Desired Compensation Adaptive Robust Control

Abstract

A desired compensation adaptive robust control (DCARC) framework is presented for nonlinear systems having both parametric uncertainties and uncertain nonlinearities. The paper first considers a class of higher order nonlinear systems transformable to a normal form with matched model uncertainties. For this class of uncertain systems, the desired values of all states for tracking a known desired trajectory can be predetermined and the usual desired compensation concept can be used to synthesize DCARC laws. The paper then focuses on systems with unmatched model uncertainties, in which the desired values of the intermediate state variables for perfect output tracking of a known desired trajectory cannot be predetermined. A novel way of formulating desired compensation concept is proposed and a DCARC backstepping design is developed to overcome the design difficulties associated with unmatched model uncertainties. The proposed DCARC framework has the unique feature that the adaptive model compensation and the regressor depend on the reference output trajectory and on-line parameter estimates only. Such a structure has several implementation advantages. First, the adaptive model compensation is always bounded when projection type adaption law is used, and thus does not affect the closed-loop system stability. As a result, the interaction between the parameter adaptation and the robust control law is reduced, which may facilitate the controller gain tuning process considerably. Second, the effect of measurement noise on the adaptive model compensation and on the parameter adaptation law is minimized. Consequently, a faster adaptation rate can be chosen in implementation to speed up the transient response and to improve overall tracking performance. These claims have been verified in the comparative experimental studies of several applications.