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The identification of a nonlinear dynamic model is an open topic in controltheory, especially from sparse input-output measurements. A fundamentalchallenge of this problem is that very few to zero prior knowledge is availableon both the state and the nonlinear system model. To cope with this challenge,we investigate the effectiveness of deep learning in the modeling of dynamicsystems with nonlinear behavior by advocating an approach which relies on threemain ingredients: (i) we show that under some structural conditions on theto-be-identified model, the state can be expressed in function of a sequence ofthe past inputs and outputs; (ii) this relation which we call the state map canbe modelled by resorting to the well-documented approximation power of deepneural networks; (iii) taking then advantage of existing learning schemes, astate-space model can be finally identified. After the formulation and analysisof the approach, we show its ability to identify three different nonlinearsystems. The performances are evaluated in terms of open-loop prediction ontest data generated in simulation as well as a real world data-set of unmannedaerial vehicle flight measurements.

Learning Reduced Nonlinear State-Space Models: an Output-Error Based Canonical Approach