Exact linear modeling using Ore algebras - Mathematics > Optimization and ControlReport as inadecuate

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Abstract: Linear exact modeling is a problem coming from system identification: Given aset of observed trajectories, the goal is find a model usually, a system ofpartial differential and-or difference equations that explains the data asprecisely as possible. The case of operators with constant coefficients is wellstudied and known in the systems theoretic literature, whereas the operatorswith varying coefficients were addressed only recently. This question can betackled either using Gr\-obner bases for modules over Ore algebras or byfollowing the ideas from differential algebra and computing in commutativerings. In this paper, we present algorithmic methods to compute -most powerfulunfalsified models- MPUM and their counterparts with variable coefficientsVMPUM for polynomial and polynomial-exponential signals. We also study thestructural properties of the resulting models, discuss computer algebraictechniques behind algorithms and provide several examples.

Author: Kristina Schindelar, Viktor Levandovskyy, Eva Zerz

Source: https://arxiv.org/

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