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 L
₁
adaptive controller. The paper includes an overview of two L
₁
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 L
₁
adaptive control, and show, purely from qualitative considerations, some of the advantages of this new control philosophy.