Estimating inputs of nonlinear dynamical systems using differential algebra techniques
| Authors: | Pillonetto Gianluigi, University of Padova, Italy
Saccomani Maria Pia, University of Padova, Italy |
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| Topic: | 1.1 Modelling, Identification & Signal Processing |
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| Session: | Observer and Filter Design |
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| Keywords: | inverse problems, characteristic set, input-output relation,Tikhonov regularization, regularization parameter, Kalman smoothing filter, Sobolev spaces |
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Abstract
The paper considers the problem of estimating the unknown input of a nonlinear dynamical system, described by polynomial or rational differential equations, from a finite set of noisy output samples.Without additional information this problem is ill-posed since it is assumed that the unknown function belongs to an infinite-dimensional space. We tackle this difficulty by designing a novel class of fast regularization algorithms that relies upon differential algebra techniques. Monte Carlo studies are used to demonstrate the goodness of the new approach.
