  This paper presents a controller design and optimization framework for
nonlinear dynamic systems to track a given reference signal in the presence of
disturbances when the task is repeated over a finite-time interval. This novel
framework mainly consists of two steps. The first step is to design a robust
linear quadratic tracking controller based on the existing control structure
with a Youla-type filter $\tilde Q$. Secondly, an extra degree of freedom: a
parameterization in terms of $\tilde Q$, is added to this design framework.
This extra design parameter is tuned iteratively from measured tracking cost
function with the given disturbances and modeling uncertainties to achieve the
best transient performance. The proposed method is validated with simulation
placed on a Furuta inverted pendulum, showing significant tracking performance
improvement.
