adaptive controller for nonlinear time-varying reference systems

This paper considers uncertain time-varying nonlinear affine-in-control systems and presents the L 1 adaptive controller for the case when the performance specifications are defined via a given time-varying nonlinear system. The L 1  adaptive controller ensures that the nonlinear, affine-in-control, uncertain system follows its ideal nonlinear model during the transient and steady-state, if the adaptation gain is selected sufficiently large and the bandwidth of the low-pass filter in the L 1 adaptive control architecture is adjusted appropriately.