Learning High-dimensional Dynamical Systems with Limited Sensing

In this paper, we focus on learning high-dimensional linear dynamical systems. To learn such systems, existing algorithms require either strong sensing capability or additional assumption on system observability. We propose an algorithm that learns the system model with a few sensors and without observability assumption. This is accomplished by integrating information from multiple data trajectories, each observing a possibly different set of coordinates of the high-dimensional states. Theoretical analysis of the algorithm is provided, showing that the system model can be learned accurately as long as every coordinate is observed in at least one trajectory. This approach significantly reduces the required number of sensors for data collection.