulate
optimal control problems for a general class of such dynamical systems and show
that the developed necessary optimality conditions for constrained free-time
controlled sweeping processes lead us to designing efficient procedures to
solve practical models of this class. Moreover, the paper contains numerical
calculations of optimal solutions to marine USVs and nanoparticle models in
specific situations. Overall, this study contributes to the advancement of
optimal control theory for constrained sweeping processes and its practical
applications in the fields of marine USVs and nanoparticle modeling.
