This paper explores the properties of adaptive systems with closed-loop
reference models. Historically, reference models in adaptive systems run
open-loop in parallel with the plant and controller, using no information from
the plant or controller to alter the trajectory of the reference system.
Closed-loop reference models on the other hand use information from the plant
to alter the reference trajectory. We show that closed-loop reference models
have one more free design parameter as compared to their open-loop
counterparts.