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We extend to $\mathrm{C}\times \mathrm{W}^{1,2}$-local minimizers andnonautonomous perturbation function, the necessary optimality conditionsderived in [1], via continuous-time approximations, for $\mathrm{W}^{1,2}\times\mathrm{W}^{1,2}$-local minimizers of an optimal control problem governed by acontrolled nonconvex sweeping process with autonomous perturbation function.

Nonsmooth optimality criterion for a $\mathrm{W}^{1,2}$-controlled sweeping process: Nonautonomous perturbation