From robust estimation to hybrid system identification
Résumé
This report elaborates on my research activities with a particular focus put on the period that
ranges from my graduation until now (2009-2016). Only a brief overview of scientific results
obtained on this period is presented. The research topic discussed is mainly concerned with
hybrid system identification from input-output measurements. Hybrid systems form a class of
dynamic systems where discrete and continuous dynamics interact. The global behavior results
from switching among a finite number of subsystems. A fundamental challenge associated with
the identification of such systems is that the available data points are not labelled beforehand
in the sense that one does not know a priori which data point is generated by which subsystem.
Ideally, one would like to partition the data points into a finite number of groups each of which
is relevant to a single subsystem. However this is typically a nonconvex procedure which does
not admit any numerically efficient solution.
We propose a robust identification approach whose principle is to fit appropriately the entire
mixed dataset to a single equation. A common thread of our results is the concept of sparse
optimization with its associated convex relaxations. This common idea is presented in the third
chapter as a solution to the robust regression problem. It is later applied to the identification
of switched linear systems and piecewise affine systems.
Domaines
Automatique / Robotique
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