Selective Tracking Using Linear Trackability Analysis and Inversion-based Tracking Control

Trackability is the ability of a system to follow arbitrary reference commands and is equivalent to a system being right invertible. For systems that are trackable, feedforward inversion-based control (along with an additional feedback loop) is a common method to achieve tracking. In this paper, we focus on trackability for linear discrete-time MIMO systems and examine the idea of selective tracking that is particularly useful when a system is not trackable but it is possible to track either certain subsets of outputs or certain combinations of them. We show that tracking each component of the output vector can be assigned a priority within the context of an inversion-based controller to provide significant flexibility in selectively tracking outputs of interest even when the system as a whole is untrackable. We further demonstrate various aspects of trackability theory and selective tracking through a few simulation examples including a quadrotor example.