Aircraft models may be considered as flat if one neglects some terms associated to aerodynamics. Computational experiments in Maple show that in some cases a suitably designed feed-back allows to follow such trajectories, when applied to the non-flat model. However some maneuvers may be hard or even impossible to achieve with this flat approximation. In this paper, we propose an iterated process to compute a more achievable trajectory, starting from the flat reference trajectory. More precisely, the unknown neglected terms in the flat model are iteratively re-evaluated using the values obtained at the previous step. This process may be interpreted as a new trajectory parametrization, using an infinite number of derivatives, a property that may be called generalized flatness. We illustrate the pertinence of this approach in flight conditions of increasing difficulties, from single engine flight, to aileron roll.

This paper deals with the interpolation of the Room Impulse Responses (RIRs) within a whole volume, from as few measurements as possible, and without the knowledge of the geometry of the room. We focus on the early reflections of the RIRs, that have the key property of being sparse in the time domain: this can be exploited in a framework of model-based Compressed Sensing. Starting from a set of RIRs randomly sampled in the spatial domain of interest by a 3D microphone array, we propose a modified Matching Pursuit algorithm to estimate the position of a small set of virtual sources. Then, the reconstruction of the RIRs at interpolated positions is performed using a projection onto a basis of monopoles, which correspond to the estimated virtual sources. An extension of the proposed algorithm allows the interpolation of the positions of both source and receiver, using the acquisition of four different source positions. This approach is validated both by numerical examples, and by experimental measurements using a 3D array with up to 120 microphones.

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We investigate different methods for testing whether a rational mapping ƒ from kn to km admits a rational inverse, or whether a polynomial mapping admits a polynomial one. We give a new solution, which seems much more efficient in practice than previously known ones using “tag” variables and standard basis, and a majoration for the degree of the standard basis calculations which is valid for both methods in the case of a polynomial map which is birational. We further show that a better bound can be given for our method, under some assumption on the form of ƒ. Our method can also extend to check whether a given polynomial belongs to the subfield generated by a finite set of fractions.