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This paper presents a new approach to neurocontrol of deterministic, discrete-time non-linear (NARMA) dynamic systems, given only input-output data of finite length. The demanding setting of scarce knowledge about the plant is motivated by practice of data acquisition and the complexity of discretised dynamics. The essence of the method is a novel modelling technique based on nonuniform multi-dimensional (N-D) sampling and Fourier Analysis. ; The right-hand side (RHS) of the NARMA model is reconstructed from nonuniformly spaced (N-D) samples. This is done by approximating the Fourier transform of the RHS. To this end a feedforward neural network is applied as an implementation of a multi-dimensional interpolating filter in the (N-D) frequency domain. The neural model obtained in this way is smooth and suitable for the purposes of non-linear control. ; In order to deal with the modelling error, a new technique of BIBO redesign of the closed-loop system is introduced. The modelling method is inspired by the ideas of Sanner and Slotine (1992), but it goes far beyond them, resulting in a novel approach. The main advantages of the new algorithm are: the realistic engineering setting, computational simplicity, applicability (mild assumptions), flexible neural implementation and relevance for control.