From robust estimation to hybrid system identification

This report elaborates on my research activities with a particular focus put on the period thatranges from my graduation until now (2009-2016). Only a brief overview of scientific resultsobtained on this period is presented. The research topic discussed is mainly concerned withhybrid system identification from input-output measurements. Hybrid systems form a class ofdynamic systems where discrete and continuous dynamics interact. The global behavior resultsfrom switching among a finite number of subsystems. A fundamental challenge associated withthe identification of such systems is that the available data points are not labelled beforehandin 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 whichis relevant to a single subsystem. However this is typically a nonconvex procedure which doesnot admit any numerically efficient solution.We propose a robust identification approach whose principle is to fit appropriately the entiremixed dataset to a single equation. A common thread of our results is the concept of sparseoptimization with its associated convex relaxations. This common idea is presented in the thirdchapter as a solution to the robust regression problem. It is later applied to the identificationof switched linear systems and piecewise affine systems