System identification, model (in)validation and their applications to computer vision.

摘要

The theme of this dissertation is Control-Oriented or Robust Identification. Its goal is to address different open problems, that are relevant to the Control community. The role that operator theoretic tools may play in emerging areas in Computer Vision has been chosen as an additional motivation for studying these open problems.; The Robust Identification area was born around 1990, in an attempt to reconcile System Identification and well established Robust Control tools. Its goal is to obtain a bounded, uncertain model set description of a plant, in the form of a nominal model and a deterministic, worst-case bound on the identification error. It is appealing because the assumptions on the plant and the noise, involved in computing the identification error bounds and in establishing the existence of convergent algorithms, are minimal (e.g. no model order or statistics of the noise are involved).; On the other hand, Computer Vision seeks to make useful decisions about real physical objects and scenes based on sensed images. In order to successfully achieve this goal, it is necessary to obtain suitable mathematical descriptions of the sensors and the world, in the sense that they can deal with uncertainty caused by many factors, such as calibration errors of the cameras, time delays of the image processing algorithms, measurement noise and clutter: Here is where the Robust Identification area plays an important role.; The contributions of this dissertation can be valued as theoretical, by providing answers to problems of significance in the Control community such as the Robust Identification of Linear Parameter Varying (LPV) systems, and of marginally stable or unstable (non Schur) plants, and the (in)validation of Linear Fractional Transformation (LFT) models subject to structured uncertainty. But they are also of practical interest, by illustrating how dynamical models and bounded deterministic uncertainty can be combined to address the problems of Robust Active Vision, Inter-Frame Tracking and Prediction, and Visual Human Activity Recognition.