Trajectory Tracking Control with Flat Inputs and a Dynamic Compensator
  This paper proposes a tracking controller based on the concept of flat inputs and a dynamic compensator. Flat inputs represent a dual approach to flat outputs. In contrast to conventional flatness-based control design, the regulated output may be a non-flat output, or the system may be non-flat. The method is applicable to observable systems with stable internal dynamics. The performance of the new design is demonstrated on the variable-length pendulum, a non-flat nonlinear system with a singularity in the relative degree. 
Jean-Francois Stumper, Ferdinand Svaricek and Ralph Kennel
cs.SY math.DS