Robust regulation of a chain of power integrators perturbed by a lower-triangular vector field

Abstract

A new technique called adding a power integrator is used, in a unified manner, to solve a number of control problems including global robust stabilization, asymptotic tracking, and adaptive regulation, for a class of uncertain nonlinear systems that are globally diffeomorphic to a chain of power integrators perturbed by an uncertain lower-triangular vector field. Sufficient conditions are presented under which a globally stabilizing smooth adaptive controller and/or robust state feedback control law can be constructed explicitly, via a Lyapunov-based inductive argument. The systematic use of the adding a power integrator technique allows us to remove two common hypotheses of the existing robust and adaptive control results in the literature, that is, the controlled plant must be feedback linearizable and linear in the control input. Copyright © 2000 John Wiley & Sons, Ltd.