Adaptive Realization of Linear Closed-Loop Tracking Dynamics in the Presence of Large System Model Errors

Abstract

A novel adaptive feedback control approach for nonlinear mechanical systems is presented. The approach applies to nonlinear trajectory tracking and has the remarkable property that the tracking error dynamics asymptotically approach a specified linear PID response for the case where the external disturbances are constant. The methodology applies to a large class of nonlinear mechanical systems, however, it is illustrated for the case of nonlinear rigid body maneuvers subject to actuator saturation constraints and large uncertainty of the system mass and inertia properties. While the system mass or inertias are not identified in this approach, the external disturbances are accurately estimated if they are constant or slowly varying with respect to the adaptation rate. A benefit of this method is that it requires no a priori knowledge of the unknown system parameters or bounds thereof.