Output-feedback stabilization control for a class of underactuated systems via high-order sliding modes identification and compensation

Abstract

We present a robust output-feedback control method for stabilizing a class of underactuated systems despite the effect of external perturbations and using only output information. Towards this aim, first, an extended high-order sliding-mode observer estimates the states and identifies the perturbations, theoretically, in finite time. The controller design relies on partial feedback linearization, compensating the coupled effect of the perturbations while stabilizing the internal dynamics. As a result, the closed-loop system is robust against external perturbations, and the system trajectories converge to a region around the origin. Depending on the system structure and control goal, two different formulations are proposed: robust non-collocated and robust collocated partial feedback linearization. The controller synthesis avoids nonlinear system transformations. The stability of the observer–controller scheme is done using the Lyapunov and input-to-state stability theories. Experimental results on a cart–pendulum system show the approach’s feasibility.