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In this paper, we present the periodic modifier-adaptation formulation of the dynamic real time optimization. The proposed formulation uses gradient information to update the problem with affine modifiers so that, upon convergence, its solution matches the optimal steady periodic trajectory. Unlike other state of the art modifier-adaptation techniques, the proposed approach is able to converge not only to optimal steady states, but also to optimal periodic trajectories. The full control scheme to take the system from its current state to the optimal periodic trajectory is detailed. The convergence of the computed reference to the optimal periodic behaviour is shown by means of a periodic version of the quadruple tank benchmark.