Linear Dynamical Systems with Sparsity Constraints: Theory and Algorithms (2019)
Abstract / truncated to 115 words
This thesis develops new mathematical theory and presents novel recovery algorithms for discrete linear dynamical systems (LDS) with sparsity constraints on either control inputs or initial state. The recovery problems in this framework manifest as the problem of reconstructing one or more sparse signals from a set of noisy underdetermined linear measurements. The goal of our work is to design algorithms for sparse signal recovery which can exploit the underlying structure in the measurement matrix and the unknown sparse vectors, and to analyze the impact of these structures on the efficacy of the recovery. We answer three fundamental and interconnected questions on sparse signal recovery problems that arise in the context of LDS. First, what ... toggle 14 keywordslinear dynamical systems – sparsity – observability – compressed sensing – sparse signal recovery – controllability – kalman rank test – pbh test – switched linear systems – kalman filter – multiple measurement vectors – sparse representation – dictionary learning – nonconvex optimization.
The current layout is optimized for mobile phones. Page previews, thumbnails, and full abstracts will remain hidden until the browser window grows in width.
The current layout is optimized for tablet devices. Page previews and some thumbnails will remain hidden until the browser window grows in width.