Nonlinear control with approximately linear tracking error

Exact feedback linearization is a well-established method in nonlinear control, where the system is transformed into a linear system by a nonlinear change of coordinates in connection with a nonlinear feedback law. For a controllable single-input system, exact linearizability is equivalent to flatness. Unfortunately, the existence conditions are quite restrictive. Even if the existence conditions are met, the explicit computation of the flat output can be very difficult. In this contribution we suggest tracking controllers based on the tangent system, where the flat output is not required explicitly. The controller can even be calculated for controllable non-flat systems.