Identification of Piecewise Linear Models of Complex Dynamical Systems

The paper addresses the realization and identification problem or a subclass of piecewise-affine hybrid systems. The paper provides necessary and sufficient conditions for existence of a realization, a characterization of minimality, and an identification algorithm for this subclass of hybrid systems. The considered system class and the identification problem are motivated by applications in systems biology

Nonlinear Hybrid System Identification with Kernel Models

CDROM DOI: 10.1109/CDC.2010.5718011International audienceThis paper focuses on the identification of nonlinear hybrid systems involving unknown nonlinear dynamics. The proposed method extends the framework of [1] by introducing nonparametric models based on kernel functions in order to estimate arbitrary nonlinearities without prior knowledge. In comparison to the previous work of [2], which also dealt with unknown nonlinearities, the new algorithm assumes the form of an unconstrained nonlinear continuous optimization problem, which can be efficiently solved for moderate numbers of parameters in the model, as is typically the case for linear hybrid systems. However, to maintain the efficiency of the method on large data sets with nonlinear kernel models, a preprocessing step is required in order to fix the model size and limit the number of optimization variables. A support vector selection procedure, based on a maximum entropy criterion, is proposed to perform this step. The efficiency of the resulting algorithm is demonstrated on large-scale experiments involving the identification of nonlinear switched dynamical systems

A continuous optimization framework for hybrid system identification

International audienceWe propose a new framework for hybrid system identification, which relies on continuous optimization. This framework is based on the minimization of a cost function that can be chosen as either the minimum or the product of loss functions. The former is inspired by traditional estimation methods, while the latter is inspired by recent algebraic and support vector regression approaches to hybrid system identification. In both cases, the identification problem is recast as a continuous optimization program involving only the real parameters of the model as variables, thus avoiding the use of discrete optimization. This program can be solved efficiently by using standard optimization methods even for very large data sets. In addition, the proposed framework easily incorporates robustness to different kinds of outliers through the choice of the loss function

A Switched System Identification Approach to Spindle Modeling

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 model- ing 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 refor- mulations, 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 Ma- chines 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 Autoregres- sive (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