Adaptive feedback linearization: implementability and robustness

The robustness to parameter mismatch in feedback-linearization-based nonlinear tracking systems is investigated. The certainty-equivalence principle gives rise to four possible feedback configurations. One is the widely used case where the states are assumed to be available; two others are observer-based; and the last one is a model-follower based on a feedforward/feedback implementation using a signal generator. It is noted that the unacceptable transient behavior of the adaptive tracking scheme is closely related to the sensitivity of the underlying certainty-equivalence-based control, which is analyzed through a perturbation approach. An example system is used to illustrate the system behavior using the four schemes