Abstract
The recently developed ℒ1 adaptive control theory is a promising approach to robust adaptive control. Due to the specific architecture used in ℒ1 adaptive controllers, robustness and adaptation are separated. High adaptation gains do not affect robustness because the input signal is limited by a low-pass filter and adaptation only occurs within the bandwidth of the system. The approach was initially developed for state feedback control. In this paper, the extension of the approach to output feedback controllers is analyzed and it is concluded that the current output feedback scheme does not provide adaptation. An equivalent LTI controller can be formulated for both output feedback approaches described in Hovakimyan and Cao [2010]. It is shown that for a specific choice of filters commonly used in applications, the equivalent LTI controller is a proportional-integral controller.
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