Optimization of fully controlled sweeping processes

The paper is devoted to deriving necessary optimality conditions in a general optimal control problem for dynamical systems governed by controlled sweeping processes with hard-constrained actions entering both polyhedral moving sets and additive perturbations. By using the first-order mainly second-order tools of variational analysis generalized differentiation, we develop well-posed method discrete approximations, obtain solutions discrete-time systems, then establish passing limit verifiable local minimizers original process that are expressed entirely terms its given data. efficiency obtained dynamics illustrated solving three nontrivial examples their own interest.