Some systems may be approximated as block cascades structures where each block of the cascade can be approximately feedback linearized. In such systems, the states of the lower subsystem blocks affect the dynamics of the upper subsystems. In generating an inverse for a given block, a subset of its lower subsystem states can be treated as virtual actuators in addition to actual direct actuation that may be available. The desired virtual actuator signal arising from the upper subsystem's inverse now appears as a command to the lower subsystem. This paper introduces an adaptive element that is capable of canceling modeling errors arising due to feedback linearization. It also introduces reference models that include a pseudocontrol hedging signal which protects the adaptive element from lower subsystem's dynamics.