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This paper addresses a new class of optimal control problems for perturbedsweeping processes with measurable controls in additive perturbations of thedynamics and smooth controls in polyhedral moving sets. We develop aconstructive discrete approximation procedure that allows us to stronglyapproximate any feasible trajectory of the controlled sweeping process byfeasible discrete trajectories and also establish a $W^{1,2}$-strongconvergence of optimal trajectories for discretized control problems to a givenlocal minimizer of the original continuous-time sweeping control problem of theBolza type. Employing advanced tools of first-order and second-ordervariational analysis and generalized differentiation, we derive necessaryoptimality conditions for discrete optimal solutions under fairly generalassumptions formulated entirely in terms of the given data. The obtainedresults give us efficient suboptimality ("almost optimality") conditions forthe original sweeping control problem that are illustrated by a nontrivialnumerical example.

Optimization and Discrete Approximation of Sweeping Processes with Controlled Moving Sets and Perturbations