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This paper concerns an optimal control problem $(P)$ related to a nonlinearFokker-Planck equation. The problem is deeply related to a stochastic optimalcontrol problem $(P_S)$ for a McKean-Vlasov equation. The existence of anoptimal control is obtained for the deterministic problem $(P)$. The existenceof an optimal control is established and necessary optimality conditions arederived for a penalized optimal control problem $(P_h)$ related to a backwardEuler approximation of the nonlinear Fokker-Planck equation (with a constantdiscretization step $h$). Passing to the limit ($h\rightarrow 0$) one derivesthe necessary optimality conditions for problem $(P)$.

Controlling a nonlinear Fokker-Planck equation via inputs with nonlocal action