  There has been substantial recent progress on the theoretical understanding
of model-free approaches to Linear Quadratic Regulator (LQR) problems. Much
attention has been devoted to the special case when the goal is to drive the
state close to a zero target. In this work, we consider the general case where
the target is allowed to be arbitrary, which we refer to as the LQR tracking
problem. We study the optimization landscape of this problem, and show that
similar to the zero-target LQR problem, the LQR tracking problem also satisfies
gradient dominance and local smoothness properties. This allows us to develop a
zeroth-order policy gradient algorithm that achieves global convergence. We
support our arguments with numerical simulations on a linear system.
