Tracking Control via Approximately Linearization

The exact input-to-state linearization is an elegant approach to controller design, where a nonlinear change of coordinates combined with a nonlinear feedback law yields a linear controllable system. In case of input-affine SISO systems, exact linearizability is equivalent to (differential) flatness. However, the existence conditions for a flat output are quite restrictive. In the papers below we derive a procedure to omit the explicit calculation of the flat output during the controller design. More precisely, the controller design is based on a linearization along the reference trajectory. This approach is in some sense dual to the extended Luenberger observer developed by Beste and Zeitz 1983.

Publications

• Röbenack, K.: Nicht­lineare Regelungs­systeme: Theorie und Anwendung der exakten Linearisierung.
  Springer Vieweg, 2017, Section 5.5.
• Röbenack, K.; Paschke, F.: Approximately linear tracking control of nonlinear systems.
  Proc. in Applied Mathematics and Mechanics, 2012, 12(1), pp. 713-714.
• Röbenack, K.; Paschke, F.; Knoll, C.: Nonlinear Control with Approximately Linear Tracking Error.
  Proc. European Control Conference (ECC) 2013, pp. 149-154.