Machines à Vecteurs de Support et Identification de Systèmes Hybrides
Fabien Lauer · HAL (Le Centre pour la Communication Scientifique Directe) · 2008
The thesis focuses on three nonlinear modeling problems: classification (or pattern recognition), regression (or function approximation) and hybrid system identification. Amongst existing approaches, Support Vector Machines (SVMs) offer a general framework for both nonlinear classification and regression. These recent methods, based on statistical learning theory, rely on convex optimization to train black-box models with good generalization performances. The study first focuses on the evolution of these models towards grey-box models, which can benefit at the same time from the universal approximation capacity of black-box models and from prior knowledge. In particular, the thesis proposes a general framework for the incorporation of a wide variety of prior knowledge in SVMs for regression, which leads to a learning algorithm written as a convex optimization program. The last part of the thesis proposes to extend SVMs to the identification of hybrid systems, that switch between different dynamics. In this context, the classification and regression problems are intrinsically mixed together and cannot be considered separately. A method based on non-convex optimization is proposed to solve these problems simultaneously. The resulting algorithm is able to deal with hybrid systems switching between arbitrary and unknown dynamics.