| Due to new advances in convex optimization, in particular, semidefinite programming, previously infeasible problems are now in the realm of possibility. Mainly, there have been new breakthroughs in the modeling of signals as the output of switched dynamical systems where the switching indicates underlying events of interest. This method is known as hybrid system identification. These problems can be formulated as polynomial optimization problems by which, through algebraic reformulations, convex optimization approaches now exist.;In this work, we explore the application of these new approaches, which lay at the intersection of systems and control with machine learning, for the detection of events in electroencephalogram (EEG) signals.;Our particular focus on EEG signals is twofold. First, these signals are routinely used to monitor the quality of sleep, which is critical to both physical and mental health. Second, the onset of the internet-of-things has driven industry to develop affordable, in home, EEG sleep monitors. Most of these devices will take advantage of cloud services where vast amounts of sleep data will be processed.;There have been various attempts to develop automatic staging systems using mostly machine learning approaches such as Support Vector Machines and Neural Networks. However, there is very limited research that explores the use of switched dynamical systems to model sleep wave- forms.;This thesis work is the first step towards this direction. It focuses on modeling spindles, found in stage two of sleep, as switched Autoregressive (AR) models where the switching events are used to determine if a spindle occurred. Various aspects of the problem are considered, such as those related to error introduced by noise and the effect of model order.;The results presented in this work reveal potential new approaches to unsupervised classification of spindles and event based feature detection in complex signals. |
