Similarities of Hedging and L1 Adaptive Control

In recent years L1 adaptive control was suggested as an advancement to model reference adaptive control (MRAC) and its benefits have been controversially discussed. This paper discusses the similarities of applying a hedging signal to the reference model used in model reference adaptive control to account for dynamic constraints in the input channel, and L1 adaptive control. In particular it is shown that in the case where the control effectiveness is known, both approaches are exactly the same, where the contribution of the L1 theory is the mathematically correct framework that provides a stability proof/condition which has not been available for the hedging approach. In the case of unknown control effectiveness, the two methods are slightly different and the L1 approach additionally adjusts D28the cutoff frequency of the low-pass filter. This difference allows for the elegant stability proof given by L1 theory. At the end the two approaches are compared based on a simple short period model of a large transport aircraft by assessing the robust performance w.r.t. model uncertainties.