  This paper is devoted to the study, for the first time in the literature, of
optimal control problems for sweeping processes governed by
integro-differential inclusions of the Volterra type with different classes of
control functions acting in nonconvex moving sets, external dynamic
perturbations, and integral parts of the sweeping dynamics. We establish the
existence of optimal solutions and then obtain necessary optimality conditions
for a broad class of local minimizers in such problems. Our approach to
deriving necessary optimality conditions is based on the method of discrete
approximations married to basic constructions and calculus rules of first-order
and second-order variational analysis and generalized differentiation. The
obtained necessary optimality conditions are expressed entirely in terms of the
problem data and are illustrated by nontrivial examples that include
applications to optimal control models of non-regular electrical circuits.
