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Benchmark problems of adaptive control revisited by L1 adaptive control

In this paper we revisit two benchmark problems of adaptive control, Rohrs' example and the two-cart example, with the recently developed L1 adaptive controller. The paper includes an overview of two L1 architectures, one in a state-feedback setting and another one in an output-feedback setting, which are suitable for the control of these two systems respectively. Also, we analyze fundamental differences between conventional adaptive control and the L1 adaptive control, and show, purely from qualitative considerations, some of the advantages of this new control philosophy.