presence of exogenous low-frequency persistent disturbances, the transient performance of this approach may not be sufficient. Because, this disturbance may not be *visible* to the update law, since the system error is (sufficiently) small due to a (sufficiently) large modification gain.

This work develops an adaptive control architecture to achieve stabilization and command following of uncertain dynamical systems with improved transient performance. The contribution of our framework comes from using a new reference system with an adaptive controller. The proposed reference system captures a desired closed-loop dynamical system behavior modified by a mismatch term

representing the high-frequency content between the uncertain dynamical system and this reference system, i.e., the system error (Figure \[early:figure:2\]). In particular, this mismatch term allows to limit the frequency content of the system error dynamics, which is used to drive the adaptive controller. That is, the update law learns through the low-frequency content of the system error, which constitutes a distinction over the approach in [@notable:3]. It is shown that this key feature of our framework yields fast adaptation without incurring high-frequency oscillations in the transient performance. We further show the effects of design parameters on the system performance, analyze closeness of the uncertain dynamical system 