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

A new technique called adding a power integrator is used, in a unified mann er, to solve a number of control problems including global robust stabiliza tion, asymptotic tracking, and adaptive regulation, for a class of uncertai n nonlinear systems that are globally diffeomorphic to a chain of power int egrators perturbed by an uncertain lower-triangular vector field. Sufficien t conditions are presented under which a globally stabilizing smooth adapti ve controller and/or robust state feedback control law can be constructed e xplicitly, via a Lyapunov-based inductive argument. The systematic use of t he adding a power integrator technique allows us to remove two common hypot heses 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 (C) 2000 John Wiley & Sons, Ltd.