Time and output warping of control systems: comparing and imitating motions. (English) Zbl 1226.93099
Summary: The problem of making one system “mimic” a motion generated by another is studied. To address this, an optimal tracking problem is introduced that, in addition to tracking, optimizes over functions that deform or “warp” the time axis and the output space. Parametric and nonparametric versions of the time-warped tracking problem are presented and reduced to standard Bolza problems. The output warping problem is treated for affine and piecewise affine output warping functions. Example applications are given, including that of controlling a marionette to mimic a human dancer.
MSC:
| 93C85 | Automated systems (robots, etc.) in control theory |
| 93C10 | Nonlinear systems in control theory |
| 93C15 | Control/observation systems governed by ordinary differential equations |
| 49N90 | Applications of optimal control and differential games |
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