Easily implementable backstepping variable structure controller for nonlinear system with unmatched uncertainties

Past papers on designing suitable controller for nonlinear system with unmatched uncertainties with Kokotovc's adaptive backstepping method are not easy to implement. We propose to combine backstepping with VSC (variable structure control) scheme to design an easily implementable controller. The distinguishing feature of our control scheme is that, the effect of unknown disturbances and unmatched uncertainties is suppressed in each step of backstepping design. In our proposed control scheme, it is not necessary to assume that the uncertainties can be expressed in some unknown parameters. Although our proposed control scheme is based on three assumptions, they are easily satisfied and do not affect the easy implementability of our control scheme. The closed loop system is globally stable and can reach the sliding surface in a finite time. The simulation results confirm that the performance of the proposed backstepping VS controller is satisfactory.