ℒ1 adaptive controller for nonlinear reference systems

In this paper, we consider nonlinear affine-in-control systems and present the L₁ adaptive controller for the case when the performance specifications are defined via a nonlinear system of similar structure. The L₁ adaptive controller ensures that the nonlinear, affine-in-control, uncertain system follows its ideal model during the transient and steady-state, if the adaptation gain is selected sufficiently large and the bandwidth of the low-pass filter is adjusted appropriately. Simulations verify the theoretical results.