Adaptive Control with Reference Model Modification

The asymptotic behavior of adaptive systems has been a well researched topic during the last couple of decades, and it is well known that asymptotic tracking can be achieved using the Lyapunov redesign method. However, the transient behavior of the input and output signals can be very oscillatory with significant excursions [1]. There has been a great deal of effort to modify the control architecture and the adaptive laws from the perspective of improving the transient behavior of the tracking error. The majority of these efforts led to nonadaptive high gain feedback [2, 3], switching control law [4] or to a parameter dependent persistent excitation condition [5]. On the other hand, the tracking error magnitude can be decreased by increasing the adaptation rate, but this results in unwanted high frequency oscillations and large overshoot in the control signal. This shortcoming is common for the majority of existing adaptive control methods. Recently some results have been appearing in the control community, which explicitly address the input signal transient behavior (see for example [6]). In this note, instead of modification of the control architecture or the adaptive laws, the reference model is modified by feeding back the tracking error signal. This approach, called here "modifiedreference-model MRAC" or M-MRAC in short, is motivated by the fact that the initial large errors in