Time and output warping of control systems: Comparing and imitating motions

How can one system “mimic” a motion generated by another? To address this question we introduce an optimal tracking problem which additionally optimizes over functions which deform or “warp” the time axis and the output space. Parametric and nonparametric versions of the time-warped tracking problem are introduced and reduced to standard Bolza problems. The output warping problem is treated for piecewise affine output warping functions.