Learning of Linear Dynamical Systems as a Noncommutative Polynomial Optimization Problem

Abstract

There has been much recent progress in time series forecasting and estimation of system matrices of linear dynamical systems. We present an approach to both problems based on an asymptotically convergent hierarchy of convexifications of a certain nonconvex operator-valued problem, which is known as noncommutative polynomial optimization problem. We present promising computational results, including a comparison with methods implemented in MATLAB System Identification Toolbox.